Water Influx Eclipse

1BUET.Moawad Reservoir Engineering 2009

Chapter 9Water Influx

BUET.Moawad Reservoir Engineering 2009

-What are the aquifers?- Nearly all hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers

What are the sizes of the aquifers?- These aquifers may be larger than the oil and gas reservoirs and appear infinite in size, or they may be so small as to be negligible in their effect on reservoir performance

What are the functions of the aquifers?- They support the pressure differential as the reservoir pressure declines because of the hydrocarbon production


What is the aquifer mechanism?As hydrocarbon is produced from the reservoir and the

pressure decline causes a response from the aquifer to offset the pressure which comes in a form of water influx or also called water encroachment. This is referred to:

-Expansion of water in the aquifer-Compressibility of the aquifer rock-Artesian flow where the water bearing is located

higher than the pay zone.


-What are the important aquifers for reservoir engineers?Reservoir engineer will focus on those aquifers in which the aquifer size is large enough and the permeability of the rock is high enough that water influx occurs as the reservoir is depleted

What are the types of the aquifers?- Aquifers for natural water drive-Aquifers for artificial water drive (water injection)


What are the types of the aquifers?-Aquifers for natural water drive-Aquifers for artificial water drive (water injection)-Reservoir-Aquifer systems are classified on the basisof:1- Degree of pressure maintenance 2- Outer boundary conditions 3- Flow regimes 4- Flow geometries


-Reservoir-Aquifer systems are classified on the basis of:1- Degree of pressure maintenance

-Active water drive-Partial water drive-Limited water drive

Active water drive means:-The rate of water influx is equal to the reservoir total

production-Gradual and slow pressure decline i.e the production rate

and reservoir pressure remain constantWater influx=Oil flow rate + Free gas flow rate + water production rate


Active water drive means:Water influx=Oil flow rate + Free gas flow rate + water production rateor

ew = QoBo + QgBg + QwBwwhereew = water influx rate, bbl/dayQo = Oil flow rate, STB/dayBo = Oil formation volume factor bbl/STBQg = Free gas flow rate, SCF/dayBg = Gas formation volume factor, bbl/scfQw = Water flow rate, STB/dayBw = Water formation volume factor bbl/STB


Active water drive means:The above equation can be expressed in terms of cumulative production by using the following derivative terms:

whereWe = Cumulative water influx, bbl, t =time, dayNp = Cumulative oil production, STB, GOR= Current gas oil ratio SCF/STBRs = Current gas solubility, SCF/STB, Wp = Cumulative water production, STBdWe/dt= daily water influx flow rate (ew), STB/daydNp/dt = daily oil flow rate Qo, STB/daydWp/dt= daily water flow rate Qw, STB/day

(GOR-Rs) dNp/dt= dialy free gas flow rate, scf/day

( ) wpgpspoew BdtdW

Bdt

dNRGOR

dtdN

Bdt

dWe ++==


Active water drive means:ExampleCalculate the water influx rate in a reservoir whose pressure is stabilized at 3700 psi where

dNp/dt = 25,000 STB/day, dWp/dt= 0, GOR=1000 scf/STB

Rs= 750 scf/STB , Bo=1.34 bbl/STB, Bg=0.00082 bbl/ScfBw=1 bbl/STBSolution

ew=(1.34)(25,000)+(1000-750)(25,000)(0.00082)+0=38,625 bbl(day

( ) wpgpspoew BdtdW

Bdt

dNRGOR

dtdN

Bdt

dWe ++==


-Reservoir-Aquifer systems are classified on the basis of:1- Degree of pressure maintenance

2-Outer boundary conditionsA- Infinite system indicates that the effect of pressure changes at the oil/aquifer boundary can never be felt at the outer boundary. This outer boundary remain at constant pressure equal to initial reservoir pressure. B- Finite system indicates that the aquifer outer boundary is affected by the water influx into the oil zone, and the pressure at the outer boundary changes with time


-Reservoir-Aquifer systems are classified on the basis of:1- Degree of pressure maintenance 2-Outer boundary conditions3-Flow regimesThere are basically three flow regimes to describe the fluid flow behavior and reservoir pressure distribution as a function of time:A- Steady state: the pressure at every location in the reservoir remains constant, i. e. the pressure does not change with time. Mathematically, This equation states that the rate of change of pressure with respect to time at any location in the reservoir is Zero. In petroleum reservoirs, this condition can only occur when the reservoir is completely supported by strong aquifer or pressure maintenance operations


-Reservoir-Aquifer systems are classified on the basis of:3-Flow regimes

B- Pseudosteady state: the pressure at every location in the reservoir change with constant declining rate with time. Mathematically,

This equation states that the rate of change of pressure with respect to time at any location in the reservoir is constant.Note that:

Pseudosteady state=Semisteady state =quasisteady state



C- Unsteady state: This states that the rate of change of pressure with respect to time at any location in the reservoir is not zero or constant.

Mathematically,

This equation states that the rate of change of pressure with respect to time is a function of both position (i) and time (t).Note that:

Unsteady state flow=Transient flow




-Reservoir-Aquifer systems are classified on the basis of: 4- Flow geometries 4.1 Reservoir Flow geometries

-Radial flow-Linear flow -Spherical and hemispherical flow

4.2 Reservoir-Aquifer flow geometries-Edge-water drive-Bottom- water drive -Linear-water drive


-Reservoir-Aquifer systems are classified on the basis of: 4- Flow geometries4.1 Reservoir Flow geometries-Radial flow:In the absence of severe reservoir heterogeneity, flow into or away from the wellbore will follow radial flow. - Radial flow is used to characterizethe flow of fluid into the well bore.


-Reservoir-Aquifer systems are classified on the basis of: 4- Flow geometries4.1 Reservoir Flow geometries- Linear flow:Linear flow occurs when flow paths are parallel and fluid flows in a single direction. The cross sectional area to flow must be constant. A common applications of linear flow equations are some cases in stratified reservoirs and the vertical fractures.


-Reservoir-Aquifer systems are classified on the basis of: 4- Flow geometries4.1 Reservoir Flow geometries-Spherical and Hemispherical flow:The wellbore completion type controls the spherical or hemispherical flow near the wellbore. A limited perforated interval could give a spherical flow. A well that penetrates only a part of the pay zone could give hemispherical flow. These conditions are very important in water coning problems

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-Reservoir-Aquifer systems are classified on the basis of: 4- Flow geometries

4.2 Reservoir-Aquifer flow geometries-Edge-water drive:

In Edge water drive, water moves intothe flanks of the reservoir as a resultof hydrocarbon production and pressure drop at reservoir aquifer boundaries


-Reservoir-Aquifer systems are classified on the basis of: 4-4- Flow geometries

4.2 Reservoir-Aquifer flow geometries- Bottom- water drive:

It occurs in reservoirs with large areal extentwhere the reservoir-water contact completelyunderlies the reservoir

-Linear-water driveIn linear water drive, the influx is from one flank of the reservoir. The flow is linear with a constant cross-sectional area

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-Indications of Natural Water Influx-Very little information can be obtained during the exploration-development period

-It may be obtained by analogy with nearby producing reservoirs

-Early reservoir performance trends can provide clues

-Low and decreasing rate of pressure decline with increasing production is an indication of fluid influx.

-If the reservoir pressure is below Pb a low rate of increase of GOR is also an indication of fluid influx.-Early water production from edge wells is indicative of water encroachment. This may be due to fractures, high permeability, thin formations.- Calculation of increasing OOIP from successive reservoir pressure surveys by using the material balance assuming no water influx is also indicative of fluid influx


-Water Influx Models

There are more uncertainties attached to aquifer information because one seldom drills wells into an aquifer to gain information about porosity, permeability, thickness and fluid properties.Several Mathematical models have been introduced for estimating water influx that based on assumptions which describes the aquifer characteristics:1- Pot aquifer2- Schilthuis steady state3- Hursts modified steady state4- Van Everdingen- Hurst unsteady-state

-Edge water drive-Bottom water drive

5- Carter-Tracy Unsteady state6-Fetkovichs method

-Radial aquifer-Linear aquifer

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1- Pot aquifer Model:- The simplest model used to estimate the water influx into gas or oil reservoirs. It is only applicable for small aquifers whose volumes are nearly equal to reservoir volumes-It depends on the basic definition of the compressibility. When the reservoir pressure drops due to the fluid production, this causes the aquifer water to expand and flow into the reservoir

or

Water influx =aquifer compressibility (Initial volume of water) (pressure drop)We=cumulative water influx, bbl, Cw=aquifer water compressibility Psi-1Cf=aquifer rock comp. psi-1, Wi= initial volume of water in aquifer, bbl, Pi=initial reservoir pressure, psi, P=current reservoir pressure (pressure at O/W Contact), psi

( ) wpgpspoew BdtdW

Bdt

dNRGOR

dtdN

Bdt

dWe ++==

PVcV =

)()( PPWccW iifwe +=



1- Pot aquifer Model:

- Calculating Initial volume of water (Wi)A- If the aquifer shape is radial and from all directions

ra=radius of aquifer, ft. re=radius of reservoir, ft.h=thickness of aquifer ,ft., = porosity of the aquifer

B- If the aquifer shape is radial and not from all directions (not circular)

( )

=

61.5

22 pi hrrW eai

00 360360

)()(

==

+=

anglentencroachmef

PPfWccW iifwe

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1- Pot aquifer Model:- Example 1: Calculate the cumulative water influx that results from a pressure drop of 200 psi at the oil-water contact with an encroachment angle of 80. The reservoir aquifer system is characterized by the following properties

Reservoir Aquifer

Radius, ft 2600 10,000

Porosity 0.18 0.12

Cf, Psi-1 4x10-6 3x10-6

Cw, Psi-1 5x10-6 4x10-6

h, ft 20 25

( ) ( )MMbblhrrW eai 5.15661.5

)12.0()25(26001000061.5

2222

=

=

=

pipi

bblPPfWccW iifwe 689,48)200)(36080(10*5.156(10)34()()( 66 =+=+=

Answer



2- Schilthuis Steady-State Model:

- Schilthuis has proposed an aquifer with steady state flow. The flow behavior can be described and determined by Darcys law

The parameter C is called the water influx constant, bbl/day/psi

[ ]pPr

r

hkdt

dWe i

e

a

w

e

w

==

ln

00708.0

[ ]pPCdt

dWe i

e

w ==

Where: ew=rate of water influx, bbl/dayK= permeability of the aquifer, mdh=thickness of the aquifer, ft.ra=radius of the aquifer, ft.re=radius of reservoir, ft.t=time, days

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2- Schilthuis Steady-State Model:

Calculation of parameter C: This can be by equating the two equations,

Although this can only be done when the reservoir pressure stabilizes, once it has been determined, it can be applied to both stabilized and changing reservoir pressures.Example 2

Pi=3500 Psi , P=3000 psi, Qo=32,000 STB/dayBo= 1.4 bbl/stb GOR=900 Scf/STB, Rs=700 scf/STBBg=0.00082 bbl/scf, Qw=0Calculate Schilthuis water influx constant

[ ]pPCdt

dWe i

e

w ==

( ) wpgpspoew BdtdW

Bdt

dNRGOR

dtdN

Bdt

dWe ++==


-Water Influx Models2- Schilthuis Steady-State Model:

Example 2

Pi=3500 Psi , P=3000 psi, Qo=32,000 STB/dayBo= 1.4 bbl/stb GOR=900 Scf/STB, Rs=700 scf/STBBg=0.00082 bbl/scf, Qw=0Calculate Schilthuis water influx constant

[ ]

[ ] psidaybblpPeC

pPCdt

dWe

i

w

ie

w

//100)30003500(048,50

=

=

=

==

( )daybbl

Bdt

dWB

dtdN

RGORdt

dNB

dtdW

e wp

gp

s

po

ew

/048,50

)0()00082.0)(000,32)(700900()000,32)(4.1(=

++=++==

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-Water Influx Models3- Hursts Modified Steady-State Model:Why Hurst? What is the problem with Schilthuis Model?One of the most associated problem with Schilthuis model is that as the water is encroached into the reservoir the aquifer radius will increase as the time increase. Therefore he introduced the dimensionless radius (ra/re) by a time dependent function (at) where:ra/re=at

in terms of cumulative water influx)ln(

)(

)ln()(00708.0

at

PPiCdt

dWe

or

at

PPikhdt

dWe

e

w

w

ew

==

==

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-Water Influx Models3- Hursts Modified Steady-State Model:A plot of (Pi-P)/ew versus ln(t) will be a straight line with a slope of (1/C) and intercept of (1/C)ln (a)


-Water Influx ModelsExample

3- Hursts Modified Steady-State Model:

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4-Van Everdingen- Hursts Unsteady-State Model:- when an oil well is brought on production at a constant flow rate after a shut-in period, the pressure behavior is essentially controlled by the unsteady state condition- the dimensionless form of the diffusivity equation which designed to model the transient flow in reservoirs or aquifer is as follow:

Van Everdingen and Hurst proposed solution to following two reservoir-aquifer boundary conditions:

-Constant rate (and calculate the pressure)-Constant Pressure (and calculate the rate)

It is preferred to calculate the flow rateThey introduced their solutions to the following systems:

-Edge water-drive system-Bottom water drive -Linear water drive



5-Carter-Tracy water Influx Model:-What is the difference between the VanEverdingen-Hurst model and Carter-Tracy model?VanEverdingen-Hurst model provides the exact solution for radial

diffusivity equation and considered the correct technique for water influx calculations. But the superposition needs complex calculations- Carter-Tracy technique assumes constant water influx rates over each finite time interval-Using the Carter-Tracy technique, the cumulative water influx at any time, tn, can be calculated directly by

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6-Fetkovichs Model:-What is the difference feature of Fetkovich model ?- Fetkovich model is used for water influx behavior of a finite aquifer for radial and linear geometries.-the method does not require the use of superposition, therefore the application is much simpler - This technique is often utilized in numerical simulation methods.- Fetkovich assumption is that the productivity index concept will describe water influx from a finite aquifer into a hydrocarbon reservoir-Water influx rate is directly proportional to the pressure drop between the average aquifer pressure and the pressure at the reservoir/aquifer boundary-This method neglects the effects of any transient period.



6-Fetkovichs Model:

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The models available in Eclipse


The models available in Eclipse are:

1-Numerical aquifers 2-Carter-Tracy aquifers3-Fetkovich aquifers 4-Constant flux aquifers

-Numerical aquifers are represented by a one-dimensional row of cells within the simulation grid.

-The other three types of aquifer, classed as analytic aquifers, are represented by computed source terms in the reservoir grid cells with which they connect.

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The models available in Eclipse are:1-Numerical aquifers Numerical aquifers are represented by a one-dimensional row of cells within the simulation grid.

-A set of cells in the simulation grid is nominated to represent the aquifer, which may then connect to specified faces of the reservoir (using the AQUCON keyword).

-The properties of the aquifer grid blocks (length, cross-sectional area, porosity, permeability, initial pressure, depth, PVT and saturation table numbers) may be declared explicitly using keyword AQUNUM in the GRID section


The models available in Eclipse are:

2-Carter-Tracy aquifers-The Carter-Tracy aquifer model is a simplified approximation to a fully transient model.- The method uses a table that supplies a constant terminal rate influence function. Although the theory has been developed for a radially symmetric reservoir surrounded by an annular aquifer, the method is applicable to arbitrarily-shaped reservoirs.

AQUCT Key word (in SOLUTION SECTION): Specifies the property data for Carter-Tracy aquifers

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The models available in Eclipse are:3-Fetkovich aquifers -AQUFET key word (in Solution section) Specification data for Fetkovich aquifers

-The Fetkovich aquifer model uses a simplified approach based on a pseudosteady state productivity index and a material balance relationship between the aquifer pressure and the cumulative influx.

-


The models available in Eclipse are:4-Constant flux aquifers

A constant flux aquifer has its water influx rate specified directly by the user, instead of being calculated by an analytic aquifer model. But for the purpose of dimensioning etc., it is classed with the other analytic aquifer models. -One use of a constant flux aquifer is to model rainfall influx for environmental applications.

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The models available in Eclipse are:4-Constant flux aquifers

-The aquifer should be defined with the AQUFLUX keyword in the SOLUTIONsection, and the aquifer connections to one or more faces of the reservoir should be made via the keyword AQUANCON.

SUMMARY file quantities for the aquifer may be obtained using AAQR (influx rate) and AAQT (cumulative influx) in the SUMMARY section.

In order to use the facility, the parameters NANAQU (the maximum number of analytic aquifers) and NCAMAX (the maximum number of grid block connected to any single analytic aquifer) should be set using the RUNSPEC section keyword AQUDIMS.

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Water Influx Eclipse