Feketes Course Notes

Rate Transient AnalysisTheory/Software Course

Introduction to Well Performance Analysis

Traditional

- Production rate only

- Using historical trends to predict future

- Empirical (curve fitting)

- Based on analogy

- Deliverables:- Production forecast- Recoverable Reserves under current conditions

Modern

- Rates AND Flowing Pressures

- Based on physics, not empirical

- Reservoir signal extraction and characterization

- Deliverables:- OGIP / OOIP and Reserves- Permeability and skin- Drainage area and shape- Production optimization screening- Infill potential

Recommended Approach

- Use BOTH Traditional and Modern together

- Production Data Analysis should include a comparison of multiple methods

- No single method always works

- Production data is varied in frequency, quality and duration

- Flow regime characterization over life of well

- Estimation of fluids-in-place

- Performance based recovery factor

- Able to analyze transient production data (early-time production, tight gas etc)

- Characterization of perm and skin

-Estimation of contacted drainage area

-Estimation of reservoir pressure

- Estimation of reserves when flowing pressure is unknown

- High resolution early-time characterization

- High resolution characterization of the near-wellbore

-Point-in-time characterization of wellbore skin

- Projection of recovery constrained by historical operating conditions

Welltest AnalysisModern Production Analysis

Empirical DeclineAnalysis

Modern Production Analysis - Integration of Knowledge

Theory

Traditional Decline Curves – J.J. Arps

- Graphical – Curve fitting exercise

- Empirical – No theoretical basis

- Implicitly assumes constant operating conditions

The Exponential Decline Curve

2001 2002 2003 2004 2005 20060.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00Gas Rate, MMscfd

Rate vs TimeUnnamed Well

2001 2002 2003 2004 2005 200610-1

1.0

101

2

3

4

567

2

3

4

567

Gas

Rat

e, M

Msc

fd

Rate vs TimeUnnamed Well

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50

Gas Cum. Prod., Bscf

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Gas

Rat

e, M

Msc

fd

Rate vs. Cumulative Prod.Unnamed Well

tDi

ieqq −=

log log2.302

ii

D tq q= −i iq q D Q= −

2.302*iD Slope= iD Slope=

iSlopeD

q=

The Hyperbolic Decline Curve

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60


0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Gas

Rat

e, M

Msc

fd


bi

i

tbDqq /1)1( +

=

( )D f t=

i bb

i

DD qq

=

Hyperbolic Exponent “b”

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60


0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Gas Rate, MMscfd


0 . 0 0 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 . 4 0 0 .4 5 0 . 5 0 0 .5 5 0 . 6 0 0 .6 5 0 . 7 0 0 .7 5 0 .8 0 0 .8 5 0 .9 0 0 .9 5 1 . 0 0 1 .0 5

G a s C u m u l a t iv e , B s c f

0 .0 0

0 .2 0

0 .4 0

0 .6 0

0 .8 0

1 .0 0

1 .2 0

1 .4 0

1 .6 0

1 .8 0

2 .0 0

2 .2 0

2 .4 0

2 .6 0

2 .8 0

3 .0 0

3 .2 0

Gas

Rat

e, M

Msc

fd

R a te v s . C u m u la t iv e P r o d .N B U 9 2 1 - 2 2 G

Mild Hyperbolic – b ~ 0

Strong Hyperbolic – b ~ 1

Analytical Solutions

Definition of Compressibility

1 VcV p

∂= −

∂

V

pi

V

dVpi-dp

Compressibility Defines Material Balance of a Closed Oil Reservoir (above bubble point)

1 p

i

pi

t

i pss p

NcN p p

Np pc N

p p m N

=−

= −

= −

Assumptions: 1. c is constant2. Bo is constant

V=N

ΔV = NpΔp = pi - p

Illustration of Pseudo-Steady-State

Distance

pres

sure

pwf1

1p

rw re

1

2p

pwf2

2

3p

pwf3

3

timeConstant Rate q

Steady-State Inflow Equation

Distance

pres

sure

rw re

p

pwf

141.2 3ln4

wf pss

epss

wa

p p qbB q rb

kh rμ

− =

⎛ ⎞= −⎜ ⎟⎝ ⎠

pi

Inflow (Darcy) pressure drop- Constant- Productivity Index

The Two Most Important Equations in Modern Production Analysis

i pss pp p m N= −

wf pssp p qb= +

Constant Pressure=

Production

Constant Rate=

Welltest

q

pwf

q

pwf

Operating Conditions - Simplified

Constant Flowing Pressure Solution

- Required: q(t), Npmax and N for constant pwf

- Take derivative of both equations and solve for q

- Integrate to find Np(t), as t goes to infinity Npgoes to Npmax

( )max

( )pss

pss

m ti wf b

pss

i wfp i wf t

pss

p pq t ebp pN p p c N

m

−−=

−= = −

Constant Flowing Pressure Solution – Relate back to Arps Exponential, Determine N

max

max

( ) ( )

i wfi

pss

pssi

pss

ip

i

t i wf t i wf i

p i

p pqb

mDb

qND

c p p c p p DNN q

−=

=

=

− −= =

Constant Rate Solution

- Required: pwf(t), Npmax and N for constant rate

- Equate left side to right and solve for pi-pwf

- Set pwf = 0 to find Npmax

- Plot pi-pwf versus Np to get N

max

( )i wf pss p pss

i pssp

pss

p p t m N b qp b qN

m

− = +−

=

Constant Rate – PSS Plot

Np

1m mpsscN

= =

i wfp p−

141.2 3ln 4

p ei wf

t wa

y mx bN B q rp pc N kh r

μ= +

⎛ ⎞− = + −⎜ ⎟⎝ ⎠

- Normalize the PSS equation with q

- Invert the PSS equation

1 1( )

1

( ) 1

pss pi wf pss psspss

pss

pssi wf

pss

qm Np p t m t bb

q

q bmp p t tb

= =− ++

=− +

Constant Rate Solution – Relate back to Arps Harmonic

Plot Constant p and Constant q together

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

Constant rate q/Δp (Harmonic)

Constant pressure q/Δp (Exponential)

1

( ) 1

pss

pssi wf

pss

q bmp p t tb

=− +

( ) 1 pss

pss

m tb

i wf pss

q t ep p b

−=

−

Transient Flow

- Early-time OR Low Permeability

- Flow that occurs while a pressure “pulse” is moving out into an infinite or semi-infinite acting reservoir

- Like the “fingerprint” of the reservoir- Contains information about reservoir properties (permeability, drainage shape)

Boundary Dominated Flow

- Late-time flow behavior

- Typically dominates long-term production data

- Reservoir is in a state of pseudo-equilibrium –physics reduces to a mass balance

- Contains information about reservoir pore volume (OOIP and OGIP)

Transient Flow

Transient and Boundary Dominated Flow

2000

2200

2400

2600

2800

3000

3200

3400

3600ps

Cross Section

Plan View

Transient Well Performance = f(k, skin, time)

Boundary Dominated Well Performance =

f(Volume, PI)

Radius (Region) of Investigation

2000

2200

2400

2600

2800

3000

3200

3400

3600ps

Cross Section

Plan View

948

948

inv

inv

ktrc

ktAc

φμπ

φμ

=

=

Transient Equation

1( ) 141.2 1 0.0063ln 0.4045

2i wf

t

q khp p B kt s

cμ

φμ

=− ⎛ ⎞

+ +⎜ ⎟⎝ ⎠

Describes radial flow in an infinite acting reservoir

q(t)’s compared

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25 30 35 40 45

Transient flow: compares to Arps “super hyperbolic” (b>1)

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 40 45

Blending of Transient into Boundary Dominated Flow

Complete q(t) consists of:Transient q(t) from t=0 to tpss

Depletion equation from t = tpss and higher

Comparison of qD with 1/pDCylindrical Reservoir with Vertical Well in Center

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14

tD

qD a

nd 1

/p

0.9

Constant Pressure Solution Exponential

Constant Rate SolutionHarmonic

Log-Log plot: Adds a new visual dynamic

Infinite Acting Boundary Dominated

Type Curves

Type Curve

- Dimensionless model for reservoir / well system

- Log-log plot

- Assumes constant operating conditions

- Valuable tool for interpretation of production and pressure data

Type Curve Example - Fetkovich

10-1 1.0 1012 3 4 5 6 7 8 9 2 3 4 5 6 7 8 2 3 4 5 6 7 8

Time

10-2

10-1

1.0

2

3

4

567

9

2

3

4

567

Rat

e,

Fetkovich Typecurve Analysis

Exponential

Harmonic

qDd

tDd

DdtDd eq −=

11

DdDd

qt

=+

tDtqtqq

iDd

iDd

=

=)(

Hyperbolic

1/

1(1 )

Dd bDd

qbt

=+

Plotting Fetkovich Type Curves- Example

Well 1 (exponential)

qi = 2.5 MMscfdDi = 10 % per year

Well 2 (exponential)

qi = 10 MMscfdDi = 20 % per year

Raw Data Plot

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 5 10 15

Time (years)

Rat

e (M

Msc

fd)

Well 1Well 2

Dimensionless Plot

0.10

1.00

0.01 0.10 1.00 10.00

tDd

qDd Well 1

Well 2

Time (years)Well 1 Well 2 Well 1 Well 2 Well 1 Well 2

0 2.50 10.00 0.00 0.00 1.00 1.001 2.26 8.19 0.10 0.20 0.90 0.822 2.05 6.70 0.20 0.40 0.82 0.673 1.85 5.49 0.30 0.60 0.74 0.554 1.68 4.49 0.40 0.80 0.67 0.455 1.52 3.68 0.50 1.00 0.61 0.376 1.37 3.01 0.60 1.20 0.55 0.307 1.24 2.47 0.70 1.40 0.50 0.258 1.12 2.02 0.80 1.60 0.45 0.209 1.02 1.65 0.90 1.80 0.41 0.17

10 0.92 1.35 1.00 2.00 0.37 0.14

Rate (MMscfd) tDd qDd

Fetkovich Typecurve Matching

In most cases, we don’t know what “qi” and “Di” are ahead of time. Thus, qi and Di are calculated based on the typecurve match (ie. The typecurve is superimposed on the data set

ttD

qtqq

Ddi

Ddi

=

=)(

Knowing qi and Di, EUR (expected ultimate recovery) can be calculated

1.0 1013 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2

Time

10-1

1.0

5

6

789

2

3

4

5

6

78

Rat

e,

Fetkovich Typecurve AnalysisNBU 921-22G

qDd

tDd

q

t

Analytical Model Type Curve

10-4 10-3 10-2 10-1 1.0 1012 3 4 567 9 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 67

Time

10-2

10-1

1.0

101

2

34

6

9

2

34

6

9

2

34

6

9

2

34

6

Rat

e,

Fetkovich Typecurve Analysis

Boundary Dominated FlowExponential

Transient Flow

re/rwa = 10 re/rwa = 100 re/rwa = 10,000qDd

tDd

Dimensionless Variable Definitions (Fetkovich)

2

2

141.2 1ln( ) 2

0.00634

1 1ln 12 2

eDd

i wf wa

waDd

e e

wa wa

q B rqkh p p r

ktctrt

r rr r

μ

φμ

⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎣ ⎦

=⎡ ⎤⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎢ ⎥⎣ ⎦

Type Curve Matching (Fetkovich)

2

141.2 1ln( ) 2

0.00634 1 ln1 1ln 12 2

141.2 0.006342( )

e

i wf wa Dd match

wwa

t Dd wae e

wa wamatch

ei wf t Dd Dd matchmatch

B r qkh p p r q

k t rr sc t rr r

r r

B q trh p p c q t

μ

φμ

φ

⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥− ⎝ ⎠⎣ ⎦

⎛ ⎞= = ⎜ ⎟⎡ ⎤ ⎝ ⎠⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎢ ⎥⎣ ⎦

=−

The Fetkovich analytical typecurves can be used to calculate three paramters: permeability, skin and reservoir radius

10-4 10-3 10-2 10-1 1.0 1012 3 4 5 678 2 3 4 5678 2 3 4 5678 2 3 4 5678 2 3 4 5678 2 3 4 5678

Time

10-3

10-2

10-1

1.0

101

2

34

68

2

34

68

2

34

68

2

34

68

Rat

e,

Fetkovich Typecurve Analysis10

Type Curve Matching - Example

Boundary Dominated FlowExponential

Transient Flow

tDd

reD = 50

qDd

q

t

k = f(q/qDd)

s = f(q/qDd * t/tDd, reD)re = f(q/qDd * t/tDd)

What about Variable Rate / Variable Pressure Production?The Principle of Superposition

Superposition in Time:

1. Divide the production history into a series of constant rate periods2. The observed pressure response is a result of the additive effect of each rate

change in the history

Example: Two Rate History

q1

q2

Effect of (q2-q1)

t1

1 2 1 1( ) ( ) ( )i wfp p q f t q q f t t− = + − −q

pwf

The Principle of Superposition - Continued

1 2 1 1( ) ( ) ( )i wfp p q f t q q f t t− = + − −Two Rate History

N - Rate History

1 11( ) ( )

N

i wf j j jj

p p q q f t t− −

=

− = − −∑f(t) is the Unit Step Response

Superposition Time

Convert multiple rate history into an equivalent single rate history by re-plotting data points at their “superposed” times

11

1

( ) ( )N

i wf j jj

N Nj

p p q q f t tq q

−−

=

− −= −∑

The Principle of Superposition – PSS Case

11

1

( ) ( )N

i wf j jj

N Nj

p p q q f t tq q

−−

=

− −= −∑

141.2 3( ) ln 4

i wf e

t wa

p p t B rf tq c N kh r

μ− ⎛ ⎞= = + −⎜ ⎟⎝ ⎠

11

1

1 ( ) 141.2 3( ) ln 4

1 141.2 3ln4

Ni wf j j e

jN t N waj

i wf p e

N t N wa

p p q q B rt tq c N q kh r

p p N B rq c N q kh r

μ

μ

−−

=

− − ⎛ ⎞= − + −⎜ ⎟⎝ ⎠

− ⎛ ⎞= + −⎜ ⎟⎝ ⎠

∑

Superposition Time: Material Balance Time

Actual Rate Decline Equivalent Constant Rate

q

Q

actual time (t)

Q

Definition of Material Balance Time(Blasingame et al)

= Q/qmaterial balance time (tc)

Features of Material Balance Time

-MBT is a superposition time function

- MBT converts VARIABLE RATE data into an EQUIVALENT CONSTANT RATE solution.

- MBT is RIGOROUS for the BOUNDARY DOMINATED flow regime

- MBT works very well for transient data also, but is only an approximation (errors can be up to 20% for linear flow)

Comparison of qD (Material Balance Time Corrected) with 1/pDCylindrical Reservoir with Vertical Well in Center

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0.000001 0.0001 0.01 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14

tD

qD a

nd 1

/p

0

0.2

0.4

0.6

0.8

1

1.2

Ratio

1/p

D to

q

Beginning of "semi-log" radial flow (tD=25)Ratio (qD to 1/pD) ~ 97%

0.97

Very early time radial flowRatio (qD to 1/pD) ~ 90%

Constant Pressure Solution qDCorrected to Harmonic

Constant Rate Solution 1/pDHarmonic

MBT Shifts Constant Pressure to Equivalent Constant Rate

Corrections for Gas Reservoirs

Corrections Required for Gas Reservoirs

• Gas properties vary with pressure– Formation Volume Factor– Compressibility– Viscosity

Corrections Required for Gas Reservoirs

141.2 3ln 4

o ei wf

o wa

qt qB rp pc N kh r

μ ⎛ ⎞− = + −⎜ ⎟⎝ ⎠

Depletion TermDepends on compressibility

Reservoir FlowTerm: Depends on “B” and Viscosity

Darcy’s Law Correction for Gas Reservoirs

Darcy’s Law states : qp ∝Δ

∫=p

pZ

pdpp0

2μ

Solution: Pseudo-Pressure

For Gas Flow, this is not true becauseviscosity (μ) and Z-factor (Z) vary with pressure

Depletion Correction for Gas Reservoirs

Gas properties (compressiblity and viscosity) vary significantly with pressure

Gas Compressibility

0

0.002

0.004

0.006

0.008

0.01

0.012

0 1000 2000 3000 4000 5000 6000

Pressure (psi)

Com

pres

sibi

lity

(1/p

si)

pc g

1≈

Solution: Pseudo-Time

( )

→

∫=

g

t

giga

cc

dtct

,

0

μμ

μ

Evaluated at average reservoir pressure

Not to be confused with welltest pseudo-time which evaluates properties at well flowing pressure

Depletion Correction for Gas Reservoirs: Pseudo-Time

Boundary Dominated Flow Equation for Gas

⎟⎠⎞

⎜⎝⎛ −+=−=Δ

43ln*6417.1

)(2

wa

ea

iig

ipwfpip

rr

khTqeqt

GZcpppp

μ

Pseudo-pressure Pseudo-time

Constant Rate Case

Variable Rate Case

pssi

pap bqGG

qp

+=Δ α

Pseudo-Cumulative Production

Overall time function -Material Balance Pseudo-time

( )∫∫

∫

==

=

t

g

igtaaca

tc

cqdt

qcqdt

qt

qdtq

t

00

0

1

1

μμ

Overall material balance pseudo-time function (corrected for variable fluid saturations and formation expansion):

( )[ ]

0

ca)(1

)(

t

ift

it dtppcc

tqqct ∫ −−

=μ

μ

Where,

ggwwooft cscscscc +++= Evaluated at average reservoir pressure

Corrected Material Balance Pseudo-time

Practice

- Traditional- Blasingame - Agarwal – Gardner and NPI - Flowing p/z analysis- Transient - Models and History Matcning

Notes About Drive Mechanism and b Value (from Arps and Fetkovich)

b value Reservoir Drive Mechanism

0 Single phase liquid expansion (oil above bubble point)Single phase gas expansion at high pressureWater or gas breakthrough in an oil well

0.1 - 0.4 Solution gas drive

0.4 - 0.5 Single phase gas expansion

0.5 Effective edge water drive

0.5 - 1.0 Layered reservoirs

> 1 Transient (Tight Gas)

Advantages of Traditional

- Easy and convenient

- No simplifying assumptions are required regarding the physics of fluid flow. Thus, can be used to model very complex systems

- Very “Real” indication of well performance

Limitations of Traditional

- Implicitly assumes constant operating conditions

-Non-unique results, especially for tight gas (transient flow)

- Provides limited information about the reservoir

Example 1: Decline Overpredicts Reserves

October November December January February March April2001 2002

4

Gas

Rat

e, M

Msc

fdRate vs TimeUnnamed Well

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50


0

1

2

3

4

Gas

Rat

e, M

Msc

fd


EUR = 9.5 bcf

Example 1 (cont’d)

Flowing Pressure and Rate vs Cumulative Production

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6 7 8 9 10

Cumulative Production (bcf)

Rate

(MM

scfd

)

0

200

400

600

800

1000

1200

Flow

ing

Pres

sure

(psi

a)

True EUR does not exceed 4.5 bcf

Rates

Pressures

Forecast is not valid here

Example 2: Decline Underpredicts Reserves

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20


0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

8.50

Gas

Rat

e, M

Msc

fd


EUR = 3.0 bcf


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Normalized Cumulative Production, Bscf

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085N

orm

aliz

ed R

ate,

MM

scfd

/(106

psi2 /

cP)Flowing Material BalanceUnnamed Well

Original Gas In Place

LegendDecline FMB

OGIP = 24 bcf


0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720

Time, days

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Gas

, MM

scfd

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Pressure, psi

Data ChartUnnamed Well

LegendPressureActual Gas Data

Operating conditions: Low drawdownIncreasing back pressure

Arps Production Forecast

0.01

0.1

1

10

Dec-00 May-06 Nov-11 May-17 Oct-22 Apr-28 Oct-33

Time

Gas

Rat

e (M

Msc

fd)

Economic Limit = 0.05 MMscfd

b = 0.25, EUR = 2.0 bcf

b = 0.50, EUR = 2.5 bcf

b = 0.80, EUR = 3.6 bcf

Example 3 – Illustration of Non-Uniqueness

Blasingame Typecurve Analysis

Blasingame typecurves have identical format to those of Fetkovich. However, there are three important differences in presentation:

1. Models are based on constant RATE solution instead of constant pressure

2. Exponential and Hyperbolic stems are absent, only HARMONIC stem is plotted

3. Rate Integral and Rate Integral - Derivative typecurvesare used (simultaneous typecurve match)

Data plotted on Blasingame typecurves makes use of MODERN DECLINE ANALYSIS methods:

- NORMALIZED RATE (q/Δp)

- MATERIAL BALANCE TIME / PSEUDO TIME

Blasingame Typecurve Analysis-Comparison to Fetkovich

log(qDd)

log(tDd)

log(q/Δp)

log(tca)

log(qDd)

log(tDd)

log(q)

log(t)

Fetkovich Blasingame

- Usage of q/Δp and tca allow boundary dominated flow to be represented by harmonic stem only, regardless of flowing conditions

- Blasingame harmonic stem offers an ANALYTICAL fluids-in-place solution

- Transient stems (not shown) are similar to Fetkovich

Blasingame Typecurve Analysis- Definitions

Normalized Rate

Typecurves Data - Oil Data - Gas

⎥⎦

⎤⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛

Δ=

21ln2.141

wa

eDd r

rPkhqq βμ

Pq

Δ

pPq

Δ

( )dttqt

qDAt

Dd

DADdi ∫=

0

1 ∫ Δ

=⎟⎠⎞

⎜⎝⎛

Δ

ct

ci

dtP

qtP

q

0

1 ∫ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

cat

pcaip

dtPq

tPq

0

1

DA

DdiDADdid dt

dqtq =

c

ic

id dtP

qdt

Pq

⎟⎠⎞

⎜⎝⎛

Δ=⎟

⎠⎞

⎜⎝⎛

Δ

ca

ipca

idp dt

Pqdt

Pq ⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ=⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Rate Integral

Rate Integral -Derivative

actual rate

Q

actual time

Q

Concept of Rate Integral(Blasingame et al)

rate integral = Q/t

actual time

Rate Integral: Like a Cumulative Average

t1

Average rate over time period“0 to t1”

q

Effective way to remove noise

Average rate over time period“0 to t2”

t2

∫ Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛Δ

ct

ci

dtp

qtp

q

0

1

Rate Integral: Definition

Typecurve Interpretation Aids: Integrals, Derivatives

Integral / Cumulative

Removing the scatter from noisy data sets

Dilutes the reservoir signal

Fetkovich, Blasingame, NPI

DerivativeAmplifying the reservoir signal embedded in production data

Amplifies noise - often unusable

Agarwal-Gardner, PTA

Integral-Derivative Maximizing the strengths of Integral and Derivative

Can still be noisy Blasingame, NPI

Used in AnalysisTypecurve Most Useful For Drawback

Other methods: Data filtering, Moving averages, Wavelet decomposition

Rate Integral and Rate Integral Derivative(Blasingame et al)

Rate Integral

Rate (Normalized)

Rate Integral Derivative

Blasingame Typecurve Analysis-Transient Calculations

Oil:

k is obtained from rearranging the definition of

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

21

rr

lnkh2.141

pqq

matchwa

eDd

βμΔ

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=21

rr

lnh2.141

qp

qk

matchwa

e

match

Dd

βμΔ

Solve for rwa from the definition of

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

21

rr

ln1rr

rc21

kt006328.0t

matchwa

e

2

matchwa

e2wat

cDd

φμ

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

21

matchwarerln1

2

matchwarer

21

tc

k006328.0

matchDdtt

war c

φμ

⎟⎟⎠

⎞⎜⎜⎝

⎛=

wa

w

rr

lns

Blasingame Typecurve Analysis-Boundary Dominated Calculations- Oil

Oil-in-Place calculation is based on the harmonic stem of Fetkovich typecurves.

In Blasingame typecurve analysis, qDd and tDd are defined as follows:

( )( ) ciDd

iDd tDt

pqpqq =

ΔΔ

= and //

Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for oil in harmonic form:

11

1

and 1

1

+=

Δ+=

ct

DdDd

tNbc

bp

qt

q

From the above equations:

NbcD

bpq

tDp

q

pq

ti

ici

i 1 and , 1

ere wh 1

==⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

Δ+Δ

=Δ

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

PSS equation for oil in harmonic form, using material balance time

Definition of Harmonic typecurve

Blasingame Typecurve Analysis- Boundary Dominated Calculations- Oil (cont’d)

Oil-in-Place (N) is calculated as follows:

Rearranging the equation for Di:

bDcN

it

1=

Now, substitute the definitions of qDd and tDd back into the above equation:

( )

( )⎥⎦

⎤⎢⎣

⎡ Δ⎥⎦⎤

⎢⎣⎡=

⎥⎦

⎤⎢⎣

⎡Δ⎥⎦

⎤⎢⎣⎡

=DdDd

c

tDd

c

Ddt

qpq

tt

cpq

qttc

N /1

/

1

Y-axis “match-point”from typecurve analysis

X-axis “match-point from typecurve analysis

Blasingame Typecurve Analysis- Boundary Dominated Calculations- Gas

Gas-in-Place calculation is similar to that of oil, with the additional complications of pseudo-time and pseudo-pressure.

In Blasingame typecurve analysis, qDd and tDd are defined as follows:

( )( ) caiDd

ip

pDd tDt

pqpqq =

ΔΔ

= and //

Recall the Fetkovich definition for the harmonic typecurve and the PSS equation for gas in harmonic form:

( ) 12

1

and 1

1

+=

Δ+=

caiit

ipDdDd

tbGcZ

pb

pq

tq

μ

PSS equation for gas in harmonic form, using material balance pseudo-time

Definition of Harmonic typecurve

From the above equations:

( ) bGcZpD

bpq

tDp

q

pq

iit

ii

ipci

i

μ2 and , 1

ere wh

1==⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

Δ+Δ

=Δ

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

Gas-in-Place (Gi) is calculated as follows:

Rearranging the equation for Di:

( )bcZDpG

iti

ii

μ2

=

Now, substitute the definitions of qDd and tDd back into the above equation:

Y-axis “match-point”from typecurve analysis

X-axis “match-point from typecurve analysis

Blasingame Typecurve Analysis- Boundary Dominated Calculations- Gas

( ) ( )( )

⎥⎦

⎤⎢⎣

⎡ Δ⎥⎦⎤

⎢⎣⎡=

Δ⎟⎠⎞

⎜⎝⎛

=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ Dd

p

Dd

ca

it

i

p

Ddit

ca

Dd

ii

qpq

tt

cZp

pqqcZ

tt

pG /2

)/(

2μ

μ

Agarwal-Gardner Typecurve Analysis

Agarwal and Gardner have developed several different diagnostic methods, each based on modern decline analysis theory. The AG typecurves are all derived using the WELLTESTING definitions of dimensionless rate and time (as opposed to the Fetkovich definitions). The models are all based on the constant RATE solution. The methods they present are as follows:

1. Rate vs. Time typecurves (tD and tDA format)

2. Cumulative Production vs. Time typecurves (tD and tDAformat)

3. Rate vs. Cumulative Production typecurves (tDAformat)

- linear format- logarithmic format

Agarwal-Gardner Typecurve Analysis

Agarwal-Gardner - Rate vs. Time typecurves

Agarwal and Gardner Rate vs. Time typecurves are the same as conventional drawdown typecurves, but are inverted and plotted in tDA (time based on area) format.

qD vs tDA

The AG derivative plot is not a rate derivative (as per Blasingame). Rather, it is an INVERSE PRESSURE DERIVATIVE.

pD(der) = t(dpD/dt) qD(der) = t(dqD/dt)

1/pD(der) = ( t(dpD/dt) ) -1

Agarwal-Gardner - Rate vs. Time typecurves

Comparison to Blasingame typecurves

Rate Integral-Derivative

Inv. Pressure Integral-Derivative

qDd and tDdplotting format

qD and tDAplotting fomat

Agarwal-Gardner - Rate vs. Cumulative typecurves

Agarwal and Gardner Rate vs. Cumulative typecurves are different from conventional typecurves because they are plotted on LINEAR coordinates.

They are designed to analyze BOUNDARY DOMINATED data only. Thus, they do not yield estimates of permeability and skin, onlyfluid-in-place.

Plot: qD (1/pD) vs QDA

Where (for oil):

( )( )tpp

tqkh

Bqwfi

D −=

μ2.141

wfi

i

wfitDADDA pp

ppppNc

QtqQ−−

−==

ππ 21ely alternativor

)(21*

Where (for gas):


( )( )t

tqkh

Teqwfi

D ψψ −=

*6417.1

( ) wfi

i

wfiiit

caDADDA GZc

qttqQψψψψ

πψψμπ −−

−==

21ely alternativor

)(2

21*


qD vs QDA typecurves always converge to 1/2π (0.159)

NPI (Normalized Pressure Integral)

NPI analysis plots a normalized PRESSURE rather than a normalized RATE. The analysis consists of three sets of typecurves:

1. Normalized pressure vs. tc (material balance time)

2. Pressure integral vs. tc

3. Pressure integral - derivative vs. tc

- Pressure integral methodology was developed by Tom Blasingame; originally used to interpret drawdown data with a lot of noise. (ie. conventional pressure derivative contains far too much scatter)

- NPI utilizes a PRESSRE that is normalized using the current RATE. It also utilizes the concepts of material balance time and pseudo-time.

NPI (Normalized Pressure Integral): Definitions

Normalized Pressure


βμqPkhPD 2.141

Δ=

qPΔ

qPpΔ

( )DA

DDd td

dPP

ln=

( )cd tdqPd

qP

ln

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

( )

( )ca

p

i

p

tdqPd

qP

ln

Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

( )dttPt

PDAt

pDA

Di ∫=0

1∫

Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ ct

ci

dtqP

tqP

0

1∫

Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ catp

cai

p dtqP

tqP

0

1

DA

DiDADid dt

dPtP =

c

ic

id dtqPd

tqP ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

ca

i

pca

id

p

dtqP

dt

qP ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

Conventional Pressure Derivative

Pressure Integral

Pressure Integral -Derivative

NPI (Normalized Pressure Integral): Diagnostics

Transient

Boundary Dominated

Integral - Derivative Typecurve

Normalized Pressure Typecruve

NPI (Normalized Pressure Integral): Calculation of Parameters- Oil

Oil - Radial

βμqPkhPD 2.141

Δ= 2

00634.0

et

cDA rC

ktt

πφμ=

match

D

qP

Ph

k⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

Δ=

βμ2.141

matchDA

c

te t

tC

kr ⎟⎟⎠

⎞⎜⎜⎝

⎛=

πφμ00634.0

matchwa

ewq

rre

rr

⎟⎟⎠

⎞⎜⎜⎝

⎛= ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

wa

w

rr

S ln

matchDA

c

match

D

t tt

qP

PSC

N ⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

Δ⎟⎠⎞

⎜⎝⎛=

1000*615.52.14100634.0 0 (MBBIS)

Gas – Radial

TqPkh

P pD 6417.1 Ε

Δ= 2

00634.0

etii

caDA rC

ktt

πφμ=

match

p

D

qP

Ph

Tk

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

ΔΕ

=6417.1

matchDA

ca

tiie t

tC

kr ⎟⎟⎠

⎞⎜⎜⎝

⎛=

πφμ00634.0

matchwa

e

ewa

rr

rr

⎟⎟⎠

⎞⎜⎜⎝

⎛= ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

wa

w

rrS ln

( )( ) 910*6417.100634.0

match

p

D

matchDA

ca

scitii

scig

qP

Ptt

PzcTPS

G

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

Δ⎟⎟⎠

⎞⎜⎜⎝

⎛Ε=

μ(bcf)

NPI (Normalized Pressure Integral): Calculation of Parameters- Gas

pG

Measured at wellduring flow

Pressure loss due to flow in reservoir (Darcy’s Law) is constant with time

iG

i

i

zp

wf

wf

zp

- Mattar L., McNeil, R., "The 'Flowing' Gas Material Balance", JCPT, Volume 37 #2, 1998

Flowing p/z Method for Gas – Constant Rate

constant+⎟⎠⎞

⎜⎝⎛=

wfzp

zp

pG


i

i

zp

wf

wf

zp

Graphical Method Doesn’t Work!

iG ?

Graphical Flowing p/z Method for Gas –Variable Rate

pG


Pressure loss due to flow in reservoir is NOTconstant

iG

i

i

zp

wf

wf

zp

pss

wf

qbzp

zp

+⎟⎠⎞

⎜⎝⎛=

Unknown

Flowing p/z Method for Gas – Variable Rate

Variable Rate p/z – Procedure (1)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70

Cumulative Production, Bscf

0

50

100

150

200

250

300

350

400

450

500

550

Flowing Pressure, psi

Flowing Material BalanceUnnamed Well


LegendStatic P/Z*

P/Z LineFlowing Pressure

Step 1: Estimate OGIP and plot a straight line from pi/zi to OGIP. Include flowing pressures (p/z)wfon plot

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70


0.00

0.40

0.80

1.20

1.60

2.00

2.40

2.80

3.20

3.60

4.00

4.40

Prod

uctiv

ity In

dex,

MM

scfd

/(106

psi2 /

cP)

0

50

100

150

200

250

300

350

400

450

500

550




LegendStatic P/Z*

P/Z LineFlowing PressureProductivity Index


Step 2: Calculate bpss for each production point using the following formula:

Plot 1/bpss as a function of Gp

line wfpss

p pz z

bq

⎛ ⎞ ⎛ ⎞−⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

=

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70


0.00

0.40

0.80

1.20

1.60

2.00

2.40

2.80

3.20

3.60

4.00

4.40

Prod

uctiv

ity In

dex,

MM

scfd

/(106

psi2 /

cP)

0

50

100

150

200

250

300

350

400

450

500

550




LegendStatic P/Z*

P/Z LineFlowing PressureProductivity Index


Step 3: 1/bpss should tend towards a flat line. Iterate on OGIP estimates until this happens

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70


0.00

0.40

0.80

1.20

1.60

2.00

2.40

2.80

3.20

3.60

4.00

4.40

Prod

uctiv

ity In

dex,

MM

scfd

/(106

psi2 /

cP)

0

50

100

150

200

250

300

350

400

450

500

550

P/Z*, Flow

ing Pressure, psi



LegendStatic P/Z*

P/Z LineFlowing P/Z*

Flowing PressureProductivity Index


Step 4: Plot p/z points on the p/zline using the following formula:

“Fine tune” the OGIP estimate

pss

data wf

p p qbz z

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

1/bpss

Transient (tD format) Typecurves

Transient typecurves plot a normalized rate against material balance time (similar to other methods), but use a dimensionlesstime based on WELLBORE RADIUS (welltest definition of dimensionless time), rather than AREA. The analysis consists of two sets of typecurves:

1. Normalized rate vs. tc (material balance time)

2. Inverse pressure integral - derivative vs. tc

- Transient typecurves are designed for analyzing EARLY-TIME data to estimate PERMEABILITY and SKIN. They should not be used (on their own) for estimating fluid-in-place

- Because of the tD format, the typecurves blend together in the early-time and diverge during boundary dominated flow (opposite of tDA and tDd format typecurves)

log(qDd)

log(tDd)log(tD)

log(qD)

Transient versus Boundary Scaling Formats

Transient (tD format) Typecurves: Definitions

Normalized Rate


PkhqqD Δ

=βμ2.141

Pq

Δ pPq

Δ

( )1

0

1/1−

⎥⎥⎦

⎤

⎢⎢⎣

⎡= ∫ dttP

tP

DAt

pDA

Di

1

0

1−

⎥⎥⎦

⎤

⎢⎢⎣

⎡ Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ∫ct

ci

dtqP

tqPInv

1

0

1−

⎥⎥⎦

⎤

⎢⎢⎣

⎡ Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ∫cat

p

cai

p dtqP

tqP

Inv

1

/1−

⎥⎦

⎤⎢⎣

⎡=

DA

DiDADid dt

dPtP1−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

c

ic

id dtqPd

tqPInv

1−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

=⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ

ca

i

pca

id

p

dtqP

dt

qP

Inv

Inverse Pressure Integral

Inverse PresssureIntegral - Derivative

Transient (tD format) Typecurves:Diagnostics (Radial Model)

Transient Transition to Boundary Dominated occurs at different points for different typecurves

Inverse Integral -Derivative Typecurve

Normalized Rate Typecurve

Transient (tD format) Typecurves:Finite Conductivity Fracture Model

Increasing Fracture Conductivity (FCD stems)

Increasing Reservoir Size (xe/xf stems)

Transient (tD format) Typecurves:Calculations (Radial Model)

O il W ells :

U s ing the de fin itio n o f q D ,

pe rm eab ility is ca lcu la ted as fo llo w s :

F rom the de fin ition o f tD ,

rw a is ca lcu la te d as fo llo w s :

S k in is ca lcu la ted as fo llo w s :

/ 2.141

matchDqpq

hBk ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ=

μ

/ 2.14100634.0 matchD

c

matchDtwa

tt

qpq

hB

cr ⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ⎟⎠⎞

⎜⎝⎛=

φ

)(

2.141wfi

Dppkh

qBq−

=μ

00634.0 2

wat

cD

rcktt

φμ=

ln w⎟⎠⎞

⎜⎝⎛=

warrs

Gas Wells:

For gas wells, qD is defined as follows:

The permeability is calculated from above, as follows:

From the definition of tD and k, rwa is calculated as follows

Skin is calculated as follows:

q6.4171p

RD

pkhTEq

Δ=

/6.4171

matchD

pR

qpq

hTEk ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ=

/6.417100634.0 matchD

p

matchD

caR

tiiwa

qpq

tt

hTE

cr ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

φμ

ln w⎟⎠⎞

⎜⎝⎛=

warrs

Modeling and History Matching

Well / Reservoir Model

Well Pressure at Sandface

Production Volumes

Constraint (Input)

Signal (Output)

Well / Reservoir Model

Production Volumes

Well Pressure at Sandface

Constraint (Input)

Signal (Output)

1. Pressure Constrained System:

2. Rate Constrained System:


Models - Horizontal Rectangular reservoir with a horizontal well located anywhere inside.

L

Models - Radial Rectangular reservoir with a vertical well located anywhere inside.

Models - Fracture Rectangular reservoir with a vertical infinite conductivity fracture located anywhere inside.

A Systematic and Comprehensive Method for Analysis

Modern Production Analysis Methodology

Diagnostics Interpretation andAnalysis


Forecasting

- Data Chart- Typecurves

- Analytical Models- Numerical Models

- Data Validation- Reservoir signal extraction

- Identifying dominant flow regimes- Estimating reservoir characteristics- Identifying important system parameters- Qualifying uncertainty

- Traditional- Fetkovich- Blasingame- AG / NPI- Flowing p/z- Transient

- Validating interpretation- Optimizing solution- Enabling additional flexibility and complexity

- Reserves- Optimization scenarios

Practical Diagnostics

• Qualitative investigation of data– Pre-analysis, pre-modeling– Must be quick and simple

What are diagnostics?

• A VITAL component of production data analysis (and reservoir engineering in general)

Illustration- Typical Dataset

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Liqu

id R

ates

, bb

l/d

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

Gas

, M

Mcf

d

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Pressure , psi



“Face Value” Analysis of Data

OGIP = 90 bcf

Go Back: Diagnostics

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Liqu

id R

ates

, bb

l/d

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

Gas

, M

Mcf

d

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Pressure , psi



Data ChartUnnam ed Well


Pressures are not representative of bhdeliverability

Correct Data Used

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540Time, days

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

Liqu

id R

ates

, bb

l/d

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

Gas

, M

Mcf

d

4600

4800

5000

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

7400

Pressure , psi

DataChartUnnamed Well

LegendPressureActual Gas DataOil ProductionWater Production

OGIP = 19 bcf

Diagnostics using Typecurves

10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7

10-11

10-10

10-9

10-8

10-7

2358

2358

23

58

2358

2358

2

Blasingame Typecurve MatchRadial Model

qDd

tDd

Base Model:- Vertical Well in Center of Circle- Homogeneous, Single Layer

Transient (concave up) Boundary Dominated

(concave down)

Material Balance Diagnostics


10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7

10-11

10-10

10-9

10-8

10-7

2358

2358

23

58

2358

2358

2


Leaky Reservoir (interference)

Reservoir With Pressure Support

Volumetric

qDd

tDd

Infinite Acting Pressure Support

Dual Depletion System

Productivity Diagnostics


10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7

10-11

10-10

10-9

10-8

10-7

2358

2358

23

58

2358

2358

2


Well Cleaning Up

Liquid Loading

Increasing Damage (difficult to identify)

qDd

tDd

Productivity Shifts (workover, unreported tubing change)

Transient Flow Diagnostics


10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7

10-11

10-10

10-9

10-8

10-7

2358

2358

2358

2358

2358

2


Transitionally Dominated Flow (eg: Channel or Naturally Fractured)

Fracture Linear Flow(Stimulated)

Radial Flow

DamagedqDd

tDd

10-1 1.0 101 102 103 104 105 106 1074 56 8 2 3 4 5 7 9 2 3 4 5 7 9 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 56 8 2 3 4 5 7 2 3 4 5 7

10-11

10-10

10-9

10-8

10-7

2358

2358

2358

2358

2358

2


Δp in reservoir is too high-Tubing size too large ?- Initial pressure too high ?- Wellbore correlations underestimate pressure loss ?

Δp in reservoir is too low-Tubing size too small ?- Initial pressure too low ?- Wellbore correlations overestimate pressure loss ?

qDd

tDd

“Bad Data” Diagnostics


Selected Topics and Examples

Tight Gas

Industry Migration to Tight Gas Reservoirs

Production Analysis – Tight Gas versus Conventional Gas

Analysis methods are no different from that of high permeability reservoirs

Transient effects tend to be more dominant – Establishing the region (volume) of influence is critical

Drainage shape becomes more important (Transitional effects)

Linear flow is more common

Layer effects are more common

Tight Gas Type Curves

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

tDd

qDd

Tight Gas- Common Geometries

Linear flow dominated Limited, bounded

drainage area

Infinite acting reservoir

1/2

1

Tight Gas Model 1

Extensive, continuous porous media; very low permeability

Pi = 2000 psi1800 psi

Pi = 1500 psi


1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

tDd

qDd

1/2

Infinite Acting System

10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 678 2 3 4 5 6 78 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678

Material Balance Pseudo Time

10-2

10-1

1.0

101

102

2

3

57

2

3

57

2

34

6

9

2

3

57

2

34

6

2

Nor

mal

ized

Rat

e

Agarwal Gardner Rate vs Time Typecurve Analysis10

Example#1 – Infinite Acting System

10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678 2 3 4 5 678


10-2

10-1

1.0

101

102

2

3

57

2

3

57

2

34

6

9

2

3

57

2

34

6

2

Nor

mal

ized

Rat

e

Agarwal Gardner Rate vs Time Typecurve Analysis10

k = 0.08 mdxf = 53 ft

OGIP = 10 bcf

k = 0.08 mdxf = 53 ft

Minimum OGIP = 2.6 bcf

No flow continuity across reservoir- Well only drains a limited bounded volume

Tight Gas Model 2

Example: Lenticular Sands


1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

tDd

qDd

1/2

1- Limited or no flow continuity in reservoir - Very small drainage areas- Very large effective fracture lengths

Bounded Reservoir

Commonly observed in practice

Example #2- Bounded Drainage Areas

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600

xf (feet)

OG

IP (b

cf)

.

0

5

10

15

20

25

30

35

10 20 30 40 50 60 70 80 90 100 More

Drainage Area (acres)

Freq

uenc

y

0%

20%

40%

60%

80%

100%

120%

Frequency Cumulative %

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78


10-2

10-1

1.0

101

23

57

23

57

23

57

2

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisROBINSON 11-1 ALT

- West Louisiana gas field - 80 acre average spacing- All wells in boundary dominated flow

Linear flow dominated system

Tight Gas Model 3

kx

ky

Example: Naturally fractured, tight reservoir

Infinite Systems versus Linear Flow Systems

Establish permeability and xfindependently

Establish xf sqrt (k) product only


1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

tDd

qDd

1/2

- Channel and faulted reservoirs- Naturally fractured (anisotropic) reservoirs- Very large effective fracture lengths- Very difficult to uniquely interpret

Linear Flow Systems

Commonly observed in practice

Example #3- Linear Flow System

101 102 1032 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8

10-8

10-7

5

79

2

3

45

7

2

3

45

Blasingame Typecurve MatchFracture Model

k = 1.1 mdxf = 511 ft

ye = 5,500 ftyw = 2,900 ft

ye

2xf

yw

More Examples

Example #3- Multiple Layers

10-1 1.03 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9


10-1

1.0

9

2

3

4

5

6

7

8

2

3

Nor

mal

ized

Rat

e

Blasingame Typecurve Analysis

1.0 101 102 103 1042 3 4 5 6 789 2 3 4 5 6 789 2 3 4 5 6 789 2 3 4 5 6 7810-10

10-9

10-8

2

34

68

2

345

7

Blasingame Typecurve MatchMulti Layer Model

Well

- Blasingame typecurve match, using Fracture Model- Pressure support indicated

- Three-Layer Model (one layer with very low permeability) used, late-time match improved

10-3 10-2 10-1 1.06 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9


10-1

1.0

3

4

567

9

2

3

4

5

67

2

3

4

5

Nor

mal

ized

Rat

e

Agarwal Gardner Rate vs Time Typecurve AnalysisWell

Example #4- Shale Gas

- Multi-stage fractures, horizontal well- Analyzed as a vertical well in a circle

k = 0.02 mds = -4

OGIP = 4.5 bcf

Tight Gas: Assessing Reserve Potential – Recovery Plots

Objectives

Determine incremental reserves that are added as the ROI expands into the reservoir (only relevant for infinite or semi-infinite systems)

To establish a practical range of Expected Ultimate Recovery

Typical Recovery ProfileRecovery Curves for k = 1 md

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Original Gas in Place (bcf)

EUR

(bcf

)

1 md reservoir, unfractured(~10 bcf / section)

100% Recovery


0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)

EUR- unlimited time

Actual EUR (qab = 0.05 MMscfd)

100% Recovery



0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)

EUR- 30 year EUR- unlimited time

30 Year Limited


100% Recovery



0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)

EUR- 30 year EUR- 20 year EUR- unlimited time

20 Year Limited30 Year Limited


100% Recovery


Tight Gas Recovery ProfileRecovery Curves for k = 0.02 md

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)

EUR- unlimited time

0.02 md reservoir, fractured(~10 bcf / section)



0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)

EUR- 30 year EUR- unlimited time

30 Year




0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)


30 Year20 Year




0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10


EUR

(bcf

)


30 Year

Max EUR (30 y) = 2 bcf


20 Year


Example – South Texas, Deep Gas Well

1.0 101 102 1032 3 4 5 6 7 8 9 2 3 4 5 6 7 89 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8

10-9

10-8

7

9

2

3

45

7

2

3

AG Typecurve MatchFracture Model

Sqrt k X xf = 155Min OGIP = 4.2 bcf

Example – South Texas, Deep Gas Well

Recovery Plot - Linear System

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600

ROI (acres)

EUR

(bc

Minimum EUR = 3.5 bcf

Maximum EUR = 6.7 bcf

Recovery period = 30 yearssqrt k X xf = 155pi = 6971 psia

Water Drive Models

Water Drive (Aquifer) Models:

Models for reservoirs under the influence of active water encroachment can be categorized as follows:

1. Steady State Models (inaccurate for finite reservoir sizes)- Schilthuis

2. Pseudo Steady-State Models (geometry independent, time discretized)

- Fetkovich

3. Single Phase Transient Models (geometry dependent)- infinite aquifer (linear, radial or layer geometry)- finite aquifer (linear, radial or layer geometry)

4. Modified Transient Models - Moving saturation front approximations- Two phase flow approximations

Water Drive (Aquifer) Models:Pseudo Steady-State Models

PSS models (such as that of Fetkovich) use a TRANSFER COEFFICIENT (similar to a well productivity index) to describe the PSS rate of water influx into the reservoir, in conjunction with a MATERIAL BALANCE model that predicts the decline in reservoir boundary pressure over time.

The Fetkovich model is generally used to determine reservoir fluid-in-place by history matching the CUMULATIVE PRODUCTION and AVERAGE RESERVOIR PRESSURE.

Water Drive (Aquifer) Models:Pseudo Steady-State Models

Advantages:

- Geometry independent (applicable to aquifers of any shape, size or connectivity to the reservoir)- Works well for finite sized aquifers of medium to high mobility- Computationally efficient

Disadvantages:

- Does not provide a full time solution (transient effects are ignored)- Does not work well for infinite acting or very low mobility aquifers

Water Drive (Aquifer) Models:Pseudo Steady-State Model- Equations

The Fetkovich water influx equation for a finite aquifer is:

( ) /1 ⎟⎠⎞⎜

⎝⎛ −= − iei

ii

eie

WtJpe-ppp

WW

The above equation applies to the water influx due to a constant pressure difference between aquifer and reservoir. In practice, the reservoir pressure “p” will be declining with time. Thus, the equation must be discretized as follows:

Initial encroachable water

Aquifer transfer coefficient

Reservoir boundary pressure

( ) /1 1 ⎟⎠⎞⎜

⎝⎛ −=Δ −

−

i

nn

eina

i

eie

WtJpep-pp

WW

The average aquifer pressure at the previous timestep (n-1) is evaluated explicitly, as follows:

1

1

11

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛Δ

−=∑

−

=−

ei

n

j

ej

iaW

Wpp n

(1)

Water Drive (Aquifer) Models:Pseudo Steady-State Model- Equations

But there is another equation that relates the average reservoir pressure to the amount of water influx: the material balance equation for a gas reservoir under water drive.

1 1 -1

⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛ −=

i

ie

i

p

i

i

GBW

GG

zp

zp

Now, we have one equation with two unknowns (water influx “We” and reservoir boundary pressure “p”)

As with the water influx equation, the material balance equation can be discretized in time:

(2) 1 1 -1

⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛

i

ie

i

p

i

i

n GBW

GG

zp

zp nn

Equations 1 and 2 are now solved simultaneously at each timestep, to obtain a discretizedreservoir pressure and water influx profile through time.

Cumulative Production

FVF at initial conditions

Gas-in-place

Water Drive (Aquifer) Models:Transient Models

Transient models use the full solution to the hydraulic DIFFUSIVITY EQUATION to model rates and pressures.

The transient equations can be used to model either FINITE or INFINITE acting aquifers. There are a number of different transient models available for analyzing a reservoir under active water drive:

- Radial Composite (edge water drive)- Linear (edge water drive)- Layered (bottom water drive)

Advantages:

- Offers full continuous pressure solution in the reservoir- Includes early time effects

Disadvantages:

- Geometry dependent (only a disadvantage if aquifer properties are unknown)- Limited to assumption of single phase flow - Does not account for water influx

Water Drive (Aquifer) Typecurves:Radial Composite Model

Blasingame, AG and NPI dimensionless formats can be used to plottypecurves for SINGLE PHASE production (oil or gas) from a reservoir under the influence of an EDGE WATER DRIVE. A typecurve match using this model can be used to predict

1. Reservoir fluid-in-place

2. Aquifer mobility

- These typecurves are designed to estimate fluid-in-place by detecting the shift in fluid mobility as the transient passes the reservoir boundaries, into the aquifer.

- Their usefulness is limited to single phase flow (ie: the transition from reservoir fluid to aquifer is assumed to be abrupt)

Water Drive (Aquifer) Typecurves: DefinitionsModel Type: Radial Composite (two zones); outer zone is of infinite extent

Reservoir Aquifer

aq

res

res

aq

res

aq

kk

MMM

μμ

==Mobility Ratio (M):

Water Drive (Aquifer) Typecurves: Diagnostics

Increasing Aquifer Mobility (M)

M=0 (Volumetric Depletion)

M=10 (Constant Pressure System (approx))

Decreasing reD value

Water Drive (Aquifer) Typecurves: Diagnostics

M=10 (Constant Pressure System (approx))

M=0 (Volumetric Depletion)

Decreasing reD value

Increasing Aquifer Mobility (M)

Water Drive (Aquifer) Models:Modified Transient Models

1. Moving aquifer front (reservoir boundary)

The radial composite model previously discussed can be enhanced to accommodate a shrinking reservoir boundary, caused by water influx. This is achieved by discretizingthe transient solution in time and using the PSS water influx equations to predict the advancement of the aquifer front. The solution still assumes single phase flow, but can now more accurately estimate the time to water breakthrough.

2. Two phase flow (after M. Abbaszadeh et al)

The previously discussed model can also be modified to accommodate a region of two-phase flow (located between the inner region - hydrocarbon phase and outer region - water phase). Thus, geometrically, the overall model is three zone composite. The pressure transient solution for the two-phase zone is calculated by superimposing the single phase pressure solution on a saturation profile determined using the Buckley-Leverettequations.

Water Drive (Aquifer) Models: Example

Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct2002 2003

0

2

4

6

8

10

12

14

16

18

20

22

Gas

, MM

scfd

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

Pressure, psi

Data ChartExample F


10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8


10-2

10-1

1.0

101

2

3

456

8

2

3

456

8

2

3

456

8

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisExample F

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8


10-2

10-1

1.0

101

2

3

456

8

2

3

456

8

2

3

456

8

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisExample F

10-1 1.0 101 1022 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 2 3 4


10-2

10-1

1.0

3

4

56

8

2

3

4

56

8

2

3

4

56

8

Nor

mal

ized

Rat

e, D

eriv

ativ

e

Agarwal Gardner Rate vs Time Typecurve AnalysisExample F

k = 8.5 mds = 0OGIP = 12 bcfM = 0.001

k = 3.1 mds = -4OGIP = 13.5 bcfIWIP = 47 MMbblPI (aq) = 0.59 bbl/d/psi

-Boundary dominated-Pressure support evident

-Gulf coast gas condensate reservoir

Transient Water DriveModel

PSS Water Drive Model

Multiple Well Analysis

1. Empirical- Group production decline plots

2. Material Balance Analysis- Shut-in data only

3. Reservoir Simulation

4. Semi-analytic production data analysis methods- Blasingame approach

Multi-well / Reservoir-based Analysis-Available Methods

Multi-well Analysis- When is it required?

1. Situations where high efficiency is required- Scoping studies / A & D- Reserves auditing

2. Single well methods sometimes don’t apply- Interference effects evident in production / pressure data- Wells producing and shutting in at different times- Predictive tool for entire reservoir is required- Complex reservoir behavior in the presence of multiple wells (multi-phase flow, reservoir heterogeneities)

Multi-well Analysis- When is it not required?

The vast majority of production data can be analyzed effectively without using multi-well methods

1. Single well reservoirs

2. Low permeability reservoirs- Pressure transients from different wells in reservoir do not interfere over the production life of the well

3. Cases where “outer boundary conditions” do not change too much over the production life of the well

- Wide range of reservoir types

Identifying Interference

q

Q Q

Well A Well B

Rate is adjusted at Well A Response at Well B

Correcting Interference Using Blasingame et al Method

A

BAtotce

qqt QQ Q +

⇒=

Define a “total material balance time” function

tce is used in place of tc to plot the data in the typecurve match

(for analyzing Well A)

Multi-Well Analysis as a Typecurve Plot

log(q/Δp)

log(tc)

tce= (QB +QA)/qA

tcA tce

MBT is corrected for interference caused by production from

Well B

Analysis of Well A:

Also applies to Agarwal-Gardner, NPI and FMB

Multi-Well Analysis- Example

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 20020.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

Oil

/ Wat

er R

ates

, bbl

/d

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

2.80

Gas

, MM

scfd

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

26000

28000

30000

32000

34000

36000

Pressure, psi

Data ChartWell 1

LegendPressureActual Gas DataPool ProductionWater Production

-Three well system-“Staggered” on-stream dates-High permeability reservoir

Aggregate production of well group

Production history of well to be analyzed

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78


10-2

10-1

1.0

101

2

3

45

7

2

3

45

7

2

3

45

7

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisWell 1


“Leaky reservoir” diagnostic

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 78


10-2

10-1

1.0

101

2

3

45

7

2

3

45

7

2

3

45

7

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisWell 1

Corrected using multi-well modelTotal OGIP = 7 bcf

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60 6.00 6.40 6.80 7.20 7.60


0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

P/Z*, psi

Flowing Material BalanceWell 1


LegendP/Z LineFlowing P/Z*


OGIP for subject well = 3.5 bcf

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60 6.00 6.40 6.80 7.20 7.60 8.00


0

200

400

600

800

1000

1200

1400

1600

1800

2000

P/Z*, psi

Flowing Material BalanceWell 1


LegendP/Z LineFlowing P/Z*

Total OGIP = 7.0 bcf

Overpressured Reservoirs

1. Analysis methods are the same as normally pressured case

2. Additional parameters to be aware of• Formation compressibility• In-situ water compressibility• Compaction effects (pressure dependent permeability)

3. Two models available, depending on required complexity• p/z* model (accounts for constant cf, cw and co in

material balance equation• Full geomechanical model (accounts for cf(p) and k(p))

Overpressured Reservoirs

Compresibilities of gas and rock

Compressibility vs. Pressure (Typical Gas Reservoir)

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

0 2000 4000 6000 8000 10000 12000

Reservoir Pressure (psi)

Com

pres

sibi

lity

(1/p

si)

gas

formation

Formation energy is critical in this regionFormation energy may be influencial in this region

Formation energy is negligible in this region

p/z* Model – Corrects Material Balance

( )ca

0

( ) 1 ( )

tt i

t f i

c q tt dtq c c p p

μμ ⎡ ⎤

⎢ ⎥⎣ ⎦

=− −∫

*

1 11 ( )

1

i

i

p

f i

p

p p Gzz c p p OGIP

p p Gzz OGIP

⎡ ⎤⎛ ⎞⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎜ ⎟⎡ ⎤ ⎢ ⎥⎝ ⎠ ⎣ ⎦⎢ ⎥⎣ ⎦

⎡ ⎤⎛ ⎞⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎣ ⎦

= −− −

= −Flowing MB

Typecurves

Geomechanical Model – Corrects Well Productivity

⎟⎠⎞

⎜⎝⎛ −+=Δ

43ln*6417.1

)(2 **

wa

e

ia

iit

ip

rr

hkTqet

GZcqpp

μ

∫=Δpi

pwfip

zpdppk

kp

μ)(2*

∫=t

ti

ita

cdtk

kct

0

* )(μ

μ

where

In the standard pressure transient equations, permeability is usually considered to be constant. There are several situations where this may not be a valid assumption:

1. Compaction in overpressured reservoirs 2. Very low permeability reservoirs in general 3. Unconsolidated and/or fractured formations

One way to account for a variable permeability over time is to modify the definition of pseudo-pressure and pseudo-time.

Pressure dependent permeability included in pseudo-pressure and pseudo-time

Overpressured Reservoirs - Example

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8


10-2

10-1

1.0

101

2

3

4

56

8

2

3

456

8

2

3

456

8

Nor

mal

ized

Rat

eBlasingame Typecurve Analysis

Gulf Coast, deep gas condensate reservoir

Boundary dominated flowOGIP = 17 bcf


June July August September October2003

0

10

20

30

40

50

60

70

80

Rat

e, M

Msc

fd

2000

4000

6000

8000

10000

12000

14000

16000

18000

Pressure, psi

History MatchRadial Model

218 Prod and Pressure Data

Good flowing pressure match,Poor shut-in pressure match

OGIP = 17 bcf

June July August September October2003

0

10

20

30

40

50

60

70

80

Rat

e, M

Msc

fd

2000

4000

6000

8000

10000

12000

14000

16000

18000

Pressure, psi

History MatchRadial Model



Good flowing pressure match,Good shut-in pressure match

OGIP = 29 bcf


0 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000

Pressure, psi(a)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

k / k

i

k (p)k (p) Permeability


LegendDefaultCustomInterpolation

Assumed permeability profile

Horizontal Wells

Horizontal Wells

Horizontal wells may be analyzed in any of three different ways, depending on

completion and petrophysical details:

1. As a vertical well,• if lateral length is small compared to drainage area

2. As a fractured well,• if the formation is very thin• if the vertical permeability is high• if the lateral is cased hole with single or multiple stage

fractures• to get an idea about the contributing lateral length

3. As a horizontal well (Blasingame model)• all others

Horizontal Wells – Blasingame TypecurvesThe horizontal well typecurve matching procedure is based on a square shaped reservoir with uniform thickness (h). The well is assumed to penetrate the center of the pay zone. The procedure for matching horizontal wells is similar to that of vertical wells. However, for horizontal wells, there is more than one choice of model. Each model presents a suite of typecurves representing a different penetration ratio (L/2xe) and dimensionless wellbore radius (rwD). The definition of the penetration ratio is illustrated in the following diagram: The characteristic dimensionless parameter for each suite of horizontal typecurves is defined as follows:

hLLD β2

=

Where is the square root of the anisotropic ratio:

v

h

kk

=β

For an input value of “L”,

L

2xe

rwa h

Plan

Cross Section

L

Lrr wa

wD2

=

Horizontal Wells – Example

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8


10-2

10-1

1.0

101

102

2

34

68

2

34

68

2

34

68

2

34

68

Nor

mal

ized

Rat

e

Blasingame Typecurve AnalysisUnnamed Well

L/2xe = 1rwD = 2e-3

Ld = 5Le = 1,968 ft

k (hz) = 0.18 mdk (v) = 0.011 mdOGIP = 1.1 bcf

Oil Wells

Oil Wells

Analysis methods are no different from that of gas reservoirs (in fact they are simpler) provided that the reservoir is above the bubble point

If below bubble point, a multi-phase capable model (Numerical) must be used

Include relative permeability effectsInclude variable oil and gas properties

Oil Wells – Example

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct2001 2002

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

Liqu

id R

ates

, bbl

/d

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

Gas

, MM

scfd

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

Pressure, psi

Data Chartexample7

LegendPressureActual Gas DataOil ProductionWater Production

- Pumping oil well- Assumed to be pumped off

Producing GOR ~ constant(indicates reservoir pressure is above bubble point


Rs input from production data,Pbp and co calculated using Vasquez and Beggs


10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8

Material Balance Time

10-2

10-1

1.0

101

2

3

456

8

2

3

456

8

2

3

456

8

Nor

mal

ized

Rat

eBlasingame Typecurve Analysisexample7

k = 1.4 mds = -3OOIP = 2.4 million bbls


2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 20220

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

Oil

Rat

e, b

bl/d

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

Pressure, psi

Numerical Radial Model - Production Forecastexample7

LegendHistory Oil RateFlow PressSyn RateHistory Reservoir PressForecasted PressForecasted Reservoir PressForecasted Rate

240 month forecastEUR = 265 Mbbls

Documents

Feketes Course Notes