AES/PE/13-09 Gas Coning Control with a Smart Horizontal

AES/PE/13-09 Gas Coning Control with a Smart Horizontal Well in a Thin Oil Rim 17.07.2013 Vegerd Veskimägi

Title : Gas Coning Control with a Smart Horizontal Well in a Thin Oil Rim Author : Vegerd Veskimägi Date : July 17th, 2013 Professor : Jan Dirk Jansen Supervisor (Statoil) : Martin Halvorsen TA Report number : AES/PE/13-09 Postal Address : Section for Petroleum Engineering Department of Geoscience & Engineering Delft University of Technology P.O. Box 5028 The Netherlands Telephone : (31) 15 2781328 (secretary) Telefax : (31) 15 2781189 Copyright ©2013 Section for Petroleum Engineering All rights reserved. No parts of this publication may be reproduced, Stored in a retrieval system, or transmitted, In any form or by any means, electronic, Mechanical, photocopying, recording, or otherwise, Without the prior written permission of the Section for Petroleum Engineering

Gas Coning Control with a Smart Horizontal Well in a Thin Oil Rim

Abstract The use of wells equipped with inflow control valves has steadily increased over the past decade. Most

of these wells are used to control the inflow from separate reservoirs or separate reservoir zones. This

solution is particularly attractive for high-rate horizontal wells in thin oil rim reservoirs. Through the

smart well technology, early gas or water breakthrough into the well can be delayed or even reduced.

The use of Inflow Control Devices (ICDs) and zonal flow control valves (FCVs) offers an opportunity to

evenly distribute the drawdown along the well, and therefore take corrective action if an early water or

gas breakthrough occurs. In September 2011, Statoil completed Troll’s first subsea three-zone horizontal

smart well. Just recently, anther well on Troll with a similar completion design was put into production.

One of the most important objectives in the study of well Q-12BH, which forms the basis for this report,

is understanding gas coning behavior. Without it, one would not be able to set appropriate operating

strategies, and therefore optimizing production would simply not reach the wanted results. The

approach taken begins by conducting an extensive literature review into coning control in thin oil rims

and horizontal well technology. Early production data of well Q-12BH is studied, because knowing

production history is a key into creating simulation models. These simulation models will analyze if the

well was put into production with the most optimal zonal valve opening positions and what could

possibly be even better setting for such a well.


Table of Contents Introduction ......................................................................................................................................1

What is an oil rim? .................................................................................................................................... 1

What is coning? ......................................................................................................................................... 1

Troll field ...........................................................................................................................................3

Field layout ................................................................................................................................................ 3

Reservoir characteristics ........................................................................................................................... 4

Production and drilling units ..................................................................................................................... 6

Operation strategy .................................................................................................................................... 7

Well 31/2-Q-12 BH .............................................................................................................................8

Introduction .............................................................................................................................................. 8

Drilling information ................................................................................................................................... 8

Completion design .................................................................................................................................. 10

Synthetic permeability ............................................................................................................................ 13

Weighted arithmetic average ............................................................................................................. 14

Relative Permeability Data...................................................................................................................... 15

PVT properties ........................................................................................................................................ 16

Procedure into simulations and theoretical methods ........................................................................ 16

Well testing ............................................................................................................................................. 16

Reservoir pressure .............................................................................................................................. 16

Gas inflow............................................................................................................................................ 17

First well test ....................................................................................................................................... 18

Discussion of flow rates in different well tests ....................................................................................... 19

Simulation Modeling ........................................................................................................................ 21

Objectives ............................................................................................................................................... 21

Parameters .............................................................................................................................................. 21

Reservoir geometry ............................................................................................................................. 24

NETool modeling ..................................................................................................................................... 26

Transmissibility and mobility .............................................................................................................. 26

NETool Results ........................................................................................................................................ 27

Theoretical pressure drop across the 3.2 bar ICD-screen ................................................................... 31

Analytical Joshi’s and Muskat’s PI Models ........................................................................................ 33


Calculations with steady-state Joshi horizontal well PI model ............................................................... 33

Steady state Joshi horizontal well analytical simulation results ............................................................. 35

Muskat’s analytical PI calculation method ............................................................................................. 35

Assumptions of the method ............................................................................................................... 35

Theory ................................................................................................................................................. 36

Results of Muskat Method ...................................................................................................................... 37

Additional simulation ....................................................................................................................... 38

Discussion of final results ................................................................................................................. 39

Limitations .............................................................................................................................................. 43

Conclusion ....................................................................................................................................... 43

Acknowledgements.......................................................................................................................... 46

References ....................................................................................................................................... 47

Appendices ………………………………………………………………………………………………………………………………………49


ACRONYMS

API American Petroleum Institute

DH Downhole

DHG Downhole Gauge

FCV Flow Control Valve

FZI Flow Zone Indicator

GCGL Gas Cap Gas Lift

GOC Gas Oil Contact

GOR Gas Oil Ratio

GRN Normalized Gamma Ray

ICD Inflow Control Device

MD Measured Depth

MSL Mean Sea Level

NCS Norwegian Continental Shelf

OWC Oil Water Contact

PI Productivity Index

PVT Pressure Volume Temperature

RCP Rate Controlled Production

RKB Rotary Kelly Bushing

SCAL Special Core Analysis TWOP Troll West Oil Province

TD Total Depth

TVD True Vertical Depth

TWGP Troll West Gas Province

TWGPN Troll West Gas Province North

WC Water cut


NOMENCLATURE

a Half the major axis of a drainage ellipse

B Formation Volume Factor

b Half the minor axis of a drainage ellipse

g Gravity

h Thickness

J Productivity Index

k Permeability

L Length

Q Flow rate

P Pressure

R Gas oil ratio

r Radius

S Saturation

T Transmissibility

w Width

Z Zone

β Influence of anisotropy

μ Viscosity

ρ Density

λ Mobility


SUBSCRIPTS

ann annulus

B blanks

b bubble point

cal calibrated

eff effective

eH horizontal drainage

g gas

H horizontal well

h horizontal

in inflow

LIQ liquid

mix mixed

o oil

r,phase relative value of a phase

RES Reservoir

s specific

seg segment

SF sandface

SICD specific ICD valve

sol solution

ST standard condition

tub tubing

v vertical

w water

wb wellbore

z zone

α phase


FIGURES

Figure 1: Gas coning in a horizontal well ...................................................................................................... 1

Figure 2: Dimensionless pressure drawdowns in a vertical and horizontal well compared to relative

distance to the well. On the left, there are pictures of water coning and cresting. ..................................... 2

Figure 3: Troll oil and gas field near Norwegian coast in the North Sea is marked in red. It is zoomed in on

the right top corner of the figure .................................................................................................................. 3

Figure 4: The division of Troll field ................................................................................................................ 4

Figure 5: Gas and water flows between TWOP and TWGP, and through the communication channels

between Troll West and Troll East. ............................................................................................................... 4

Figure 6: Subcrop map through the geomodel (2009) in the area of well Q-12BH at 1560m TVD from the

MSL. Gamma logs lie on top of the well paths.............................................................................................. 5

Figure 7: The infrastructure of Troll West including the subsea templates on TWOP and TWGP and the

two operating platforms Troll B and Troll C .................................................................................................. 6

Figure 8: Geological cross-section of a well Q-12BH with the main three producing zones in 3CC clean

sands, 4Ac fine mica-rich sands and 4/5 heterolithic sands. ........................................................................ 9

Figure 9: Example of a multilateral Q-12 BH well completion where this sidetrack has a zonal separation

.................................................................................................................................................................... 10

Figure 10: Premium ICD screen used on the Troll Field ............................................................................... 11

Figure 11: Illustration of cable feed-through swellable packers used in smart wells ................................. 12

Figure 12: Downhole equipment and clarification of pressures ................................................................. 13

Figure 13: LET relative permeability curves for oil and water with respect to water saturation ................ 15

Figure 14: LET relative permeability curves for gas and oil with respect to gas saturation ....................... 15

Figure 15: Reservoir pressure decrease as a function of time. ................................................................... 17

Figure 16: First well test DHG pressure data together with reservoir and wellhead pressures, and FCV

openings. ..................................................................................................................................................... 19

Figure 17: Reservoir flow rates of all the well tests for different phases. ................................................... 20

Figure 18: Phase flow contribution comparison with all the well tests. ..................................................... 20

Figure 19: NETool reservoir geometry from the top and front view including yellow streamlines ............ 24

Figure 20: Simulated flow rates with varying reservoir geometry .............................................................. 25

Figure 21: NETool reservoir pressure and completion diagram. ................................................................. 29

Figure 22: NETool sandface (blue), annulus (purple) and tubing (red) pressures with respect to the length

of the well. Zonal separation is shown with dashed oval shaped circles. ................................................... 29

Figure 23: Reservoir geometry model for the three-zone horizontal well ................................................. 34

Figure 24: A box-shaped reservoir seen as a sink that drains water and oil (front view - the well runs into

the page) ..................................................................................................................................................... 36

Figure 25: Productivity Index results with different methods ..................................................................... 39

Figure 26: Total flow rate results with different methods .......................................................................... 40

Figure 27: Zonal liquid inflow contribution with different methods ........................................................... 40

Figure 28: Productivity Index for all the possible FCV openings before free gas production (See Table 3 for

FCV positions) .............................................................................................................................................. 41


Figure 29: DH zonal flow contribution with all the possible FCV openings before free gas production (See

Table 3 for FCV positions) ........................................................................................................................... 42

Figure 30: Liquid influx with all the possible FCV openings before free gas production (See Table 3 for FCV

positions) ..................................................................................................................................................... 42

Figure 31: Water cut with all the possible FCV openings before free gas production (See Table 3 for FCV

positions) ..................................................................................................................................................... 43

Figure 32: Simulated NETool model with equal zonal influx ....................................................................... 45

TABLES

Table 1: Reservoir and fluid properties of TWGPN during the production start-up of well 31/2-Q-12BH .... 6

Table 2: Completion design parameter lengths and positions.................................................................... 10

Table 3: FCV positions for Zone 2 and Zone 3 ............................................................................................. 12

Table 4: FCV positions for Zone 1 ................................................................................................................ 12

Table 5: Gas cap gas lift valve positions and flow area .............................................................................. 13

Table 6: Penetrated lithology layers of Q-12BH and weighted arithmetic average permeabilities. .......... 14

Table 7: 31/2-Q-12 BH first well test data (16.09.2011) ............................................................................. 18

Table 8: Parameters used for productivity indices calculation ................................................................... 22

Table 9: Reservoir width and thickness sensitivities. .................................................................................. 24

Table 10: Simulation model results of the first well test ............................................................................. 27

Table 11: NETool and well test results data comparison ............................................................................ 28

Table 12: NETool simulation model results with fully opened downhole FCVs. .......................................... 30

Table 13: DHG pressures of the actual well running with 100% opened FCV positions for two consecutive

days ............................................................................................................................................................. 31

Table 14: Pressure tag recordings in January 2012 compared with NETool simulation model results ...... 31

Table 15: Troll field ICD-valve and screen calibrated coefficients ............................................................... 31

Table 16: DH flow rate phase fractions with two different FCV openings .................................................. 32

Table 17: Average theoretical pressure drop across a single ICD-screen in all three zones ....................... 32

Table 18: Variation between NETool and theoretical pressure drop across a single ICD-screen................ 33

Table 19: Steady state Joshi horizontal well analytical simulation results ................................................. 35

Table 20: Muskat’s analytical model results .............................................................................................. 37

Table 21: Simulation #3 – Steady state Joshi’s NETool analytical method ................................................. 38

Table 22: Results of different methods ....................................................................................................... 39

Table 23: Productivity Index, zonal contribution (DH), total liquid rate (ST) and water cut of all the

possible valve positions of Q-12BH before free gas production ................................................................. 41


1

Introduction

What is an oil rim? An oil rim is a thin oil column in a reservoir located between a large gas cap and an aquifer. Its

production mechanism is complicated due to a very thin oil zone. One of the most challenging tasks in

such a reservoir is to keep the gas oil contact (GOC) and oil water contact (OWC) stable during the

production because drawdown causes their movement. Drawdown is also the main cause for gas and

water coning. [1]

What is coning? Coning is a tendency of gas and water to push oil towards the well in a cone shaped contour. As soon as

the cone breaks through the oil column, gas or water production increases substantially. The reason for

gas or water breakthrough is due to lower viscosity of these phases and therefore they are more mobile.

Coning phenomenon is known to reduce oil production and influence the overall recovery efficiency of

the well. It cannot be avoided, but there are some strategies that allow minimizing gas or water inflow

by delaying the breakthrough of the cone. For a better visual understanding see Figure 1, how the shape

of a gas cone forms in horizontal wells. Cone shape is also influenced by permeability. On this drawing,

the heel zone has a higher permeability, which results in a wider cone. Higher permeability zones cause

higher flow rates into the well and faster drainage compared to lower permeability sands in the toe

area. Usually high-permeability reservoirs have lower drawdowns, and therefore fewer problems related

to coning. On the opposite, lower permeability reservoirs form a narrower cone. The pressure drop

along the well is typically higher, because of the high flow rates, which leads to a strongly uneven

drawdown, and therefore inflow and coning along the well. This uneven behavior of drawdown and

inflows has a negative effect on oil production.

Figure 1: Gas coning in a horizontal well [1]

There are more parameters that affect coning. Coning tendencies are inversely proportional to density

differences and directly proportional to viscosities. For example, water coning is more likely to occur at

the same drawdown than gas coning, because the difference between water and oil density is much


2

smaller than the difference between gas and oil density. However, gas coning is more likely to occur

when viscosities are compared because gas is less viscous and due to the faster flow rate of gas, it is able

to finger through the oil column easier than water. In the end, both gas and water cones are likely to

occur and thereby the best theoretical solution recommends placing the wells in the center of the oil

column. Nonetheless, the current strategy on Troll places the wells almost at the OWC. As a result, Troll

wells experience much higher water cut, but more importantly they restrict gas cusping problems.

Coning is highly affected by drawdown, and drawdown is proportional to fluid production rates. This

situation makes maximizing oil production a challenge. Therefore, inflow and drawdown both need to

be reduced for production optimization. A good way to delay or reduce coning problems is using

horizontal wells as they are able to minimize pressure drop and sustain higher production rates. The

production rates can remain high because of their long wellbores. Figure 2 shows horizontal and vertical

well pressure drawdowns with respect to relative distance to the well. The pressure drop for horizontal

wells is lower and the increase much more steady. In addition, water coning and cresting are pictured on

the left side of Figure 2.

Figure 2: Dimensionless pressure drawdowns in a vertical and horizontal well compared to relative distance to the well. On the left, there are pictures of water coning and cresting. [4]

In this particular study about Troll field oil well, coning is a daily problem. Besides it being a problem, it

also helps to drive oil towards the well using gravity driven forces. This is especially helpful during the

start-up process of a well, but later the strategy of dealing with gas coning requires choking back wells

to keep the cone from reaching the wellbore. In other words, preventing coning behavior means

minimizing the gas-oil ratio (GOR) to maximize oil production. [1], [2], [3], [4]


3

Troll field The first seismic on the Troll field in the North Sea was done in 1972. From then onwards, it took 23

years of intense research and innovative planning before the field started oil production in 1995. The

location of the field is about 80 km North West of the Norwegian city of Bergen. It lies on the edge of a

Viking Graben, which has been forming for the past 125 million years dividing Norwegian coast from the

British Isles. The field evolved by the underwater rifting processes, where the layers of C-sand and M-

sand accumulated along the eastern edge of the Sognefjord Formation. The discovery showed a massive

gas cap on top of the thin oil rim, which was initially thought not to have any commercial value.

However, time and technology proved this thin oil column to become one of the most important oil

fields in Europe. Today, Statoil ASA is the main operator on Troll field, and more than 500 well

tracks/branches have been drilled on Troll since the beginning of production. The field location on the

map is seen on Figure 3. [2], [5]

Figure 3: Troll oil and gas field near Norwegian coast in the North Sea is marked in red. It is zoomed in on the right top corner of the figure. [6]

Field layout North Sea area is divided into blocks, where Troll field is covering partly four of those blocks: 31/2, 31/3,

31/5, and 31/6. The estimated area of Troll field is about 750 km2. This area is divided into two main

production areas: Troll East and Troll West. Troll East operates with gas only, while Troll West still

remains the main oil producing area. In addition, Troll West is divided into two provinces based on the


4

type of reservoir fluids: Troll West Gas Province (TWGP) and Troll West Oil Province (TWOP). Most of the

upcoming study concentrates on the field characteristics of TWGPN where the well Q-12BH was drilled.

A closer layout of Troll West provinces is seen on Figure 4a. [2], [7], [8]

Figure 4: The division of Troll field. [2]

Figure 5: Gas and water flows between TWOP and TWGP, and through the communication channels between Troll West and Troll East. [2]

Reservoir characteristics The two most important reservoir formations on Troll are Fensfjord and Sognefjord. Fensfjord formation

formed during the Middle Jurassic period and it is much smaller in contributing size than Sognefjord

formation. Sognefjord formation, where most of the Troll wells have been drilled, developed during the

Late Jurassic period. This formation lies on top of the Viking Group and was formed near shore

environment in a shallow marine setting through transgression and regression of the sea. The entire

Troll field consists of three main fault blocks, where the pressure communication between Troll East and

West has been proven. It is defined though three of the communication channels on the eastern part of

Troll West shown on Figure 5. In addition, the field is heavily faulted because the bottom of the Viking

Graben continues to sink due to underwater rifting processes. These processes have enabled

hydrocarbons to migrate upwards into reservoir rock, where they are currently produced. [2], [5]

Sognefjord formation thickness varies substantially, but on average it is about 160 m thick. The actual

reservoir, where most of the oil wells are drilled in Troll West, is located about 1560 m from the mean

sea level (MSL). MSL is on average 300 m from the sea bed to the surface. On top of the formation,

there is a large gas cap present that can extend up to 200m on TWGP. Beneath it, lies an underlying

aquifer. Right in the middle of those two phases is the thin oil rim. In the beginning of production on


5

Troll West, the oil column thickness on TWOP was determined to be 22m to 26m, and for TWGP

between 8m to 13m. [1], [6], [8], [9]

The Sognefjord formation is slightly tilted and consists of high permeability alternating sand bodies,

which have excellent reservoir characteristics. Besides few calcite bodies on the way, the lithology is

divided into three different sands: clean and coarse sands (c-sands) with a typical permeability of 1-30 D,

micaceous sands (m-sands) with permeability less than 600 mD, and heterolithic sands which have

alternating characteristics. The porosities for c-sands and m-sands are found 30 – 35% and 20 – 28%,

respectively. About 60% of the lithology within the oil window on TWGP is formed of coarse-grained

clean sands, and the rest is mostly mica rich fine-grained sands or heterogeneous sands. The geomodel

at the depth of 1560 m in the area of interest is seen in Figure 3. Orange and red colours on the map

represent 3-series sands, while green and grey represent 4-series and heterolithic sands respectively.

The gamma log is shown on top of the well path. The yellow and green colours on the gamma logs stand

for c-sands (gravity lower than 68 API) and m-sands (gravity higher than 68 API) respectively. [2], [3], [6]

Figure 6: Subcrop map through the geomodel (2009) in the area of well Q-12BH at 1560m TVD from the MSL. Gamma logs lie on top of the well paths. [3]


6

Reservoir and fluid properties for the northern part of TWGP are found in Table 1. Many of these values

were determined from the PVT properties. For well 31/2-Q-12 BH, it gives an overview of oil, gas, water

and rock properties of TWGPN found in Table A.1 in Appendix A.

Reservoir parameters used for Q-12 well start up Symbol Units Value

Bubble point pressure pb Bar 159.06

Reservoir temperature TRES oC 68

Solution gas oil ratio at the start-up RSOL Sm3/Sm3 47.8

Gas density at SC ρG kg/m3 0.75

Oil density at SC ρO kg/m3 890

Water density at SC ρW kg/m3 1045

Gas formation volume factor BG m3/Sm3 0.00765

Oil formation volume factor BO m3/Sm3 1.136

Water formation volume factor BW m3/Sm3 1.017

Gas viscosity μG mPa*s 0.017

Oil viscosity μO mPa*s 1.9

Water viscosity μW mPa*s 0.45

Water compressibility βW 1/bar 4.3*10^-5 Table 1: Reservoir and fluid properties of TWGPN during the production start-up of well 31/2-Q-12BH. [10]

Production and drilling units The Troll field has three offshore operating production units: Troll A, Troll B and Troll C. Troll A operates

on Troll East. It is a large gas processing platform with vertical wells. Troll B is a concrete floater that

drains both TWOP and TWGP, and Troll C is a steel semi-floater that has most of its operating wells on

TWGP with an exception of one template, which is installed on the northern part of Troll East.

Figure 7: The infrastructure of Troll West including the subsea templates on TWOP and TWGP and the two operating platforms Troll B and Troll C. [6]


7

The Troll C platform is also a processing facility for a well 31/2-Q-12BH. It started production in

November 1999, and has a current processing capacity of 40000 Sm3/day of oil, 40000 Sm3/day of water

and 10.3 million Sm3/day of gas. Currently, Troll C has 15 interconnected templates with 59 producing

wells, but it also receives production from four further north located templates draining Fram oil field.

These subsea templates are routed to the platform through two production lines. During well testing

period, one of those lines is used for testing only. There are two test separators installed on Troll C, but

one is used for the Fram wells. In the end, when the production gets separated, oil is sent to onshore

refinery in Mongstad and gas is moved to Kollsnes through Troll A platform. Troll B production is routed

the same way, except some gas is injected back into the reservoir. Figure 7 shows an overall picture how

all the templates on the sea bottom are connected to the platforms through production lines, and how

these platforms separate oil and gas and send it out through different pipelines.

The Troll field is also one of the most actively drilled regions in the North Sea. Currently, there are four

drilling rigs actively at work. All the infill horizontal drilling is done from the subsea templates. On

average, subsea templates have four slots for drilling, except a few have six. The use of time-lapse

seismic and geosteering during the drilling process prevent hitting other wells and increase the

probability of drilling into better producing sands, where gas gusping is less of a problem. All the wells

on Troll West are horizontal and mostly multilaterals with 2 to 4 horizontal branches. [2], [8]

Operation strategy A good strategy develops with practice and learning. Therefore, knowing the history of a field is

important. The pilot holes that were drilled into different reservoir compartments during the field

development phase showed high hydrocarbon levels. The main concern was how to produce this thin oil

rim that was found. At that point in time the entire oil zone was seen as non-profitable. It took many

years until successful outcomes were received through horizontal well technology. Afterwards, Troll oil

field became world known. In September 1995, Troll B platform operated by Hydro, started production

on the TWOP. Less than a year later oil production started also from TWGP, which had a considerably

thinner oil zone. The strategy on Troll West has originated by producing the most productive zones with

the thickest oil column first and after that the more challenging prospects. That is why production on

TWOP started before TWGP.

The most important strategy on Troll West is to minimize oil column movement during slowly

decreasing reservoir pressure. Based on reservoir shut-in information, reservoir pressure is known to

decrease about 1.5 to 2 bars per year. As gas expansion and gusping are the driving flow mechanisms in

this reservoir, it is important to observe the changes in the reservoir pressure. Pressure drops can cause

GOC to move downwards as free gas expands. Therefore, on Troll Oil field the wells are not drilled in the

center of the oil column, but rather very near the OWC.

Another challenge on such a mature field is gas gusping. Today, gas gusping on Troll West can happen

immediately after a well is put on stream. The objective for production engineers is to maximize oil

production by keeping the gas oil ratio (GOR) as low as possible for as long as possible. However, there

are some limitations - Troll B and C have gas handling capacity on the platforms. Therefore, only as

much oil can be produced as gas limiting capacity allows. In other words, production optimization goal is


8

to lower the total gas production of all the wells on stream, which then lowers the GOR and increases oil

production. This procedure requires good understanding of wells and their behavior in different sands.

The long term oil production on Troll West is expected to extend into the next decade. This strategy

requires extracting more oil from m-sands through infill drilling technology. Even though, oil extraction

is becoming more challenging as the pressure in the reservoir keeps decreasing and the fluid contact

depths changing, the efforts have proven success on Troll. [1], [2]

Well 31/2-Q-12 BH

Introduction The main production problems for horizontal wells are caused from uneven inflow and drawdown along

the horizontal well. For wells without inflow control, the drawdown is often larger at the heel than at

the toe, therefore the production along the wellbore is not uniform, but rather increasing from the toe

towards the heel. Likewise, the tendency for gas and water coning is much higher in the heel if such a

pressure profile is presented. It would also raise questions whether it is worth drilling very long

wellbores if the toe zone is hardly contributing to production. [11]

Well 31/2-Q-12BH has a more advanced completion design to improve production recovery. It is

completed with ICD screens and a long stinger that has three remotely controllable FCVs. These

adjustable FCVs are used to even out the drawdown and balance liquid rates from different zones.

Furthermore, such completion design decreases gas and water coning problems as adjustable FCVs help

to reduce and delay gas coning. [12]

Drilling information 31/2-Q-12BH well path is located near the central communication channel on the TWGP in the

Sognefjord reservoir formation about 1560m TVD MSL. This horizontal well path was drilled from the Q

subsea template and sidetracked from the original mother well 31/2-Q-12AH at 1602.2m MD/1480m

TVD MSL. Most of the horizontal section of this sidetrack was drilled parallel to an old well in the

southeast direction found in Figure 6. At the depth of 1559m TVD MSL, the well was leveled out in the

3CC sand. Then, 4Ac and 4 Am sands were reached, and finally the total depth (TD) was set in the 4/5

heterolithic sands at 6068m MD. The cross section of the geomodel along the drilled well path is shown

in Figure 8.


9

Figure 8: Geological cross-section of a well Q-12BH with the main three producing zones in 3CC clean sands, 4Ac fine mica-rich sands and 4/5 heterolithic sands. [3]

Based on the drilling experience, the areal structural interpretation quality was confirmed to be good.

The minor faults seen along the well path have very little influence, but there are three bigger

surrounding faults in the area. Namely, Q-12BH is bounded by two close to parallel faults on both sides

of the reservoir running from northwest to southeast. In the end of the channel there is a sealing

boundary fault with Troll East gas reservoir.

The horizontal part of the well was drilled about 0.5m above the OWC most of the way to avoid free gas

coning problems from the gas cap. It was drilled entirely with 9 ⅟₂” drill bit from 1602.2m MD to the

total depth of 6068m MD. Oil column thickness was only observed in the landing area of the well, where

it was found to be 7.1 m. Since Q-12BH is located near the central communication region, where Troll

East and Troll West meet, the pressure communication between those two areas had to be tested. Troll

East and Troll West pressure communication was proven, but mostly through the Northern

communication channel. The central communication channel might have connecting aquifers further

below, but now it is considered a sealing boundary. As Troll East gas is depleted on a fast rate, the

pressure on that part of the field also declines faster. Therefore, reservoir pressure near the central

communication channel should be continuously observed to reassure the sealing condition; otherwise it

can affect the oil production as the fluid contact lines can move. [2], [3]


10

Completion design

Figure 9: Example of a multilateral Q-12 BH well completion where this sidetrack has a zonal separation [8]

31/2-Q-12BH well completion design is similar to Figure 9 sidetrack design. It is separated into three

production zones based on its lithology. Zone 1 is the longest and deepest production zone in the

heterolithic sands reaching up to the toe of the well. Zone 2 is the shortest production zone running in

the 4-series sands in the middle section of the well. Zone 3 is the highest producing zone starting from

the heel and running mostly in the 3CC sands. Zonation lithology is shown in Table 6. [3]

A more detailed well completion diagram can be found in Table A.2 in Appendix A, however, some more

important Q-12BH well completion design parameters together with the depths and lengths are given in

Table 2:

Parameter (MD from the RKB) RKB to MSL = 35.5 m Zone 3 (Heel) Zone 2 (Middle) Zone 1 (Toe)

Zonal length [m] 1277 1150 1558

Blanks length [m] 286 96 12

Swellpacker position (Top MD) [m] 2059 3340 4495

Dual gauge tub-ann position (Top MD) [m] 2084 3372 4524

FCV position (Top MD) [m] 2087 3374 4527

Table 2: Completion design parameter lengths and positions [13]


11

A short description of some completion equipment that was observed more thoroughly during the study

process is given below:

ICD-screens are known to protect the well from sand production, but they are also used to restrict the

flow rate from the well. The flow rate with ICDs is lowered by the additional pressure drop they cause.

This additional pressure drop helps to increase well’s volumetric oil recovery. In other words, ICD-

screens contribute towards a more uniform production profile and are able to lower GOR by delaying

gas breakthrough. For erosion prevention, ICDs maintain a low flow velocity through the screens. For

well Q-12BH, ICD-screens are installed throughout the horizontal well section up to 6058m MD. The

diameter of those ICDs is 7in, except for the last 1000m it changes to 6 ⅝ in. Flow resistance elements

for Q-12BH are 3.2 bars per ICD with the water flow rate of 26 Sm3/d. If the well path drops below OWC,

then blanks are installed instead of ICD screens. Figure 10 shows a picture of an ICD-screen. [14], [15]

Figure 10: Premium ICD screen used on the Troll Field [14]

The tubing/stinger runs from the well head down to 4543m MD RKB. It is fixed inside the ICD-screens by

swellable packers. There are many installations set on the stinger – most importantly, the pressure and

temperature gauges for each downhole production zone and FCVs. Outer tubing diameters through the

horizontal well path vary between 3.5in to 4.5in. [13]

Swellpackers are used to divide and isolate production zones. On Q-12BH, they are installed between

inner tubing and inside the 7” screens. Swellpackers are also installed between screens and formation

for sectioning within the zones. Figure 9 shows their placement in the zonal well and Figure 11 shows an

illustration of a swellable packer. [13]


12

Figure 11: Illustration of cable feed-through swellable packers used in smart wells [8]

Flow control valves (FCVs) are important installations on the stinger. On Figure 12, they are installed

behind the dual gauges, and illustrated in red for zone 3, in blue for zone 2 and in green for zone 1. In

more detail, Zone 1 is operated by a hydraulic sliding sleeve (HCM+), which has only two different valve

positions, 100% open and closed. Zones 2 and 3 FCVs have different settings. They are operated by

HCM-A adjustable chokes through the same hydraulic line. In total, there are 14 positions available, but

every second position sets both of the valves 100% open. The possible valve positions include 2%, 5%,

27% and 100% openings. The diameter of the FCVs is 2.75”. The different positions of the FCVs are

found in Tables 3 and 4. [12]

FCV Zone 2 (HCM-A non-shrouded) (Middle)

FCV Zone 3 (HCM-A) (Heel)

Position % Open Flow area (in2) dVolume (mL)

Position % Open Flow area (in

2) dVolume (mL)

1 Closed 0 449

1 Closed 0 449

2 100 5.94 449

2 100 5.94 449

3 2 0.119 140

3 27 1.604 77

4 100 5.94 140

4 100 5.94 77

5 5 0.297 126

5 27 1.604 77

6 100 5.94 126

6 100 5.94 77

7 Closed 0 449

7 27 1.604 77

8 100 5.94 449

8 100 5.94 77

9 27.1 1.61 77

9 2 0.119 140

10 100 5.94 77

10 100 5.94 140

11 27.1 1.61 77

11 5 0.297 126

12 100 5.94 77

12 100 5.94 126

13 27.1 1.61 77

13 Closed 0 449

14 100 5.94 77

14 100 5.94 449 Table 3: FCV positions for Zone 2 and Zone 3 [12]

FCV Zone 1 (HCM+)

Position % Open

1 100

2 0 Table 4: FCV positions for Zone 1 [12]


13

Pressure and temperature dual gauges are installed in the beginning of each zone in front of the FCVs

to measure annulus and tubing conditions after inflow for each zone separately. Troll wells do not have

flow meters installed, but based on the pressure gauges, flow rates can be calculated. Pressure tags

provide continuous information about the well, and all the simulation models and flow rate calculations

use them as an input. They are illustrated in yellow color on Figure 12. [13]

Figure 12: Downhole equipment and clarification of pressures

Gas cap gas lift valve is used during initial start-up, production start-up following shut down, revision

stop, etc. It is also used if the well has high water cut and low GOR/gas rate, and therefore it is not able

to flow by itself. [12]

Baker HCM-A GCGL

Position Flow area (in2) % Open

1 0 Closed

2 0.5 100

3 0.2 40

4 0.1 20

5 0.05 10

6 0.02 4 Table 5: Gas cap gas lift valve positions and flow area [12]

Synthetic permeability Both horizontal and vertical permeability logs for well Q-12BH were calculated based on rock qualities in

September 2011. The parameter, which was measured under rock quality evaluation, was the flow zone

indicator (FZI). This is a function of normalized gamma ray (GRN). The method used is based on Carmen-

Kozeny relationship and the Amaefule FZI, where permeabilities are determined from porosity logs and

normalized gamma ray. In addition, the same method is also a function of density and gamma ray log.

For Sognefjord and Fensfjord formations the equations were slightly edited. Since both horizontal and

vertical permeability logs were already calculated, the derivations of such are outside the scope of this

study. [3], [16]


14

Both calculated permeability logs run from 1611m MD down to 6047m MD. Theoretical and simulation

models use them for productivity index calculations. The method for averaging permeabilities depends

on rock formations – how they have deposited and what type of secondary processes they have

experienced. For Q-12BH, weighted arithmetic average method is the most appropriate one to use,

because the surrounding deposits extend laterally with the well path and calculated permeability logs

are equally spaced over one meter intervals. [17]

Weighted arithmetic average

Both horizontal and vertical permeability logs were divided into zones. The separation of zones was

done by drawing a line where the log values made a sudden jump or fall. After that, the entire log was

divided into three zones based on the installed swellpackers - zone 3 (Z3), zone 2 (Z2) and zone 1 (Z1).

Since the thicknesses of the layers in a single zone varied, arithmetic permeabilities had to be weighted

first. The formula for arithmetic average permeability is

where w is the weight (length of the layer over the total length of the zone), and k is the average

permeability of a certain layer out of the many that can be present in one zone. Subscript Z stands for

the zone, and h and v stand for horizontal and vertical permeabilities. Table 6 shows the lithology based

on synthetic permeability logs, and also calculated arithmetic average permeabilities for each zone.

Zonal length Top MD (m) Bottom MD (m) Length (m) Stratigraphy Kh (mD) Kv (mD)

ZONE 3 2059 2064 5 Packer 6153 4258

1277m

2064 3031 967 3CC(2) 7282 5058

3031 3175 144 3CM(2) 199 103

3175 3340 165 3CC(3) 4771 3222

ZONE 2 3340 3345 5 Packer 1517 958

1150m

3345 3395 50 3CC(3) 4531 3022

3395 3438 43 ? (M) 67 32

3438 3551 113 3CC(3) 2681 1720

3551 3891 340 4AM(2) 447 257

3891 4172 281 4AC(2) 1913 1188

4172 4258 86 ? (M) 42 20

4258 4481 223 4AC(2) 2320 1485

4481 4495 14 4_5HETR 82 41

ZONE 1 4495 4500 5 Packer 1503 1017

1558m 4500 6058 1558 4_5HETR 1503 1017 Table 6: Penetrated lithology layers of Q-12BH and weighted arithmetic average permeabilities. [3], [13]


15

Relative Permeability Data Relative permeability curves were changed during the study process from Corey to LET relative

permeability correlations. This data was provided by Statoil ASA Troll department, because Corey values

seemed to be wrong. For LET curve calculations, reservoir properties had to be upscaled, and adjusted

to match single and two-phase historic production. Upscaling relative permeabilities is difficult because

they depend on saturations, and some scientists still debate about this method. Even though, the

calculations of LET relative permeabilities are outside the scope of this study, they were a good match

for a well Q-12BH. Thus, standard type of unnormalized LET family of correlations is used. All the

unnormalized basic imbibition data is provided for gas and oil, and oil and water relative permeabilities

in Table A.3 in Appendix A. Figure 13 and 14 show a graphical display of this data. [18]

Figure 13: LET relative permeability curves for oil and water with respect to water saturation

Figure 14: LET relative permeability curves for gas and oil with respect to gas saturation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Re

lati

ve p

erm

eab

iliti

y, K

r,α

Water saturation, Sw

Krw

Kro

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Re

lati

ve p

erm

eab

ility

, K,rα

Gas saturation, Sg

Krg

Kro


16

PVT properties The data used for Troll field modeling is gathered from the PVT report and Special Core Analysis (SCAL)

data. This report includes a list of pilot wells that were drilled and measured for gas, oil and rock

reservoir properties. The closest pilot well for Q-12BH was 31/2-3. It was drilled in the northern part of

TWGP. Based on the changing reservoir pressures, one can interpolate viscosity (μ), formation volume

factor (FVF) and solution gas (RSOL) for Q-12BH. Table A.1 in Appendix A provides PVT data for TWGPN.

[10]

Procedure into simulations and theoretical methods

Well testing Production data is collected via well testing and it is used as a reference for constructing simulations.

Wells at Troll are normally tested at least once during a six month period. New wells and wells in

development are tested more frequently. Testing is used for production verification. Since there are no

flow meters installed on the individual Troll C and B wells, testing them helps to tune the well allocation

and optimize oil production. Currently, there are 14 well test results available for Q-12BH, but only the

first one of them is relevant in this study. The reason for using only that particular test data is explained

more thoroughly in the upcoming text. For comparative purposes between simulation models and well

test results, few of the parameters need to be calculated and explained in more detail. The following

subparagraphs will focus on these parameters.

Reservoir pressure

Reservoir pressure during the first well test is extrapolated from the well shut-in data gathered from

Aspen Process Explorer software. Table B.1 with all these values is found in Appendix B. For better linear

relationship, only the first four shut-in times are used. The time period for these four data recordings is

roughly half year and seen graphically in Figure 15. This graph represents shut-in pressures with respect

to the number of days since Q-12BH was put on stream. Since the trend lines are matching well,

reservoir pressure during day 6 can be extrapolated by the equations shown in the legend.


17

Figure 15: Reservoir pressure decrease as a function of time.

Gas inflow

Gas coning is unpredictable, it may start immediately after a new well is put on stream or it may take

months/years for the gas cone to reach the well. As the field matures and the oil column becomes

thinner, gas breakthrough will generally occur at an earlier stage in a wells life. This scenario makes well

simulations a challenge. Once the cone reaches the well, it will be more difficult to model and

understand well’s behavior.

In general, there are three different types of gases being produced from the well. They all vary slightly in

their chemical compositions, but it is still difficult to know exactly the fraction of each gas. A large gas

cap on top of the oil column is called free gas. Free gas enters into the well during gas coning. High free

gas production diminishes oil flow rate, and therefore production engineers try to avoid producing free

gas for as long as possible. In some cases like starting up a high water cut well, free gas inflow is

required, but then it is done through the gas cap gas lift valve, and not from the zones.

The second type of gas being produced is solution gas. Solution gas cannot be separated from oil at

reservoir conditions. It remains in the oil as long as the pressure and temperature conditions are

unchanged. During production process, the pressure in the wellbore keeps decreasing as oil travels

towards the surface and such a decrease helps solution gas to bubble out from the oil. Solution gas rates

are calculated and found from the PVT data in Table A.1 in Appendix A. For calculations, solution GOR

needs to be interpolated from the PVT data based on the actual reservoir pressures and then, solution

gas rate can be determined by multiplying solution GOR with oil flow rate in standard conditions.

Thirdly, there is riser gas injection, which is injected to the production line near the sea bed to push the

oil column upwards. This injection technique is also used during starting up high water cut wells. Thus,

based on injection rate and calculated solution gas rate, a rough estimate of free gas can be determined

as well tests provide total gas inflow rate.

y = -0.0043x + 136.33 R² = 0.9916

y = -0.007x + 136.59 R² = 0.9979

y = -0.009x + 136.49 R² = 0.9995

134.8

135.0

135.2

135.4

135.6

135.8

136.0

136.2

136.4

0 25 50 75 100 125 150 175 200

Re

serv

oir

Pre

ssu

re [

Bar

]

Number of days since well start up

Zone 3

Zone 2

Zone 1


18

In the end, for well productivity calculations, gas inflow needs to be simplified. A few important

assumptions need to be made. The first simplification excludes free gas production from the well as

there is no gas saturation log present. Without gas saturation, it is extremely difficult to predict gas

behavior across different zones. Hence, this assumption can only be relevant when the gas cone has not

yet reached the wellbore, and the flow into the well is a two-phase flow of oil and water. Based on well

testing data, this situation does not exist. The first well test, done only six days after Q-12BH was put on

stream, shows some free gas production. Since this is calculated by subtracting solution gas and riser gas

from the total gas rate, it is considered to be a value in that range. However, since free gas rate is low, it

is still worth trying to match the first well test with a two-phase simulation model excluding gas as long

as liquid rates and downhole pressures can be matched.

First well test

The first well test was run six days after the well was put on stream in September 11th, 2011. It was a

twelve hour long test with the following zonal FCV openings: 5% opened for Zone 3, 27% opened for

Zone 2 and 100% opened for Zone 1. As a reminder, these valves are located on the stinger and have

adjustable settings for production optimization. All the measured pressures, flow rates and ratios for the

first well test are found in Table 7. This well test data shows that there is already some gas influx present

in the well, but it also includes solution gas since it all flows together into the same separator. In the

separator all the rates can be determined. There is also an illustration shown on Figure 16 with all the

DHGs, reservoir and wellhead pressures, and flow control valve opening positions. This data is later

compared with the simulation models to conclude whether these FCV positions were the most optimal

ones to start up the production on Q-12BH. [19]

31/2 Q-12 BH WELL TEST #1

Start Stop Duration

16.09.2011 01:14 16.09.2011 13:14 12:00:00

ZONAL FLOW CONTROL VALVE (FCV) OPENINGS (HEEL → TOE)

Zone 3 Zone 2 Zone 1

5 % 27 % 100 %

ANNULUS PRESSURE (DHG) [Bar]


134.6 134.2 135.2

TUBING PRESSURE (FBHP) [Bar]


125.4 133.1 135.04

FLOW RATES, WATER CUT AND GAS OIL RATIO

QO, ST [Sm3/d] QW, ST [Sm

3/d] QG, ST [Sm

3/d]

1443 933 83784

QLIQ, ST [Sm3/d] GOR Water cut

2376 58.1 39.3

Table 7: 31/2-Q-12 BH first well test data (16.09.2011) [19]


19

Figure 16: First well test DHG pressure data together with reservoir and wellhead pressures, and FCV openings.

Discussion of flow rates in different well tests All the 14 well tests experienced gas influx. The least amount of gas was measured during the first well

test found in Table B.2 in Appendix B. First of all, solution gas rate was subtracted from the total gas

influx found by well tests, and then it was multiplied by gas FVF. Free gas rate during the first well test

was found to be 113 Rm3/d, which formed only 4% of the total influx. For modeling purposes, this 4% of

free gas inflow is neglected for simplicity in order to use the two-phase liquid model. In Figures 17 and

18, well test comparisons with respect to reservoir flow rates and contribution of the phases at DH

conditions are shown respectively.


20

Figure 17: Reservoir flow rates of all the well tests for different phases.

Figure 18: Phase flow contribution comparison with all the well tests.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

WT1 WT2 WT3 WT4 WT5 WT6 WT7 WT8 WT9 WT10WT11WT12WT13WT14

Re

serv

oir

flo

w r

ate

, Qα [

Rm

3 /d

]

Well tests

Water

Free gas

Oil

35 37 39 37 32 36

30 24

7

29 20 17 16

22

4

16 15 20 22

28 44 58 83

53 69 73 75 65

61

47 46 42 46 36

26 18

10 18

12 10 9 13

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Co

ntr

ibu

tio

n o

f p

has

e f

low

Number of days since well start up

Oil

Free gas

Water


21

Simulation Modeling There are three analytical simulation models built to resemble the first well test behavior.

1. NETool model with built-in steady-state Joshi inflow equations [21]

2. Theoretical steady-state Joshi PI model for horizontal wells [22]

3. Muskat’s analytical PI model for horizontal wells [20]

First, NETool model is used to determine the productivity index of each zone. Then, the two other

methods are used to determine the difference between numerical NETool model and two other

analytical models.

Objectives NETool model result should resemble the first well test result. Thus, parameters such as completion

string design, correct FCV openings, saturation, permeability and hydrostatic reservoir pressure logs,

PVT data and relative permeabilities need to be set into NETool just like they were during the time of

the first well test. After set-up, tubing and annulus pressures are tried to be matched with the first well

test pressures for each zone. These pressures are not average zonal pressures. They are recorded at the

DHG sensors and therefore NETool pressures should be matched at the same location. The exact

measured depths of all the DHGs are found in Table 2. Then, flow rates and water cut should be

matched with the same data. Gas rate will be different, because NETool only calculates solution gas rate.

Once there is a close match with the first well test, NETool pressures will be tested by fully opening all

the FCVs, and comparing annulus and tubing pressures with the pressure tags. If these pressure tag

values are similar or almost matching, then NETool simulation model is considered reliable and

independent of FCV positions. In the end, NETool model is tested with the two analytical models to

determine the difference with productivity indices.

Parameters NETool is software used for numerical simulation modeling. Horizontal well productivity index in NETool

is calculated by a steady-state Joshi homogeneous flow equation. Homogeneous flow equation, which is

common in the oil industry, uses average properties of the phases present in each of the segments. A

segment in NETool is set to 12 meters with a few exceptions in the beginning of every zone as some of

the shorter equipment is modeled right there. This Joshi model assumes constant reservoir pressure

over time with constant reservoir pressure boundaries. It also assumes that the well is centered in the

middle of the reservoir, and drains an ellipsoid shape in the horizontal plane and a thickness of the layer

in the vertical plane. Table 8 gives some of the average parameters used for flow rate calculations and

productivity indices in NETool and in analytical models. These parameters are discussed more

thoroughly in the following text. [21]


22

Parameter Symbol Units Zone 3 Zone 2 Zone 1 Comments

Reservoir dimensions

Length of a zone LZ m 1277 1150 1558 Fixed

Total length of the zones LTOTAL m 3985 Fixed

Blanks in each zone LB m 286 96 12 Fixed

Width of the reservoir wR m 120 120 120 Assumption

Thickness of the reservoir h m 20 20 20 Assumption

Wellbore radius rwb m 0,12 0,12 0,12 Fixed

Pressures

Reservoir pressure pRES Bar 136.22 136.48 136.38 NETool FCVs 100% open

Sandface pressure pSF Bar 135.88 135.81 135.65 NETool FCVs 100% open

Drawdown (pRES - pSF) Δp Bar 0.34 0.67 0.72 Calculated

Reservoir properties

Horizontal permeability (Synt.) kH mD 6134 1510 1503 Calculated

Vertical permeability (Synt.) kV mD 4245 954 1017 Calculated

Oil viscosity (PVT) µO cp 1.903 1.901 1.902 Interpolated

Water viscosity (PVT) µW cp 0.45 0.45 0.45 Fixed

Oil formation volume factor (PVT) BO Rm3/Sm

3 1.136 1.136 1.136 Interpolated

Water formation volume factor (PVT) BW Rm3/Sm

3 1.017 1.017 1.017 Fixed

Relative permeability data

Average effective saturation per zone Sw - 0.462 0.456 0.594 Averaged from a log

Relative permeability of oil kro - 0.122 0.130 0.024 Calculated from Sw log

Relative permeability of water krw - 0.050 0.047 0.157 Calculated from Sw log

Oil mobility λo 1/cp 0.06 0.07 0.01 Calculated

Water mobility λw 1/cp 0.11 0.10 0.35 Calculated

Total mobility (no gas) λ 1/cp 0.17 0.17 0.36 Calculated

Table 8: Parameters used for productivity indices calculation [10], [12]

Fixed values are simply unchangeable and usually known after the completion is set. They are the most

reliable parameters. For Q-12 BH, fixed values are:

Zonal length and the total length

Blanks of the zone

Wellbore radius

Water viscosity

Water formation volume factor

Calculated values could vary, if they are not calculated from the fixed values. In Q-12BH, calculated

values are:

Drawdown

It is calculated by subtracting the average sandface pressure from the hydrostatic reservoir

pressure. Both pressures vary with respect to the segments in NETool.


23

(Horizontal and vertical) synthetic permeability

Since synthetic permeabilities are calculated from the log values that only reach a certain radius

from the wellbore, overall permeability of the zone could vary.

Relative permeabilities

These are dependent on saturations, and saturation log is calculated without including gas.

(Oil and water) mobility

Both of them are based on relative permeability curves, which in addition depend on

saturations.

Interpolated values depend on the accuracy of reservoir pressures. They are interpolated from the PVT

data and for Q-12BH, they are the following:

Oil viscosity

Oil formation volume factor

Averaged values could have a large variation depending on their discrepancies. In Q-12BH, averaged

values are:

Effective saturation

This is a log calculated from Archie equations.

Assumed values are the parameters most difficult to determine. Some reservoir geometry values for Q-

12BH are assumed:

Reservoir thickness

Reservoir width

These last two parameters are described in more detail since they were determined having the least

amount of references.


24

Reservoir geometry

Figure 19: NETool reservoir geometry from the top and front view including yellow streamlines [21]

In NETool, reservoir widths and thicknesses were tested to determine how these two parameters affect

pressures and flow rates. The intension was to match NETool with the first well test data. Many

simulations were run in NETool only by changing the thickness and width of the reservoir zones. As a

result, Table 9 was created. The yellow columns indicate the first good pressure match going from lower

to higher thickness values. Figure 20 shows it graphically.

Thickness (m)

RESERVOIR GEOMETRY w/h ratio Width (m)

0 120 200 300 400 500 6.18

10 2185 2151 2117 2087 2059

20 2203 2185 2166 2151 2132 6

30 2210 2197 2183 2171 2159 6.67

40 2212 2203 2192 2182 2173

50 2214 2206 2197 2189 2181 6

60 2215 2206 2201 2194 2187 6.67

70 2215 2210 2203 2197 2191

80 2215 2210 2204 2199 2194

90 2215 2211 2206 2201 2196 5.56

100 2215 2211 2207 2202 2198

110 2215 2212 2207 2203 2199

120 2215 2212 2208 2204 2200

130 2215 2212 2210 2205 2201

140 2215 2212 2209 2205 2202

150 2214 2212 2209 2206 2203

160 2215 2212 2209 2206 2203 Table 9: Reservoir width and thickness sensitivities.


25

Figure 20: Simulated flow rates with varying reservoir geometry

Figure 20 shows the behavior of changing flow rates as a function of reservoir geometry. Around 2200

Sm3/d, NETool DHG pressures are closely matched with the first well test pressures. Hence, the flow

rates at these pressures were used to calculate the ratio of width to thickness for Q-12BH reservoir. It

was found to be 6, and used as a reference to determine reservoir geometry. However, the width and

thickness were still unknown as they could vary having the same ratio. This question was solved by

reading “Advanced well optimization in thin oil rim reservoirs” report that had the following statement

about the lateral extent of Q-12AH (mother well), which well path runs parallel to Q-12BH trajectory:

There were no natural structural limitations sufficiently close. … The lateral extent of the box model is

adjusted to cover a typical drainage radius of 60 m for the horizontal Troll wells and to incorporate the

nearby faults. [1]

Based on this calculated ratio and the text material above, reservoir geometry was determined.

Reservoir width, which is equal to two times the length of a drainage radius, is equal to 120m, and the

thickness is 20m. Even though, reservoir geometry was now finalized and set the same for every zone in

the reservoir, it is still an assumption. In reality, different zonal permeabilities would cause drainage

radiuses to be different.

2040

2060

2080

2100

2120

2140

2160

2180

2200

2220

2240

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Flo

w r

ate

, Q, (

Sm3

/d)

Reservoir thickness, h (m)

width 120m

width 200m

width 300m

width 400m

width 500m


26

NETool modeling The following paragraphs describe the theory and equations how NETool calculations are set up. The

reservoir model used for this horizontal well is AMAP2013-PRED-3FLUX-MA with a starting date of

01.04.2012. It is an Eclipse model made by the Statoil ASA reservoir engineers and entered into NETool.

First of all, horizontal well path going from the heel to the toe needs to be entered into NETool.

Geographic coordinates together with measured and true vertical depths make up this well path.

Entering the path is the foundation for modeling completions, where many other reservoir parameters

are required. Since the actual well was completed with 12m string pipes, the segments in NETool were

also set to 12m intervals. That made hole and completion design modeling easier. NETool completion

design is found in Table C.1 in Appendix C. [13]

For every segment, the inflow of every component (phase) is calculated separately by the following

formula

[1]

where the letter indicates different phases – oil, solution gas and water. is the mobility of the

phase. is the transmissibility and is the pressure drop from reservoir to sandface. [21]

For zonal productivity indices, one should understand how mobility and transmissibility influence the

final result, because these terms vary over every segment when specific productivity index, , is

calculated

[2]

Transmissibility and mobility

Transmissibility forms part of PI modeling. It is calculated by NETool based on upscaled permeabilities

and other geometric parameters. Every segment has the following formula

(

)

(

) [3]

where √

There are many parameters in this equation that do affect the inflow and productivity index. The most

influential ones are horizontal permeability that varies between segments; then influence of anisotropy

factor ; and lastly both assumed geometry values: reservoir width and thickness, which are considered

the same for all the three zones.

Another important term in flow rate calculations is phase mobility:


27

[4]

For flow rate calculations, transmissibility is multiplied with the difference between reservoir pressure

and sandface pressure, and the mobility of each phase separately seen in Equation (1). That results in

three different flow rates of gas, oil and water at reservoir condition. Next, these separate phase flow

rates are added together to calculate the total flow rate per segment. Then, the total flow rate per

segment is divided by the pressure drop between reservoir pressure and sandface pressure resulting in

specific productivity index found in Equation (2). [21]

NETool Results Table 10 shows the best simulation model results when matching the first well test data.

Pressures in NETool (FCV openings Z3 = 5%, Z2 = 27%, Z1 = 100%)

Parameter Symbol Units Zone 3 Zone 2 Zone 1

Reservoir pressure pRES Bar 136.22 136.48 136.38

Sandface pressure pSF Bar 136.09 135.76 135.52

Average annulus pressure pANN Bar 135.76 135.26 135.25

Annulus pressure (at DHG) pANN_DHG Bar 134.86 133.70 135.24

Average tubing pressure pTUB Bar 128.72 133.93 135.22

Flowing tubing hole pressure (at DHG) pTUB_DHG Bar 125.40 132.92 135.03

Drawdown (pRES - pSF) Δp Bar 0.14 0.72 0.86

Pressure drop across ICDs (pSF - pANN) ΔpICD Bar 0.32 0.50 0.26

Pressure drop across stinger (pANN - pTUB) ΔpSTI Bar 7.04 1.33 0.03

Flow rates in NETool (FCV openings Z3 = 5%, Z2 = 27%, Z3 = 100%)

Oil rate QO Sm3/d 1326

Water rate QW Sm3/d 877

Gas rate QG Sm3/d 63362

Total liquid rate (ST condition) QLIQ Sm3/d 2203

Gas to oil ratio (solution gas) GOR % 47.8

Water cut WC % 39.8

Total liquid rate per zone (ST condition) QIN,LIQ_ST Sm3/d 615 739 848

Oil rate per zone QOIL,ST Sm3/d 388 556 382

Water rate per zone QWAT,ST Sm3/d 227 184 466

Gas rate per zone QGAS,ST Sm3/d 18526 26553 18283

Total influx per zone (DH condition) QIN,DH Rm3/d 673 821 909

Oil rate per zone QOIL,DH Rm3/d 440 630 434

Water rate per zone QWAT,DH Rm3/d 232 187 474

Gas rate per zone QGAS,DH Rm3/d 1 4 1

Inflow contribution per zone %Q % 28 34 38

Productivity Index J Sm3/d/bar 4523 1030 985

Table 10: Simulation model results of the first well test


28

A comparison of NETool simulation model results and the first well test data is found in Table 11. The

following parameters are compared: DHG pressure measurements, liquid inflow rates and water cut.

Table 11: NETool and well test results data comparison

This was the best match between the first well test and NETool simulation model in terms of these

parameters. Reservoir pressure calculated through extrapolation of well shut-ins gives slightly higher

values than reservoir pressure calculated by hydrostatic pressure log used in NETool. The difference is

less than 0.1 bars for all the three zones. Hydrostatic pressure calculation is explained more thoroughly

under theoretical steady-state Joshi’s model. NETool reservoir pressure can be found in Figure 21.

Overall, the tubing pressures and annulus pressures at the DHG sensors have a small difference. The

most difficult zone to match the pressures was zone 2, because neither tubing nor annulus pressures

Comparisons Zone 3 Zone 2 Zone 1

Reservoir pressure [Bar]

Well test (shut-in) 136.31 136.55 136.44

NETool (hyd stat P) 136.22 136.48 136.38

Difference (Bar) 0.09 0.07 0.06

Annulus pressure at DHG [Bar]

Well test 134.6 134.2 135.2

NETool 134.9 133.7 135.2

Difference (Bar) 0.3 0.5 0

Tubing pressure at DHG [Bar]

Well test 125.4 133.1 135.0

NETool 125.4 132.9 135.0

Difference (Bar) 0 0.2 0

Oil flow rate in ST [Sm3/d]

Well test 1443

NETool 1326

Difference 8.11 %

Water flow rate in ST [Sm3/d]

Well test 933

NETool 877

Difference 6.03 %

Total flow rate in ST [Sm3/d]

Well test 2376

NETool 2203

Difference 7.29 %

Water cut in ST [%]

Well test 39.3

NETool 39.8

Difference 1.36 %


29

gave an exact result. NETool annulus and tubing pressure graph is given in Figure 22. Notice how the

pressures have a sudden change due to zonal separations.

Figure 21: NETool reservoir pressure and completion diagram.

Figure 22: NETool sandface (blue), annulus (purple) and tubing (red) pressures with respect to the length of the well. Zonal separation is shown with dashed oval shaped circles.


30

In terms of flow rates, NETool oil flow rate in standard condition is off by 8.11 % and water flow rate is

off by 6.03 % in comparison to the first well test. Hence, the total liquid rate is 7.29 % lower from the

total well test liquid rate. On the other hand, water cut varied only by 1.36 %.

In the next step, all the downhole FCVs in the same NETool model were fully opened. This was done to

compare productivity indices when FCV positions are different and for later comparisons with the other

two theoretical models. NETool simulation results with three 100% open FCVs are found in Table 12.

Pressures in NETool (All FCVs are 100% opened)


Reservoir pressure pRES Bar 136.22 136.48 136.38

Sandface pressure pSF Bar 135.88 135.81 135.65

Average annulus pressure pANN Bar 133.66 135.36 135.46

Annulus pressure (at DHG) pANN_DHG Bar 128.15 133.97 135.46

Average tubing pressure pTUB Bar 129.97 134.42 135.41

Flowing tubing hole pressure (at DHG) pTUB_DHG Bar 126.39 133.61 135.29

Drawdown (pRES - pSF) Δp Bar 0.34 0.67 0.72

Pressure drop across ICDs (pSF - pANN) ΔpICD Bar 2.22 0.45 0.19

Pressure drop across stinger (pANN - pTUB) ΔpSTI Bar 3.69 0.94 0.05

Flow rates in NETool (All FCVs are 100% opened)




Total liquid rate (ST condition) QLIQUID Sm3/d 3047

Gas to oil ratio (solution gas) GOR % 47.8

Water cut WC % 38.3











Table 12: NETool simulation model results with fully opened downhole FCVs.

Notice that the difference between productivity indices in Table 10 and Table 12 is small, but FCV

openings do affect the inflow contribution per zone. Throughout Q-12BH production period, this well

was operated only two days with three 100% opened FCVs. The pressure tag values of these two days

are shown in Table 13 and compared with NETool pressure calculations in Table 14. If these values are

similar, then NETool simulation model is considered reliable.


31

Date PANN_Z3 PANN_Z2 PANN_Z1 PTUB_ Z3 PTUB_Z2 PTUB_Z1

23-Jan-12 128.08 133.64 134.35 126.90 133.40 134.46

24-Jan-12 128.05 133.62 134.35 126.85 133.39 134.45

Average 128.06 133.63 134.35 126.87 133.39 134.46

Table 13: DHG pressures of the actual well running with 100% opened FCV positions for two consecutive days

CASE PANN_Z3 PANN_Z2 PANN_Z1 PTUB_ Z3 PTUB_Z2 PTUB_Z1

Actual 128.06 133.63 134.35 126.87 133.39 134.46

NETool 128.15 133.97 135.46 126.39 133.61 135.29

Difference (Bar) 0.09 0.34 1.11 0.49 0.22 0.84

Table 14: Pressure tag recordings in January 2012 compared with NETool simulation model results

There is a small difference between NETool and the actual situation, because in January 2012 when the

actual pressure tags where measured, the well Q-12BH was experiencing a much larger gas influx.

Therefore, actual DHG annulus and tubing pressures should be lower than NETool calculated pressures.

Just like pre-assumed, the difference seems to be in correlation with the NETool results where only

solution gas is present.

The next objective is to determine the pressure drop across the ICD-screens for the accuracy of sandface

pressures. NETool calculates sandface pressures, but theoretically they could also be calculated by

adding a pressure drop across the ICD-screens to an average zonal annulus pressure in NETool.

Theoretical pressure drop across the 3.2 bar ICD-screen

Pressure drop across the 3.2 bar single ICD-screen is calculated by Equation [5]:

(

) ⁄

(

)

[5]

where and are multiphase densities and viscosities calculated by downhole flow rate

volumetric fractions found in NETool and shown in Table 16. is the total liquid rate of a zone at

reservoir condition, and the following three parameters in Table 15 are Troll field specific calibrated

coefficients:

Parameter Value Units

aSICD 3.46E-03 Bar/(Rm³/day)²

ρ_cal 1000.3 kg/m³

µ_cal 1.45 cP Table 15: Troll field ICD-valve and screen calibrated coefficients

Table 16 gives DH flow rates with two different FCV openings:


32

Segments Opening

Total Influx DH

Oil Fraction

Gas Fraction

Water Fraction

Oil flow rate

Gas flow rate

Water flow rate

[Rm³/day] αo αg αw [Rm³/day] [Rm³/day] [Rm³/day]

ZONE 3 100 % 1771 64.68 % 1.38 % 33.93 % 1145 24 601

ZONE 2 100 % 773 76.89 % 0.44 % 22.68 % 594 3 175

ZONE 1 100 % 801 48.33 % 0.09 % 51.58 % 387 1 413

ZONE 3 5 % 673 65.37 % 0.21 % 34.41 % 440 1 232

ZONE 2 27 % 821 76.72 % 0.49 % 22.79 % 630 4 187

ZONE 1 100 % 909 47.75 % 0.12 % 52.14 % 434 1 474 Table 16: DH flow rate phase fractions with two different FCV openings

Table 17 shows calculated mixed densities and viscosities. It also gives an average theoretical pressure

drop across a single ICD-screen in all the three zones. From the screen tally of Q-12BH, Zone 3 includes

80 x 7” ICD-screens, Zone 2 includes 86 x 7” ICD-screens, and Zone 1 includes 44 x 7” ICD-screens and 82

x 6 ⅝” ICD screens, which makes a total of 126 ICD-screens in Zone 1. The total number of ICD- screens

in the entire well is 292. [23]

Fluid properties at reservoir pressure 136.3 Bar and 68 oC

Parameter Zone 3 Zone 2 Zone 1 Units

Oil density 890.0 kg/m³

Water density 1045.0 kg/m³

Gas density 0.75 kg/m³

ρ_mix (3*100% opened FCVs) 930.3 921.3 969.1 kg/m³

ρ_mix (5%,27%,100% opened FCVs) 941.4 921.0 969.8 kg/m3

Oil viscosity 1.903 1.901 1.902 cP

Water viscosity 0.45 cP

Gas viscosity 0.017 0.017 0.017 cP

µ_mix (3*100% opened FCVs) 1.38 1.56 1.15 cP

µ_mix (5%,27%,100% opened FCVs) 1.40 1.56 1.14 cP

Average pressure drop across a single ICD-screen with two different FCV openings

Length of the zone 1277 1150 1558 m

Number of ICD-screens per zone 80 86 126

Pressure drop across ICDs (3*100% opened FCVs) 1.59 0.27 0.13 Bar

Pressure drop across ICDs (5%,27%,100% opened FCVs) 0.23 0.30 0.17 Bar Table 17: Average theoretical pressure drop across a single ICD-screen in all three zones

Thus, Table 18 compares NETool simulated average pressure drop across the single ICD-screen and the

theoretical pressure drop values calculated in Table 17.

Pressure drop across the ICD-screens

CASE Units Zone 3 Zone 2 Zone 1

FCV openings % 100 100 100

NETool Bar 2.22 0.45 0.19

Theoretical Bar 1.59 0.27 0.13

Difference % 28 40 30


33

FCV openings % 5 27 100

NETool Bar 0.32 0.50 0.26

Theoretical Bar 0.23 0.30 0.17

Difference % 29 41 36 Table 18: Variation between NETool and theoretical pressure drop across a single ICD-screen

There is a difference between NETool and theoretical pressure drop across the ICDs, but it has a similar

trend with respect to zones. This difference in bars is not large, and therefore one can consider that the

actual sandface pressure is about the same as in NETool. Hence, NETool model is considered reliable.

Analytical Joshi’s and Muskat’s PI Models

The next two methods are Joshi’s analytical steady-state inflow method for horizontal wells assuming an

elliptical reservoir, and Muskat’s analytical streamline model method assuming a box-reservoir. Both

methods are described in following text.

Calculations with steady-state Joshi horizontal well PI model Theoretical steady state Joshi model is set up to calculate reservoir inflows and productivity indices for

the three separate zones of the well Q-12BH. Therefore, Joshi’s theoretical model drains three ellipsoids

in the horizontal plane through all the zones.

Reservoir pressure is averaged NETool pressure, which is calculated for each segment and derived from

hydrostatic pressure Equation (6)

[6]

where is the calculated reservoir pressure of each separate segment, is the interpolated

reservoir pressure based on well shut-ins at the heel pressure gauge, is the density of oil, is the

gravity, is the fixed true vertical depth of the heel pressure gauge, and is the varying

true vertical depth of each segment.

Drawdown is calculated by taking the difference between an average reservoir pressure and an average

sandface pressure found in NETool. For flow calculations in standard condition, Joshi’s model for

horizontal wells uses the following Equation (7):

[ √ ⁄

]

(

)

for [7]

⁄ [

√

⁄]

, √

, √ and √ ⁄


34

where subscript indicates the phase; is the calculated horizontal well flow rate in bbl/d converted

to Sm3/d; and are the horizontal and vertical permeabilities respectively in D converted to m2; is

the thickness of the reservoir in m; is the drawdown from the reservoir boundary up to wellbore in

bars; is the phase viscosity in cp converted to bars*d; is the phase formation volume factor in

Rm3/Sm3; is half the major axis of a drainage ellipse in m; is half of the minor axis of drainage ellipse

in m; is the length of the zone in m; is the dimensionless influence coefficient for anisotropy; and

is the wellbore radius in m. All the parameters described here are found in Table 8. Reservoir geometry

model is shown in Figure 23. [22]

Figure 23: Reservoir geometry model for the three-zone horizontal well

Equation (7) calculates the flow rates of two different phases, oil and water, separately. The difference

with a single phase Joshi formula lies in mobility term. Mobility is a multiplier of the equation formed by

relative permeability term in the numerator, and viscosity term in the denominator. For permeability,

the zonal weighted averages based on synthetic permeability logs were calculated and used in the same

equation. In addition, the influence coefficient for anisotropy was calculated by permeability averages.

In terms of reservoir geometry, Equation (7) considers a constant pressure boundary around the

horizontal drainage radius, and that is how the steady state condition is met. On top and bottom of the

reservoir, there is no-flow boundary and the well is assumed to lie in the center of the reservoir. Thus,

this equation is highly dependent on reservoir geometry parameters like thickness, h, drainage radius,

reH, zonal length, L, and half the major axis of drainage ellipse, a. Since Rend from Figure 19 is very small,

the overlap of the ellipses is negligible.

However, this method is set up just like NETool, except it does not have segments in the zones, but

instead it uses a single average values for each zone. The difference between analytical Joshi’s inflow

model and NETool Joshi’s inflow model is shown in Appendix D. [21], [22]


35

Steady state Joshi horizontal well analytical simulation results

Joshi's Theoretical Method (SPE 15375 eq.10a for two phase situation)

Influence of anisotropy β - 1.20 1.26 1.22

Horizontal drainage radius reH ft 643 611 710

Half the minor axis of a drainage ellipse b ft 197 197 197

Half the major axis of a drainage ellipse a ft 2103 1897 2563

Distance from the end of the zone until ellipse boundary Rend ft 9.2 10.2 7.6

First term in the denominator ln[(a+...)] - 0.094 0.104 0.077

Second term in the denominator βh/LZ*ln(...) - 0.087 0.102 0.072

Denominator - - 0.18 0.21 0.15

Numerator - rB/d 2466 1192 2688

Oil flow rate qO rB/d 5002 2301 637

Water flow rate qW rB/d 8659 3492 17411

Total liquid rate qH rB/d 13660 5793 18048

Zonal contribution QZ % 36 15 48

Rates in Standard condition

Oil flow rate qO STB/d 4403 2025 561

Water flow rate qW STB/d 8514 3434 17120

Total liquid rate qH STB/d 12917 5459 17681

Total flow rate QLIQ STB/d 36056

Productivity Index of a zone J STB/d/psi 2643 562 1681

Conversion to SI units

Oil flow rate qO Sm3/d 700 322 89

Water flow rate qW Sm3/d 1354 546 2722

Flow rate into horizontal well qH Sm3/d 2054 868 2811

Total flow rate QLIQ Sm3/d 5732

Water cut WC % 80.62

Productivity Index of a zone J Sm3/d/Bar 6094 1295 3877

Table 19: Steady state Joshi horizontal well analytical simulation results

Muskat’s analytical PI calculation method

Assumptions of the method

This anisotropic reservoir has a box-shaped geometry with two constant horizontal pressure boundaries

and two vertical no-flow boundaries. The well is centralized between all the boundaries and could be

visualized as a sink. The flow into the well is two -phase steady-state flow through a reservoir. There is

no gas influx, and the two liquid phases flowing together are calculated separately. The streamlines of

the well are have a specific shape shown in Figure 24.


36

Figure 24: A box-shaped reservoir seen as a sink that drains water and oil (front view - the well runs into the page)

Theory

As known, well Q-12BH has three producing zones in the wellbore. The objective of the study is to

understand the production of each zone separately, and therefore every zone is treated on its own. This

method calculates specific PIs, JS,(x) of the zone. Specific PI has units Sm2/d/bar, and it needs to be

multiplied by specific zonal length for the actual PI values.

[8]

The specific zonal inflow, , has units Sm3/d/m. For the normal inflow of the zone, specific inflow needs

to be multiplied by the length of the zone just like specific PI. The sum of all reservoir zone inflows

equals the total production of the well.

[9]

The governing equation for PI is based on a classic flow potential of a well per unit length expression.

This this case unit length is zonal length. The principle analytical function describing two-dimensional

flow of incompressible fluid has two parts: real part and imaginary part. The real part describes potential

distribution, whereas its imaginary part describes the stream function. For PI determination, only the

real part is required. Thus, pressure Equation (10) is explained and derived in the Appendix E. [20], [24]

(

) [10]

Here and are the scaled coordinates that count for anisotropy just like specified reservoir

coordinates and that stand for reservoir width and thickness respectively. The additional term c is

the integration constant, µ is viscosity, and k is permeability.

√

√

√

√

[11]


37

These initially derived scaled coordinates and from Equation (10) are now replaced with reservoir

dimensions as width and as reservoir thickness. Both parameters are multiplied with the

permeability ratios to count for anisotropy.

Next, pressure Equation (10) is substituted into specific productivity index Equation (8). To simplify the

result of this substitution, two reference points are chosen. The first one at the reservoir boundary is

. The second one at the wellbore is . Then, mobility term,

⁄ , and FVF are added to this specific PI equation to calculate two phase liquid rates and PI.

[ (

)]

[12]

Subscript indicates liquid phase; is specific flow rate changed to standard condtition; is

drawdown; is effective permeability; is relative permeability of a phase; is the viscosity of a

phase; and is the wellbore diameter. This specific PI Equation (12) is only valid if . [20]

Results of Muskat Method

Muskat's Theoretical Method (ŵZ >> ĥZ)

Effective permeability k m2 5.10E-12 1.20E-12 1.24E-12

Scaled zone width ŵR m 109.4 107.0 108.8

Scaled zone thickness ĥR m 21.9 22.4 22.1

Wellbore diameter dW m 0.24 0.24 0.24

Specific zone oil inflow qs,O Rm2/d 0.5 0.3 0.1

Specific zone water inflow qs,W Rm2/d 0.9 0.4 1.5

Specific zone liquid inflow qs,H Rm2/d 1.5 0.7 1.6

Oil flow rate (DH) qO Rm3/d 680 316 87

Water flow rate (DH) qW Rm3/d 1178 480 2375

Total reservoir liquid rate (DH) per zone qH Rm3/d 1858 796 2462



Specific zone oil inflow qs,O Sm2/d 0.47 0.24 0.05

Specific zone water inflow qs,W Sm2/d 0.91 0.41 1.50

Specific zone liquid inflow qs,H Sm2/d 1.38 0.65 1.55



Total liquid rate per zone qH Sm3/d 1757 751 2412

Total flow rate QLIQ Sm3/d 4919


Specific productivity index Js Sm2/d/Bar 4.1 1.0 2.1

Productivity index per zone J Sm3/d/Bar 5213 1120 3327

Table 20: Muskat’s analytical model results


38

Additional simulation There is one other simulation model which was run with the same reservoir properties. It is a steady

state Joshi NETool method made in Excel with average zonal values, transmissibilities and mobilities.

This will show the difference between NETool numerical calculations and theoretical Joshi’s method.

This simulation #3 is expected to have similar flow rates and productivity indices as Joshi’s theoretical

method. Therefore, if there is a difference between NETool and the theoretical steady state Joshi’s

model results, it can be concluded that one should not average some parameters over the entire

reservoir zone.

Simulation #3 uses NETool Joshi’s equations and drains three ellipses from each reservoir zone.

Simulation #3. Joshi's NETool Analytical Method (three zones draining three ellipses)

Influence of anisotropy β - 1.20 1.26 1.22

Half reservoir thickness d m 10 10 10

Half zone length c m 638 575 779

Half the minor axis of a drainage ellipse b m 60 60 60

Half the major axis of a drainage ellipse a m 641 578 781

Distance from end of zone until ellipse boundary Rend m 2.8 3.1 2.3

First term in the denominator cosh-1

(a/c) - 0.094 0.104 0.077

Second term in the denominator βh/LZ*ln(...) - 0.087 0.102 0.072

Denominator - - 0.18 0.21 0.15

Numerator - Rm3/d 392 190 427

Flow rate into horizontal well qH Rm3/d 2172 921 2869

Transmissibility factor A ATRANS cp*Rm3/d/Bar/m 277.0 65.2 67.1

Transmissibility factor B BTRANS - 9.6 9.4 9.5

Total transmissibility T cp*Rm3/d/Bar/m 28.9 6.9 7.0

Oil flow rate qO Rm3/d 795 366 101

Water flow rate qW Rm3/d 1377 555 2768

Flow rate into horizontal well qH Rm3/d 2172 921 2869





Flow rate into horizontal well qH Sm3/d 2054 868 2811

Total flow rate QLIQUID Sm3/d 5732


Productivity Index of a zone J Sm3/d/Bar 6094 1295 3877

Table 21: Simulation #3 – Steady state Joshi’s NETool analytical method


39

Discussion of final results Table 22 lists all the productivity indices, flow rates, water cuts and zonal liquid contributions for all the

different methods used in this study. The largest difference between NETool and the other three

simulation methods is the fact that NETool averages different parameters by the segment size of 12m

and other simulations average the same parameters by the size of the zone. Hence, NETool results are

considered the closest to the actual results.

Productivity Index (Sm3/d/Bar)

Zones NETool Joshi Muskat Sim # 3

Zone 3 4760 6094 5213 6094

Zone 2 1039 1295 1120 1295

Zone 1 1030 3877 3327 3877

Flow rate in ST (Sm3/d)

Zone 3 1604 2054 1757 2054

Zone 2 696 868 751 868

Zone 1 747 2811 2412 2811

Total 3047 5732 4919 5732

Zonal contribution (%)

Zone 3 53 36 36 36

Zone 2 23 15 16 15

Zone 1 24 48 48 48

Total 100 100 100 100

Water cut (%)

Well 38.3 80.6 80.6 80.6

Table 22: Results of different methods

The following Figures 25, 26 and 27 show the difference between NETool data and all the rest of the

analytical methods.

Figure 25: Productivity Index results with different methods

0

1000

2000

3000

4000

5000

6000

7000

NETool Joshi Muskat Sim # 3

Pro

du

ctiv

ity

Ind

ex,

J, (

Sm3 /

d/B

ar)

Zone 3

Zone 2

Zone 1


40

Figure 26: Total flow rate results with different methods

Figure 27: Zonal liquid inflow contribution with different methods

Theoretical results in comparison to NETool results for Zone 1 and Zone 3 have larger differences than

Zone 2. Zone 2 has a more similar trend and productivity index, but it also had the worst matching

annulus and tubing pressures for the first well test. Zone 1 is the only zone with heterolithic sands and

high permeability fluctuations. This zone’s permeabilities are not weighted compared to the other two

zones. Zone 3 has the highest average permeability. Liquid flow rate behavior seen on Figure 26 seems

to be in correspondence with the zonal length. The longest zone in the well is Zone 1 and it also shows

the highest production based on theoretical methods. One should also keep in mind that reservoir

geometry in each zone is based on assumptions and not very strongly reliable, since all the zones are set

to have the same thickness and width. Averaging saturation logs, synthetic permeability logs and

0

500

1000

1500

2000

2500

3000


Liq

uid

flo

w r

ate

in S

T (S

m3 /

d)

Zone 3

Zone 2

Zone 1

0

10

20

30

40

50

60

70

80

90

100


Zon

al L

iqu

id In

flo

w C

on

trib

uti

on

. %

Zone 1

Zone 2

Zone 3


41

hydrostatic reservoir pressure over the zones could also cause an error to the calculations, if there are

high fluctuations over a long zone interval. For example, averaging saturations over the entire zone

should not be done, because saturations are used to calculate relative permeabilities, and relative

permeabilities are used to calculate mobilities. If zonal saturations fluctuate highly, then average

mobilities can be erroneous.

For zonal inflow optimization with NETool, all the possible FCV positions were tested.

FCV position

Valve openings (%)

PI (Sm3/d/bar)

Zonal contribution DH (%)

QLIQ

(Sm3/d)

WC (%)

Z3 Z2 Z1 Z3 Z2 Z1 Z3 Z2 Z1 All zones All

zones

Pos 2 (Z1 open) 100 100 100 4760 1039 1030 53 23 24 3047 38,3

Pos 2 (Z1 closed) 100 100 0 4774 967 - 60 40 0 2744 32,5

Pos 3 (Z1 open) 27 2 100 4756 1171 913 55 7 38 2758 43,1

Pos 3 (Z1 closed) 27 2 0 4766 1136 - 85 15 0 1915 34,8

Pos 5 (Z1 open) 27 5 100 4750 1120 943 53 13 33 2824 41,4

Pos 5 (Z1 closed) 27 5 0 4761 1069 - 74 26 0 2153 33,6

Pos 7 (Z1 open) 27 0 100 4754 - 882 58 0 42 2677 45,3

Pos 7 (Z1 closed) 27 0 0 4770 - - 100 0 0 1655 36,8

Pos 9 (Z1 open) 2 27 100 4183 1027 977 16 40 44 1928 40,4

Pos 9 (Z1 closed) 2 27 0 4218 954 - 21 79 0 1472 28,4

Pos 11 (Z1 open) 5 27 100 4523 1030 985 28 34 38 2203 39,8

Pos 11 (Z1 closed) 5 27 0 4511 957 - 35 65 0 1772 29,9

Pos 13 (Z1 open) 0 27 100 - 1022 971 0 47 53 1659 41,1

Pos 13 (Z1 closed) 0 27 0 - 951 - 0 100 0 1182 26,1

Average zonal PI 4627 1047 955

Table 23: Productivity Index, zonal contribution (DH), total liquid rate (ST) and water cut of all the possible valve positions of Q-12BH before free gas production

Figure 28: Productivity Index for all the possible FCV openings before free gas production (See Table 3 for FCV positions)

0

1000

2000

3000

4000

5000

6000

Pro

du

ctiv

ity

Ind

ex,

J, (

Sm3 /

d/B

ar)

Zone 3

Zone 2

Zone 1


42

Figure 29: DH zonal flow contribution with all the possible FCV openings before free gas production (See Table 3 for FCV positions)

Figure 30: Liquid influx with all the possible FCV openings before free gas production (See Table 3 for FCV positions)

0

20

40

60

80

100

120D

H z

on

al f

low

co

ntr

ibu

tio

n, (

%)

Zone 3

Zone 2

Zone 1

0

500

1000

1500

2000

2500

3000

3500

Pos 2(Z1

open)

Pos 2(Z1

closed)

Pos 3(Z1

open)

Pos 3(Z1

closed)

Pos 5(Z1

open)

Pos 5(Z1

closed)

Pos 7(Z1

open)

Pos 7(Z1

closed)

Pos 9(Z1

open)

Pos 9(Z1

closed)

Pos 11(Z1

open)

Pos 11(Z1

closed)

Pos 13(Z1

open)

Pos 13(Z1

closed)

Liq

uid

Infl

ux

(Sm

3/d

)


43

Figure 31: Water cut with all the possible FCV openings before free gas production (See Table 3 for FCV positions)

Limitations Numerical NETool model is considered the most accurate simulation tool out of the four simulation

models created in this study, because it can take into account well completions. For theoretical models,

well completions are not used. All the logs in NETool are averaged over 12m long segments, but for

theoretical methods, there are no segments and all the parameters are averaged over the length of the

zone. All the three zones are over a kilometer long, and therefore averaging parameters is not the best

solution. Especially, when the data fluctuates and it is later used as an input for other parameters.

Unfortunately, Troll wells have no gas saturation logging data present. This could have been entered

into NETool to model free gas production, because free gas production had already started when the

first well test data was taken. Therefore, modeling correct phase flow rates even for the first well test

was difficult, and with increasing free gas influx rate, the later well test were not even used in NETool. In

the end, NETool model calculated the two liquid phases and solution gas rate. In addition, there are

definitely more limiting factors that cause small errors, which are hard to estimate. Some of them can

be calculated logs, such as synthetic permeability, effective saturation or LET relative permeabilities, etc.

Conclusion It difficult to predict the current production behavior of well Q-12BH based on these simulations,

because it is missing gas saturation data. However, there is enough data to discuss that this well was put

on stream with the most optimal FCV opening positions. Q-12BH can be operated in 14 different FCV

0

10

20

30

40

50

60

70

80

90

100

Pos 2(Z1

open)

Pos 2(Z1

closed)

Pos 3(Z1

open)

Pos 3(Z1

closed)

Pos 5(Z1

open)

Pos 5(Z1

closed)

Pos 7(Z1

open)

Pos 7(Z1

closed)

Pos 9(Z1

open)

Pos 9(Z1

closed)

Pos 11(Z1

open)

Pos 11(Z1

closed)

Pos 13(Z1

open)

Pos 13(Z1

closed)

Wat

er

Cu

t (%

)


44

positions and all the simulation results of all the positions are given in Table 23. After simulating all the

data with different FCV settings in the same NETool simulation model, it is clear that this well had the

most optimal FCV settings during the initial production and during the first well test. The reason why this

conclusion is reached is seen on Table 23 and Figure 29, where FCV opening position 11 (5% opened in

Zone 3, 27% opened in Zone 2, and 100% opened in Zone 1) shows the most balanced zonal liquid inflow

contribution – 28 % inflow from Zone 3, 34% inflow from Zone 2, and 38% inflow from Zone 1. All the

other FCV positions are not able to equalize the flow that well, when there is no free gas present.

However, the other positions might be more useful when gas influx becomes higher. Average PI values

for all the three zones were found to be the following:

Zone 3 PI: 4627

Zone 2 PI: 1047

Zone 1 PI: 955

The most optimal FCV settings in NETool were calculated by trial and error method found in Table 32.

These results indicated 6,5% opening in Zone 3, 27% opening in Zone 2 and 23% opening in Zone 1.

Hence, these FCV openings for a new well are irrelevant, because if a well with the same completion

design is put on stream at some other reservoir location, then these FCV openings need to be in

accordance with the new reservoir parameters.

Pressures in NETool (FCV openings 6,5%, 27%, 23%)


Reservoir pressure pRES Bar 136,22 136,48 136,38

Sandface pressure pSF Bar 136,05 135,74 135,61

Average annulus pressure pANN Bar 135,54 135,21 135,40

Annulus pressure (at DHG) pANN_DHG Bar 134,16 133,59 135,39

Average tubing pressure pTUB Bar 128,78 133,69 135,32

Flowing tubing hole pressure (at DHG) pTUB_DHG Bar 125,52 132,79 134,66

Drawdown (pRES - pSF) Δp Bar 0,17 0,74 0,77

Pressure drop across ICDs (pSF - pANN) ΔpICD Bar 0,51 0,53 0,21

Pressure drop across stinger (pANN - pTUB) ΔpSTI Bar 6,77 1,52 0,08

Flow rates in NETool (FCV openings 6,5%, 27%, 23%)




Total liquid rate (ST condition) QLIQUID Sm3/d 2311

Gas to oil ratio (solution gas) GOR % 47,8

Water cut WC % 38,9






45







Figure 32: Simulated NETool model with equal zonal influx


46

Acknowledgements

This master thesis was conducted for MSc. Applied Earth Sciences with concentration to Petroleum

Engineering for Delft University of Technology. My appreciation goes out to many Statoil ASA Troll

department engineers, especially to my company supervisor Martin Halvorsen, Gunn Helen Tonning,

Farzad Farshbaf Zinati and Mathias Vikøren Mo. In addition, I appreciated the help of NETool

Development Learder Vitaly Khoriakov. Most importantly, I want to thank my university supervisor Dr.

Jan-Dirk Jansen for all the advice and directions I was given throughout this study.


47

References

[1] Aashelm, R., Gyllensten, A., Zadeh, A.M., Arland, K., Videla, J.: "Advanced well optimisation in thin

oil rim reservoirs," Statoil ASA Internal document, (2012).

[2] Madsen,T. and Abtahi, M.: "Handling the Oil Zone on Troll," paper OTC 17109 presented at the

2005 Offshore Technology Conference, Houston, 2 - 5 May.

[3] Solheimsnes,K., Gjengedal, J.A., Hamnes, G. M., Ahmadhadi, F., Tonning, G.H.: "Final Well Report

Norway 31/2-Q-12 BH Troll Field," Statoil ASA Internal document, (2012).

[4] Joshi, S.D.: Horizontal Well Technology, PennWell Publishing Company, Tulsa, Oklahoma (1991) 251

- 253.

[5] Waldeland, T.M. (Director): Troll Oil - Raising the Bar, visCo AS Production (Film), Norway (2005).

[6] Halvorsen, M., Elseth, G., Nævdal, O.M.: "Increased oil production at Troll by autonomous inflow

control with RCP valves," paper SPE 159634 presented at the 2012 SPE Annual Technical

Conference and Exhibition, San Antonio, 8-10 October.

[7] Richard, J.D., Saeverhagen, E., Thorsen, A.K., Gard, S.: "Troll West Oilfield Development - How a

Giant Gas Field Became the Largest Oil Field in the NCS through Innovative Field and Technology

Development," paper SPE 112616 presented at the 2008 IADC/SPE Drilling conference, Orlando, 4 -

6 March.

[8] Dahle, B.O., Smith, P.E., Gjelstad, G., Solhaug, K.: "First Intelligent Well Completion in the Troll Field

Enables Feed-Through Zonal Isolation: A Case History," paper SPE 160060 presented at the 2012

SPE Annual Technical Conference and Exhibition, San Antonio, 8 - 10 October.

[9] Kydland, T., Wennemo, S., Olsen, G.: "Reservoir Management Aspects of Producing Oil from Thin Oil

Rims in the Troll Field," paper OTC 7173 presented at the 1993 25th Annual Offshore Technology

Conference, Houston, 3 - 6 May.

[10] Norsk Hydro, "Fluid and Rock Properties," Statoil ASA Internal document, (November 1991).

[11] Jansen, J.-D., Wagenvoort, A.M., Droppert, V.S., Daling, R., Glandt, C.A.: "Smart Well Solutions for

Thin Oil Rims: Inflow Switching and the Smart Stinger Completion," paper SPE 77942 presented at

the 2002 SPE Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, 8 - 10 October.

[12] Birkeland, Ø., Halvorsen, M., Midtkandal, P.A.: "Oppstartsprogram for Q-12 BH," Statoil ASA

Internal document, (May 2011).


48

[13] Mjølhus, S., "31/2-Q-12 BH Final Completion String Diagram," Statoil ASA Internal document, (18

October 2011).

[14] Henriksen,K.H., Gule, E.I., Augustine, J: "Case Study: The Application of Inflow Control Devices in the

Troll Oil Field," paper SPE 100308 presented at the 2006 SPE Europec/EAGE Annual Conference and

Exhibition, Vienna, 12 - 15 June.

[15] Mathiesen, V., Aakre, H., Werswick, B. and Elseth, G.: "The Autonomous RCP Valve - New

Technology for Inflow Control In Horizontal Wells," paper SPE 145737 presented at the 2011 SPE

Offshore Europe Oil and Gas Conference and Exhibition, Aberdeen, 6 - 8 September.

[16] Rodgers, S., Smaaskjaer, G., Midtkandal, P.A.: "Troll Field, Sognefjord Formation: FZI Synthetic

Permeability Model," Statoil ASA Internal document,(2000).

[17] Brendsdal, A. and Halvorsen, C.: "Quantification of Permeability Variations across Thin Laminae in

Cross Bedded Sandstone," (1992). [Online]. http://www.scaweb.org/assets/papers/1992_papers/1-

SCA1992-02EURO.pdf.

[18] Lomeland, F., Hasanov, B., Ebeltoft, E., Berge, M.: "A Versatile Representation of Upscaled Relative

Permeability for Field Applications," paper SPE 154487 presented at the 2012 EAGE Annual

Conference and Exhibition, Copenhagen, 4 - 7 June.

[19] Troll PROTEK Teamsite, 31/2-Q-12 BH well tests, Statoil ASA Internal document," [Online].

[20] Jansen, J.-D.: "A Semianalytical Model for Calculating Pressure Drop Along Horizontal Wells With

Stinger Completions," SPE J. 8 (2): 138-146. Paper SPE 74212, (2003).

[21] Halliburton, "NETool 5000.1.x User Guide," Landmark Graphics Corporation, Houston, TX, 2012.

[22] Joshi, S.D.: "Augmentation of Well Productivity with Slant and Horizontal Wells," paper SPE 15375

presented at the 1988 SPE Annual Technical Conference and Exhibition, New Orleans, June.

[23] Bindl, B., Hodnefjell, B., Hansen, S.: "Screen Tally of Well Q-12BH Mainbore as Run," Statoil ASA

Internal document, (2011).

[24] Bear, J.: Dynamics of Fluids in Porous Media, Elsevier, New York City (1972). Reprinted by Dover

Publishers, Mineola, New York (1988) 312 - 322.


49

APPENDIX A

TABLE A.1: PVT data for the TWGPN

Pressure Oil viscosity

(μo) Oil FVF (Bo) Solution GOR

(RS) Gas viscosity

(μg) Gas FVF (Bg)

[Bar] [cP] [Rm3/Sm

3] [Sm

3/Sm

3] [cP] [Rm

3/Sm

3]

20 1.044

40 3.311 1.060 13.6 0.0128 0.02660

60 2.848 1.076 20.4 0.0136 0.01860

80 2.504 1.091 27.4 0.0143 0.01370

100 2.242 1.107 34.5 0.0151 0.01060

120 2.037 1.123 41.8 0.0160 0.00875

140 1.873 1.139 49.2 0.0170 0.00741

159.06* 1.747 1.154 56.4 0.0179 0.00645

* Bubble point pressure

TABLE A.2: 31/2-Q-12BH Screen tally (confidential)

Table A.3: LET family of correlations for relative permeability

LET Family of Correlations for relative permeability

Unnormalized Base case

Imbibition

Imbibition

SWOF

SGOF

Sw Krw Kro

Sg Krg Kro

0.1500 0 1.0

0.3000 0 1.0

0.1685 0.00002 0.96229

0.3120 0.00003 0.99154

0.1870 0.00014 0.91025

0.3240 0.00017 0.97458

0.2055 0.00039 0.85029

0.3360 0.00047 0.95066

0.2240 0.00084 0.78512

0.3480 0.00099 0.92017

0.2425 0.00151 0.71694

0.3600 0.00177 0.88344

0.2610 0.00247 0.64774

0.3720 0.00287 0.84090

0.2795 0.00377 0.57924

0.3840 0.00435 0.79318

0.2980 0.00547 0.51292

0.3960 0.00625 0.74108

0.3165 0.00762 0.44998

0.4080 0.00863 0.68561

0.3350 0.01030 0.39128

0.4200 0.01157 0.62791

0.3535 0.01359 0.33738

0.4320 0.01513 0.56920

0.3720 0.01756 0.28860

0.4440 0.01938 0.51070

0.3905 0.02230 0.24498

0.4560 0.02441 0.45354

0.4090 0.02792 0.20643

0.4680 0.03030 0.39873


50

0.4275 0.03451 0.17270

0.4800 0.03715 0.34708

0.4460 0.04218 0.14345

0.4920 0.04506 0.29918

0.4645 0.05105 0.11830

0.5040 0.05413 0.25544

0.4830 0.06123 0.09684

0.5160 0.06449 0.21604

0.5015 0.07286 0.07867

0.5280 0.07625 0.18100

0.5200 0.08604 0.06340

0.5400 0.08954 0.15022

0.5385 0.10090 0.05065

0.5520 0.10452 0.12347

0.5570 0.11755 0.04008

0.5640 0.12131 0.10048

0.5755 0.13607 0.03139

0.5760 0.14009 0.08091

0.5940 0.15653 0.02430

0.5880 0.16100 0.06442

0.6125 0.17898 0.01857

0.6000 0.18421 0.05066

0.6310 0.20341 0.01398

0.6120 0.20989 0.03930

0.6495 0.22978 0.01035

0.6240 0.23820 0.03002

0.6680 0.25797 0.00751

0.6360 0.26933 0.02253

0.6865 0.28783 0.00532

0.6480 0.30341 0.01657

0.7050 0.31909 0.00366

0.6600 0.34062 0.01189

0.7235 0.35145 0.00244

0.6720 0.38108 0.00828

0.7420 0.38449 0.00156

0.6840 0.42492 0.00556

0.7605 0.41774 0.00094

0.6960 0.47223 0.00356

0.7790 0.45066 0.00053

0.7080 0.52307 0.00215

0.7975 0.48263 0.00027

0.7200 0.57747 0.00119

0.8160 0.51301 0.00012

0.7320 0.63540 0.00059

0.8345 0.54106 0.00004

0.7440 0.69679 0.00024

0.8530 0.56595 0.00001

0.7560 0.76149 0.00007

0.8715 0.58657 0

0.7680 0.82932 0.00001

0.8900 0.6 0

0.7800 0.9 0


51

APPENDIX B

TABLE B.1: Well shut-in data used for reservoir pressure calculations (1st

well test pressures are interpolated)

Well shut-in date (until it reached

constant pressure)

Number of days Reservoir pressure [Bar]

since well start up Zone 3 Zone 2 Zone 1

11.09.2011 START UP 136.33 136.59 136.49

16.09.2011* 6 136.31 136.55 136.44

21.10.2011 40 136.18 136.33 136.14

05.11.2011 55 136.10 136.19 136.00

17.12.2011 97 135.88 135.88 135.60

07.03.2012 178 135.59 135.34 134.90

11.03.2012 182 135.61 135.39 134.90

29.04.2012 231 135.31 135.15 134.73

30.04.2012 232 135.31 135.15 134.73

23.05.2012 255 135.15 135.15 134.75

11.06.2012 274 135.17 134.94 134.46

20.06.2012 283 135.08 134.91 134.47

02.09.2012 357 134.79 134.76 134.33

29.09.2012 384 134.76 134.85 134.45

13.10.2012 398 134.61 134.67 134.27

13.11.2012 429 134.49 134.51 134.09

18.11.2012 434 134.50 134.58 134.17

06.12.2012 452 134.50 134.56 134.15

28.01.2013 505 134.18 134.24 133.84

04.02.2013 512 134.23 134.14 133.73

27.02.2013 535 134.07 134.14 133.73


52

TABLE B.2: Reservoir influx (DH rates) and phase contribution per well test with different FCV positions

Test No.

FCV Z3

FCV Z2

FCV Z1

PRES Z3 PRES Z2 PRES Z1 Bo avg

Bg avg

Bw avg

Qoil res

Qgas total

Qgas solut.

Qgas free

Qwat res

Qtot res

QoilDH

QgasDH

QwatDH

Start % % % Bar Bar Bar Rm3/S

m3 Rm3/Sm3

Rm3/Sm3

Rm3/d Rm3/d Rm3/d Rm3/d Rm3/d Rm3/d % % %

1 5 27 100 136.31 136.55 136.44 1.136 0.00765 1.017 1639 641 528 113 949 2701 61 4 35

2 5 27 100 136.25 136.46 136.33 1.136 0.00765 1.017 1363 901 439 462 1072 2896 47 16 37

3 5 27 100 136.23 136.43 136.28 1.136 0.00766 1.017 1365 871 440 431 1171 2968 46 15 39

4* 5 27 0 136.23 136.42 136.27 1.136 0.00766 1.017 1227 989 395 594 1091 2912 42 20 37

5* 0 27 100 136.17 136.33 136.15 1.136 0.00766 1.017 1445 1168 466 702 1021 3168 46 22 32

6 5 27 100 136.06 136.14 135.92 1.136 0.00768 1.017 1465 1620 473 1147 1453 4065 36 28 36

7 5 27 100 135.95 135.96 135.69 1.136 0.00769 1.017 1187 2390 383 2007 1373 4567 26 44 30

8 5 27 100 135.80 135.73 135.38 1.136 0.00770 1.017 917 3299 297 3002 1243 5163 18 58 24

9* 0 27 0 135.77 135.68 135.32 1.135 0.00771 1.017 306 2631 99 2532 214 3052 10 83 7

10* 27 2 0 135.76 135.67 135.31 1.135 0.00771 1.017 392 1296 127 1169 647 2208 18 53 29

11 5 27 100 135.48 135.30 134.87 1.135 0.00773 1.017 719 4479 233 4246 1204 6169 12 69 20

12 5 27 100 135.35 135.19 134.77 1.135 0.00774 1.017 597 4669 193 4476 1059 6132 10 73 17

13 5 27 100 135.20 135.07 134.65 1.135 0.00775 1.017 564 4801 182 4619 999 6182 9 75 16

14 5 27 100 134.42 134.45 134.07 1.134 0.00779 1.017 432 2390 140 2250 760 3442 13 65 22

*FCV positions are changed


53

APPENDIX C Table C.1: NETool completion diagram

Seg Segment Segment Casing/Liner Sand Inflow Stinger Tubing

# Top MD Length Control Control

1 2052.000 7.000 - - Blank Pipe Blank Pipe Open

2 2059.000 3.000 - Packer Blank Pipe Blank Pipe Open

3 2062.000 2.000 - Packer Blank Pipe Packer Open

4 2064.000 2.000 - - Blank Pipe Packer Open


6 2076.000 7.600 - - Baker Spiral ICD, Troll Blank Pipe Open





11 2086.700 4.300 - - Baker Spiral ICD, Troll ICV Open

































54


















































55










































132 3373.600 4.300 - - Blank Pipe ICV Open








56


















































57


















































58









243 4526.700 2.620 - - Baker Spiral ICD, Troll ICV Open



246 4542.000 6.000 - - Baker Spiral ICD, Troll Blank Pipe Plug

247 4548.000 12.000 - - Baker Spiral ICD, Troll - Open







254 4626.000 6.000 - Packer Blank Pipe - Open






























59











293 5064.000 6.000 - - Blank Pipe - Open







































60


















































61




382 6058.000 2.000 - - Baker Spiral ICD, Troll - Plug

383 6060.000 10.000 - - Baker Spiral ICD, Troll - Plug

TOE 6070.000

APPENDIX D Derivation of NETool inflow model equations

NETool inflow model runs on Joshi’s horizontal well technology theory. The following chapter covers the

derivation of the formula. Before derivation, one should know that the well model in NETool is divided

into segments of 12 meters. This value is used because the joint length on the real well is around 12m.

Near the FCVs and DHGs, the completion equipment lengths are shorter and modeled more precisely.

Each segment, , has three phase components – oil, gas and water. The equation that calculates inflow is

the following

[D.1]

Here, is the mobility of a phase, is transmissibility and is the drawdown. Transmissibility, that

forms part of the PI modeling for each segment is calculated as:

[D.2]

where and are the two factors of transmissibility equation. Parameter stands for

skin, but skin is considered zero for the Troll field. It means there is no formation damage near the

wellbore, which can often be the case when the reservoir sands are less permeable.

In order to understand transmissibility, one should know how the factors and are

calculated. First of all, see Table D.1 for all the parameters.

β √ ⁄

d

c

b

a √ rwb

Table D.1: NETool inflow equation parameters


62

Transmissibility factors are described below:

[D.3]

(

) (

) [D.4]

Substitution of these factors into transmissibility equation shows similarities with Joshi’s equation (10a)

from paper SPE 15375. This equation (10a) is shown in Equation (D.5). The flow rate is calculated in

standard condition since the numerator is divided by FVF. [22]

[ √ ⁄

]

(

)

[D.5]

Hyperbolic arccosine term in in Equation (D.4) is the same term as the first natural logarithmic

term in the denominator of Equation (D.5). Both terms in the denominator are compared below:

[ √ ] [D.6]

(

) [(

) √(

) ] [D.7]

Next, Table 1 values (except ) are substituted into Equation (D.7)

(

) [(

) √(

) ] [D.8]

(

) [(

) √

] [D.9]

(

) [(

) √

] [D.10]

(

) [(

)

√

] [D.11]

(

) [

√

] [D.12]

It is important to know that parameters and are the major and minor axes of the drainage ellipse.

√ √(

)

(

)

[

√

⁄ ]

[D.13]

Half of the major axis of drainage ellipse, , can be calculated in two ways shown in Equation (D.13).

One of the formulas includes horizontal drainage radius term, and the other one, does not. The result is


63

the same for both of them, and therefore it does not matter which formula is used. For example, NETool

uses the method with Pythagoras theorem, and Joshi’s paper SPE 15375 presents the one with

horizontal drainage radius ( ) term for the theoretical method.

Next, transmissibility factors are substituted into transmissibility equation with no skin present.

(

) (

) [D.14]

Then, the top and bottom term are multiplied with ⁄ . This results the following

(

)

(

) [D.15]

In the next step, Table 1 parameters are substituted into the previous Equation (D.15):

(

)

(

) [D.16]

Now, some terms can be cancelled

(

)

(

) [D.17]

The denominator for transmissibility equation used in NETool, and the denominator for Joshi’s

horizontal well inflow model used for analytical calculations, is exactly the same for both equations.

Mobility in NETool is calculated based on effective water saturations and relative permeabilities shown

in Equation (D.18)

[D.18]

The formulas that NETool uses for reservoir inflow and productivity indices calculations are as followed:

(

)

(

) [D.19]

(

)

(

) [D.20] [D.20]


64

APPENDIX E Explanation of the theoretical PI from J.Bear book “Dynamics of Fluids in Porous Media” [24]

Flow potential, which is a real part of the function of an infinite array of sinks, is derived as follows

[ ] ∑ [ ]

[E.1]

Here z is the complex number, and ⁄ . is the flow rate, and d is the total distance on x-axis.

To keep it simple, m is changed later.

The problem requires finding a complex function, where the interest remains for the real part. This

function also has a conjugate part, z*.

[E.2]

[E.3]

Based on the rule ⁄ and complex number identities, the following flow potential

equation can be written as

(

)

[(

) (

)]

[ (

) (

)] [E.4]

Next, trigonometric part of the function has to be transferred into complex exponential function

(

)

( ) [E.5]

(

)

( ) [E.6]

Then, substitution of these exponential identities from [E.5] and [E.6] should be entered into Equation

[E.4]. This results in [E.7].

[

( ) (

) ( ) ] [E.7]

[

(

) ] [E.8]

As a reminder

[E.9]

[E.10]

Then, reorganize the terms by substituting in x and y

[

(

) ] [E.11]


65

The previous equation can now be written as

[

(

) ] [E.12]

(

) [E.13]

The following trigonometric identities are shown how the real part of the flow potential equation was

found

[E.14]

[E.15]

As a result, flow potential formula is

(

) [E.16]

For the upcoming calculations, paper SPE 74212 is followed. Variable d is the thickness of the reservoir,

ĥR. Variable m is flow to the sink divided by 2π (L2t-1) while considering Darcy flow characteristics such as

viscosity, µ, and permeability, k. One should also remember that with the use of Darcy’s Law, the flow

has a negative sign in front of it as the fluid flows from high pressure zones to low pressure zones.

Therefore, the equation can be rewritten as

[E.17]

[

(

) ] [E.18]

Then, both sides are integrated

∫ ∫

[

(

) ] [E.19]

[

(

) ] [E.20]

where c is the integration coefficient.

Finally, a specific productivity index formula is created. In order to simplify this formula, two reference

points are used. One of the reference points is at the constant reservoir boundary

,

and the second one is at the wellbore (sandface)

. Notice that the term cancels

out.


66

[

(

) ]

[

(

) ] [E.21]

Therefore,

[ [

(

) ] [

(

) ]]

[E.22]

[

(

)

(

)]

[E.23]

The final theoretical PI formula from the SPE 74212 paper was derived and found in Equation (E.24)

[ (

)]

[E.24]

Next, Equation (E.24) was edited by phase mobility ⁄ and FVF term, ,shown in Equation

(E.25). This allows calculation of two-phase liquid flow in standard condition. The flow rates of the

phases are calculated separately, and then added afterwards. After addition, specific productivity index

seen in Equation (E.26) is calculated and multiplied by the length of the zone for zonal productivity

index, found in Equation (E.27)

[ (

)]

[E.25]

[ (

)]

[E.26]

[ (

)]

[E.27]

Documents

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