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Modern Production Data Analysis

Day 1 - Theory1. Introduction to Well Performance Analysis

2. Arps – Theory

a) Exponential

b) Hyperbolic

c) Harmonic

3. Analytical Solutions

a) Transient versus Boundary Dominated

Flow

b) Boundary Dominated Flow

i. Material Balance Equation

ii. Pseudo Steady-State Concept

iii. Rate Equations

c) Transient Flow

i. Radius of Investigation Concept

ii. Transient Equation (Radial Flow)

4. Theory of Type Curves

a) Dimensionless variables

b) The log-log plot

c) Type Curve matching

5. Principle of Superposition

a) Superposition

b) Desuperposition

c) Material Balance Time

6. Gas Corrections

a) Pseudo-Pressure

b) Pseudo-Time

Modern Production Data Analysis

Day 2 - Practice7. Arps – Practical Considerations

a) Guidelines

b) Advantages

c) Limitations

8. Analysis Using Type Curves

a) Fetkovich

b) Blasingame (Integrals)

c) AG and NPI (Derivatives)

d) Transient

e) Wattenbarger

9. Flowing Material Balance

10. Specialized

11. Modeling and History Matching

12. A Systematic and Comprehensive

Approach

13. Practical Diagnostics

a) Data validation

b) Pressure support

c) Interference

d) Liquid loading

e) Accumulating skin

damage

f) Transient flow regimes

14. Tutorials

15. Selected Topics and Examples

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

Welltest Analysis

- High resolution

early-time

characterization

- High resolution

characterization

of the near-

wellbore

-Point-in-time

characterization

of wellbore skin

- Estimation of

reserves when

flowing pressure

is unknown

Empirical Decline

Analysis

- 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

- Projection

of recovery

constrained

by historical

operating

conditions

Modern Production Analysis

Modern Production Analysis -

Integration of Knowledge

Arps - Empirical

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 2006

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

Gas R

ate,

MMscf

d

Rate vs TimeUnnamed Well

2001 2002 2003 2004 2005 2006

10-1

1.0

101

2

3

4

5

6

7

2

3

4

5

6

7

Gas R

ate

, M

Mscfd


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 R

ate

, M

Mscfd

Rate vs. Cumulative Prod.Unnamed Well

tDi

ieqq

log log2.302

ii

D tq q

i iq q DQ

2.302*iD SlopeiD Slope

iSlope

Dq

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 R

ate

, M

Mscfd


bi

i

tbD

qq

/1)1(

( )D f t

i b

bi

DD q

q

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 R

ate,

MMsc

fd


Mild Hyperbolic – b ~ 0

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

Gas Cumulative, Bscf

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

3.00

3.20

Gas

Rat

e,

MM

scfd

Rate vs. Cumulative Prod.NBU 921-22G

Strong Hyperbolic – b ~ 1

Analytical Solutions

Transient vs Boundary Dominated Flow

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)

Definition of Compressibility

V

pi

V

dV

pi-dp

p

V

Vc

1

Compressibility Defines Material Balance of a

Closed Oil Reservoir (above bubble point)

1 p

i

pi

t

i pss p

Nc

N p p

Np p

c N

p p m N

Note: only valid if c is constant

V=N

DV = NpDp = pi - p

Single Phase Oil MB

ip p

pN

pssmslope

ppssi Nmpp

mxy

Distance

pre

ssure

rw

Constant Rate q

1p1

Illustration of Pseudo-Steady-State

pwf1

re

2p

pwf2

2

3p

pwf3

3

time

Flowing Material Balance

pN

pssmslope

bNmpp

bmxy

ppsswfi

wfi pp

b

Steady-State Inflow Equation

Distance

pre

ssure

rw re

p

pwf

pi

Inflow (Darcy) pressure drop- Constant-

Productivity Index

),,( areaskhfb

qbpp

pss

psswf


Variable Rate

q

Np

pssmslope

pssppsswfi

bq

Nm

q

pp

bmxy

q

pp wfi

pssb

The Three Most Important Equations

in Modern Production Analysis

i pss pp p m N

wf pssp p qb

pssppsswfi qbNmpp

Constant Pressure

=

Production

Constant Rate

=

Welltest

q

pwf

q

pwf

Operating Conditions - Simplified

- Invert the PSS equation

1 1

( )

1

( )1

pss pi wf pss psspss

pss

pssi wf

pss

q

m Np p t m t bb

q

q b

mp p tt

b

Constant Rate Solution

Relate Back to Arps Harmonic

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 Np goes to Npmax

max

( )

pss

pss

mti wf b

pss

i wfp i wf t

pss

p pq t e

b

p 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 pq

b

mD

b

qN

D

c p p c p p DN

N q

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/Dp (Harmonic)

Constant pressure q/Dp (Exponential)

1

( )1

pss

pssi wf

pss

q b

mp p tt

b

( ) 1pss

pss

mt

b

i wf pss

q te

p p b

Transient Flow

-4000 -3600 -3200 -2800 -2400 -2000 -1600 -1200 -800 -400 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000

Radii, ft

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Pre

ssu

re,

psi

Cross Section Pressure Plot

Numerical Radial Model10

Cross Section

Plan View

Transient and Boundary Dominated Flow

Boundary Dominated

Well Performance =

f(Volume, PI)

Transient Well

Performance = f(k, skin,

time)

-4000 -3600 -3200 -2800 -2400 -2000 -1600 -1200 -800 -400 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000

Radii, ft

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

Pre

ssu

re,

psi

Cross Section Pressure Plot

Numerical Radial Model10

Cross Section

Plan View

948

948

inv

inv

ktr

c

ktA

c

Radius (Region) of Investigation

Transient Equation

1

( ) 141.2 1 0.0063ln 0.4045

2

i wf

t

q kh

p p B kts

c

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)

Type Curves

Blending of Transient into


0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 40 45

Complete q(t) consists of:

Transient q(t) from t=0 to tpss

Depletion equation from t = tpss and higher

Log-Log Plot: Adds a New

Visual DynamicComparison of qD with 1/pD

Cylindrical 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

an

d 1

/pD

0.9

Constant Pressure Solution Exponential


Harmonic

Infinite Acting Boundary Dominated

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

5

6

7

9

2

3

4

5

6

7

Rate

,Fetkovich Typecurve Analysis

Exponential

Harmonic

qDd

tDd

DdtDd eq

1

1Dd

Dd

qt

tDt

q

tqq

iDd

i

Dd

)(

Hyperbolic

1/

1

(1 )Dd

bDd

qbt

Plotting Fetkovich Type Curves-

ExampleWell 1 (exponential)

qi = 2.5 MMscfd

Di = 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)

Rate

(M

Mscfd

)

Well 1

Well 2

Dimensionless Plot

0.10

1.00

0.01 0.10 1.00 10.00

tDd

qD

d 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 1.00

1 2.26 8.19 0.10 0.20 0.90 0.82

2 2.05 6.70 0.20 0.40 0.82 0.67

3 1.85 5.49 0.30 0.60 0.74 0.55

4 1.68 4.49 0.40 0.80 0.67 0.45

5 1.52 3.68 0.50 1.00 0.61 0.37

6 1.37 3.01 0.60 1.20 0.55 0.30

7 1.24 2.47 0.70 1.40 0.50 0.25

8 1.12 2.02 0.80 1.60 0.45 0.20

9 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

t

tD

q

tqq

Ddi

Dd

i

)(

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

7

8

9

2

3

4

5

6

7

8

Rate

,

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 5 6 7 9 2 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 7

Time

10-2

10-1

1.0

101

2

3

4

6

9

2

3

4

6

9

2

3

4

6

9

2

3

4

6

Rate

,

Fetkovich Typecurve Analysis


Exponential

Transient Flow

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

tDd

Modeling Skin using Apparent Wellbore

Radius

rw re

rwa (s)

rwa(d)

swwa err ΔP(s)

ΔP(d)

Dimensionless Variable Definitions

(Fetkovich)

2

2

141.2 1ln

( ) 2

0.00634

1 1ln 1

2 2

eDd

i wf wa

waDd

e e

wa wa

q B rq

kh p p r

kt

ctrt

r r

r r

Type Curve Matching (Fetkovich)

2

141.2 1ln

( ) 2

0.00634 1ln

1 1ln 1

2 2

141.2 0.006342

( )

e

i wf wa Ddmatch

wwa

t Dd wae e

wa wamatch

e

i wf t Dd Dd matchmatch

B r qk

h p p r q

k t rr s

c t rr r

r r

B q tr

h p p c q t

The Fetkovich analytical typecurves can be used to calculate three parameters:

permeability, skin and reservoir radius

Type Curve Matching - Example

10-4 10-3 10-2 10-1 1.0 1012 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 2 3 4 5 6 78

Time

10-3

10-2

10-1

1.0

101

2

3

4

6

8

2

3

4

6

8

2

3

4

6

8

2

3

4

6

8

Rat

e,

Fetkovich Typecurve Analysis10


Exponential

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)

Superposition

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 periods

2. 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

1 2 1 1( ) ( ) ( )i wfp p q f t q q f t t

Two Rate History

N - Rate History

1 1

1

( ) ( )N

i wf j j j

j

p p q q f t t

f(t) is the Unit Step Response

Superposition versus Desuperposition

Simple

- Unit step response f(t)

- Type Curve

- Superposition Time

Complex

- Real rate and pressure

history

- Modeling (history

matching)

Superposition

Desuperposition

q

pwf

q

pwf

Superposition Time

Convert multiple rate history into an equivalent single rate history by re-plotting

data points at their “superposed” times

11

1

( )( )

Ni wf j j

j

N Nj

p p q qf t t

q q

The Principle of Superposition –

PSS Case

11

1

( )( )

Ni wf j j

j

N Nj

p p q qf t t

q q

141.2 3( ) ln

4

i wf e

t wa

p p t B rf t

q c N kh r

11

1

1 ( ) 141.2 3( ) ln

4

1 141.2 3ln

4

Ni wf j j e

j

N t N waj

i wf p e

N t N wa

p p q q B rt t

q c N q kh r

p p N B r

q c N q kh r

Superposition Time: Material Balance Time

Definition of Material Balance Time

(Blasingame et al)

Actual Rate Decline Equivalent Constant Rate

q

Q

actual time (t)

Q

= 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

an

d 1

/pD

0

0.2

0.4

0.6

0.8

1

1.2

Rati

o 1

/pD

to

qD

Beginning of "semi-log" radial flow (tD=25)

Ratio (qD to 1/pD) ~ 97%

0.97

Very early time radial flow

Ratio (qD to 1/pD) ~ 90%

MBT Shifts Constant Pressure to

Equivalent Constant Rate

Constant Pressure Solution qD

Corrected to Harmonic


1/pD

Harmonic

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 p

c N kh r

Depletion Term

Depends on

compressibility

Reservoir FlowTerm:

Depends on “B” and

Viscosity

Darcy’s Law Correction for Gas

Reservoirs

Darcy’s Law states : qp D

p

p

Z

pdpp

0

2

Solution: Pseudo-Pressure

For Gas Flow, this is not true because

viscosity () and Z-factor (Z) vary with pressure

Depletion Correction for Gas

Reservoirs Gas properties (compressibility 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)

Co

mp

ressib

ilit

y (

1/p

si)

pcg

1

Solution: Pseudo-Time

g

t

g

iga

c

c

dtct

,

0

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


Equation for Gas

D

4

3ln

*6417.1

)(

2

wa

ea

iig

ipwfpip

r

r

kh

Tqeqt

GZc

pppp

Pseudo-pressure Pseudo-time

Constant Rate Case

Variable Rate Case

pss

i

papb

qG

G

q

p

D

Pseudo-Cumulative Production

Overall time function - Material

Balance Pseudo-time

t

g

igta

aca

t

c

c

qdt

q

cqdt

qt

qdtq

t

00

0

1

1

0

ca

)(1

)(

t

ift

itdt

ppcc

tq

q

ct

Improved Material Balance

Pseudo-time

Overall material balance pseudo-time function (corrected for

variable fluid saturations, water encroachment, in-situ fluids & formation expansion and

desorption):

Arps – Practical Consideration

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 pressure

Water 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 April

2001 2002

4

Gas R

ate

, M

Mscfd


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 R

ate

, M

Mscfd


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

(M

Mscfd

)

0

200

400

600

800

1000

1200

Flo

win

g P

ressu

re (

psia

)

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 R

ate

, M

Mscfd


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

0.085

No

rmalized

Rate

, M

Mscfd

/(10

6p

si

2/c

P)

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

Pre

ssu

re,

psi

Data ChartUnnamed Well

LegendPressure

Actual Gas Data

Operating conditions: Low drawdown

Increasing 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 R

ate

(M

Mscfd

)

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

Analysis using Type Curves

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 typecurves are used (simultaneous typecurve match)

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

- NORMALIZED RATE (q/Dp)

- MATERIAL BALANCE TIME / PSEUDO TIME

Blasingame Typecurve Analysis-

Comparison to Fetkovich

log(qDd)

log(tDd)

log(q/Dp)

log(tca)

log(qDd)

log(tDd)

log(q)

log(t)

Fetkovich Blasingame

- Usage of q/Dp 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


Definitions

Normalized Rate

Typecurves Data - Oil Data - Gas

D

2

1ln

2.141

wa

e

Ddr

r

Pkh

qq

P

q

D

pP

q

D

dttqt

qDAt

Dd

DA

Ddi 0

1 D

D

ct

ci

dtP

q

tP

q

0

1 D

D

cat

pcaip

dtP

q

tP

q

0

1

DA

DdiDADdid

dt

dqtq

c

ic

id dt

P

qd

tP

q

D

D

ca

ip

ca

idp dt

P

qdt

P

q

D

D

Rate Integral

Rate Integral - Derivative

Q

rate

integral =

Q/t

actual rate

Q

actual

time

Concept of Rate Integral

(Blasingame et al)

actual

time

Rate Integral: Like a Cumulative

Average

Effective way to remove noise

t1

Average rate over time period

“0 to t1”

q

Average rate over time period

“0 to t2”

t2

D

D

ct

ci

dtp

q

tp

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

Derivative

Amplifying the reservoir

signal embedded in

production data

Amplifies noise -

often unusable

Agarwal-Gardner,

PTA

Integral-DerivativeMaximizing the strengths

of Integral and DerivativeCan 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


Transient CalculationsOil:

k is obtained from rearranging the definition of

2

1

r

rln

kh

2.141

p

qq

matchwa

eDd

D

2

1

r

rln

h

2.141

q

pq

k

matchwa

e

match

Dd

D

Solve for rwa from the definition of

2

1

r

rln1

r

rrc

2

1

kt006328.0t

matchwa

e

2

matchwa

e2

wat

cDd

2

1

matchwar

er

ln1

2

matchwar

er

2

1

tc

k006328.0

matchDdt

t

war c

wa

w

r

rlns


Boundary Dominated Calculations-OilOil-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

pq

pqq

D

D and

/

/

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

harmonic form:

11

1

and 1

1

D

c

t

DdDd

tNbc

b

p

q

tq

From the above equations:

NbcD

bp

q

tD

p

q

p

q

t

i

i

ci

i 1 and ,

1

ere wh

1

D

D

D

PSS equation for oil in

harmonic form, using

material balance time

Definition of Harmonic

typecurve


Boundary Dominated Calculations-Oil

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:

D

D

DdDd

c

tDd

c

Ddt

q

pq

t

t

c

pq

q

t

tc

N/1

/

1

Y-axis “match-point”

from typecurve analysis

X-axis “match-point from

typecurve analysis

bGcZ

pD

bp

q

tD

p

q

p

q

iit

ii

i

pci

i

2 and ,

1

ere wh

1

D

D

D

Blasingame Typecurve Analysis- Boundary

Dominated Calculations- GasGas-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

p

Dd tDtpq

pqq

D

D and

/

/

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

harmonic form:

1

2

1

and 1

1

D

ca

iit

ipDdDd

tbGcZ

pb

p

q

tq

PSS equation for gas in

harmonic form, using

material balance pseudo-

time

Definition of Harmonic

typecurve

From the above equations:

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

Rearranging the equation for Di:

bcZD

pG

iti

ii

2

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


Boundary Dominated Calculations- Gas

D

D

Dd

p

Dd

ca

it

i

p

Ddit

ca

Dd

ii

q

pq

t

t

cZ

p

pq

qcZ

t

t

pG

/2

)/(

2

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 tDA

format)

3. Rate vs. Cumulative Production typecurves (tDA

format)

- 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


Time TypecurvesComparison to Blasingame Typecurves

Rate Integral-

Derivative

Inv. Pressure

Integral-

Derivative

qDd and tDd

plotting format

qD and tDA

plotting fomat


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, only fluid-in-place.

Plot: qD (1/pD) vs QDA

Where (for oil):

tpp

tq

kh

Bq

wfi

D

2.141

wfi

i

wfit

DADDApp

pp

ppNc

QtqQ

2

1ely alternativor

)(2

1*

Where (for gas):



t

tq

kh

Teq

wfi

D

*6417.1

wfi

i

wfiiit

caDADDA

GZc

qttqQ

2

1ely alternativor

)(

2

2

1*



qD vs QDA typecurves

always converge to 1/2

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


q

PkhPD

2.141

D

q

PD

q

PpD

DA

DDd

td

dPP

ln

cdtd

q

Pd

q

P

ln

D

D

ca

p

i

p

td

q

Pd

q

P

ln

D

D

dttPt

PDAt

p

DA

Di 0

1

D

D ct

ci

dtq

P

tq

P

0

1

D

D cat

p

cai

pdt

q

P

tq

P

0

1

DA

DiDADid

dt

dPtP

c

i

c

iddt

q

Pd

tq

P

D

D

ca

i

p

ca

id

p

dt

q

Pdt

q

P

D

D

Conventional

Pressure Derivative

Pressure Integral

Pressure Integral -

Derivative


Diagnostics

Transient

Boundary

Dominated

Integral - Derivative

Typecurve

Normalized

Pressure

Typecruve


Calculation of Parameters- Oil

Oil - Radial

q

PkhPD

2.141

D

2

00634.0

et

c

DArC

ktt

match

D

q

P

P

hk

D

2.141

matchDA

c

t

et

t

C

kr

00634.0

matchwa

e

wq

r

re

rr

wa

w

r

rS ln

matchDA

c

match

D

t t

t

q

P

PS

CN

D

1000*615.5

2.14100634.0 0(MBBIS)

Gas – Radial

Tq

PkhP

p

D6417.1

D

2

00634.0

etii

caDA

rC

ktt

match

p

D

q

P

P

h

Tk

D

6417.1

matchDA

ca

tii

et

t

C

kr

00634.0

matchwa

e

ewa

r

r

rr

wa

w

r

rS ln

910*

6417.100634.0

match

p

D

matchDA

ca

scitii

scig

q

P

P

t

t

Pzc

TPSG

D

(bcf)


Calculation of Parameters- Gas

Transient (tD format) Typecurves

Transient typecurves plot a normalized rate against material balance time

(similar to other methods), but use a dimensionless time 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)

Transient versus Boundary

Scaling Formats

log(qDd)

log(tDd)log(tD)

log(qD)

Transient (tD format) Typecurves:

Definitions

Normalized Rate


Pkh

qqD

D

2.141

P

q

D pP

q

D

1

0

1/1

dttP

tP

DAt

p

DA

Di

1

0

1

D

Dct

ci

dtq

P

tq

PInv

1

0

1

D

Dcat

p

cai

pdt

q

P

tq

PInv

1

/1

DA

DiDADid

dt

dPtP

1

D

D

c

ic

iddt

q

Pd

tq

PInv

1

D

D

ca

i

p

ca

id

p

dt

q

Pdt

q

PInv

Inverse Pressure

Integral

Inverse Presssure

Integral - Derivative


Diagnostics (Radial Model)

Transient Transition to Boundary

Dominated occurs at

different points for

different typecurves

Inverse Integral -

Derivative

Typecurve

Normalized Rate

Typecurve


Finite Conductivity Fracture Model

Increasing Fracture

Conductivity (FCD

stems)

Increasing

Reservoir Size

(xe/xf stems)


Calculations (Radial Model)Oil Wells:

Using the definition of qD,

permeability is calculated as follows:

From the definition of tD,

rwa is calculated as follows:

Skin is calculated as follows:

/

2.141

matchDq

pq

h

Bk

D

/

2.14100634.0

matchD

c

matchDt

wa

t

t

q

pq

h

B

cr

D

)(

2.141

wfi

D

ppkh

qBq

00634.0

2

wat

cD

rc

ktt

ln w

war

rs

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:

q6.4171

p

RD

pkh

TEq

D

/6.4171

matchD

pR

q

pq

h

TEk

D

/6.417100634.0

match

D

p

matchD

caR

tii

wa

q

pq

t

t

h

TE

cr

D

ln w

war

rs

Flowing p/z Method for Gas –

Constant Rate

pG

Measured at well

during flow

Pressure loss due to flow

in reservoir (Darcy’s Law)

is constant with time

iG

i

i

z

p

wf

wf

z

p

- Mattar L., McNeil, R., "The 'Flowing' Gas

Material Balance", JCPT, Volume 37 #2, 1998

constant

wfz

p

z

p

pG

Measured at well

during flow

wf

wf

z

p

Graphical Method Doesn’t

Work!

Graphical Flowing p/z Method

for Gas – Variable Rate

iG ?

i

i

z

p

pG

Measured at well

during flow

Pressure loss due to flow

in reservoir is NOT

constant

iG

i

i

z

p

wf

wf

z

p

pss

wf

qbz

p

z

p

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

Flo

win

g P

ressu

re,

psi



LegendStatic P/Z*

P/Z Line

Flowing Pressure

Step 1: Estimate OGIP and

plot a straight line from pi/zi

to OGIP. Include flowing

pressures (p/z)wf on 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

Pro

du

cti

vit

y In

dex,

MM

scfd

/(10

6p

si

2/c

P)

0

50

100

150

200

250

300

350

400

450

500

550

Flo

win

g P

ressu

re,

psi



LegendStatic P/Z*

P/Z Line

Flowing Pressure

Productivity Index

Step 2: Calculate bpss for

each production point using

the following formula:

Plot 1/bpss as a function of

Gp

line wfpss

p p

z zb

q


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

Pro

du

cti

vit

y In

dex,

MM

scfd

/(10

6p

si

2/c

P)

0

50

100

150

200

250

300

350

400

450

500

550

Flo

win

g P

ressu

re,

psi



LegendStatic P/Z*

P/Z Line

Flowing Pressure

Productivity 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

Pro

du

cti

vit

y In

dex,

MM

scfd

/(10

6p

si

2/c

P)

0

50

100

150

200

250

300

350

400

450

500

550

P/Z

*, Flo

win

g P

ressu

re,

psi



LegendStatic P/Z*

P/Z Line

Flowing P/Z*

Flowing Pressure

Productivity Index

Step 4: Plot p/z points on the

p/z line using the following

formula:

“Fine tune” the OGIP estimate

pss

data wf

p pqb

z z

1/bpss

Specialized

Modeling and History Matching


Well / Reservoir

ModelWell Pressure at Sandface Production Volumes

Constraint (Input) Signal (Output)

Well / Reservoir

ModelProduction 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 and

AnalysisModeling and

History Matching

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

• A VITAL component of production data

analysis (and reservoir engineering in

general)

What are diagnostics?

Illustration- Typical Dataset

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

Time, days

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Liq

uid

Rate

s , b

bl/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

Mcfd

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Pre

ssu

re , p

si


Legend

Pressure

Actual Gas Data

“Face Value” Analysis of Data

OGIP = 90 bcf

Go Back: Diagnostics

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

Time, days

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Liq

uid

Rate

s , b

bl/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

Mcfd

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Pre

ssu

re , p

si


Legend

Pressure

Actual Gas Data


Legend

Pressure

Actual Gas Data

Pressures are not

representative of

bh deliverability

Correct Data Used

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

Time, 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

Liq

uid

Rates , b

bl/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

Mcfd

4600

4800

5000

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

7400

Pressu

re , p

si


Legend

Pressure

Actual Gas Data

Oil Production

Water 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

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

Blasingame Typecurve Match

Radial Model

qDd

tDd

Base Model:- Vertical Well in Center of Circle

- Homogeneous, Single Layer

Transient

(concave up) Boundary Dominated

(concave down)

Material Balance DiagnosticsDiagnostics 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

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2


Radial Model

Leaky Reservoir

(interference)

Reservoir With

Pressure Support

qDd

tDd

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

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2


Radial Model

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

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2


Radial Model

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

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2

3

5

8

2


Radial Model

Dp in reservoir is too high-Tubing size too large ?

- Initial pressure too high ?

- Wellbore correlations

underestimate pressure loss ?

Dp 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- Common Geometries

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

qD

d

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 psi

1800 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

qD

d

1/2

Infinite Acting System

Example#1 – Infinite Acting System

10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 78 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 2 3 4 5 6 7 8

Material Balance Pseudo Time

10-2

10-1

1.0

101

102

2

3

5

7

2

3

5

7

2

3

4

6

9

2

3

5

7

2

3

4

6

2

No

rmalized

R

ate

Agarwal Gardner Rate vs Time Typecurve Analysis10

10-5 10-4 10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 78 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 2 3 4 5 6 7 8


10-2

10-1

1.0

101

102

2

3

5

7

2

3

5

7

2

3

4

6

9

2

3

5

7

2

3

4

6

2

No

rmalized

R

ate

Agarwal Gardner Rate vs Time Typecurve Analysis10

k = 0.08 md

xf = 53 ft

OGIP = 10 bcf

k = 0.08 md

xf = 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

Bounded Reservoir


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

qD

d

1/2

1- Limited or no flow continuity in reservoir

- Very small drainage areas

- Very large effective fracture lengths

Commonly observed in practice

Example #2- Bounded Drainage

Areas

0

5

10

15

20

25

30

35

10 20 30 40 50 60 70 80 90 100 More

Drainage Area (acres)

Fre

qu

en

cy .

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

2

3

5

7

2

3

5

7

2

3

5

7

2

No

rmal

ized

Rat

e

Blasingame Typecurve AnalysisROBINSON 11-1 ALT

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600

xf (feet)

OG

IP (

bc

f)

.

- 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

xf independently

Establish xf sqrt

(k) product only

Linear Flow Systems


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

qD

d

1/2

- Channel and faulted reservoirs

- Naturally fractured (anisotropic) reservoirs

- Very large effective fracture lengths

- Very difficult to uniquely interpret

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

7

9

2

3

4

5

7

2

3

4

5


Fracture Model

k = 1.1 md

xf = 511 ft

ye = 5,500 ft

yw = 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

No

rmalized

R

ate


1.0 101 102 103 1042 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

10-10

10-9

10-8

2

3

4

6

8

2

3

4

5

7


Multi Layer ModelWell

- Blasingame typecurve match, using Fracture Model

- Pressure support indicated

- Three-Layer Model (one layer with very low

permeability) used, late-time match improved

Example #4- Shale Gas

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

5

6

7

9

2

3

4

5

6

7

2

3

4

5

No

rmalized

R

ate

Agarwal Gardner Rate vs Time Typecurve AnalysisWell

- Multi-stage fractures, horizontal well

- Analyzed as a vertical well in a circle

k = 0.02 md

s = -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 Profile

Recovery 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)

EU

R (

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


EU

R (

bcf

)

EUR- unlimited time

Actual EUR (qab = 0.05 MMscfd)

100% Recovery


(~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


EU

R (

bcf)

EUR- 30 year EUR- unlimited time

30 Year Limited


100% Recovery


(~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


EU

R (

bcf)

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

20 Year Limited

30 Year Limited


100% Recovery


(~10 bcf / section)

Tight Gas Recovery Profile

Recovery 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


EU

R (

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


EU

R (

bcf)

EUR- 30 year EUR- unlimited time

30 Year


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


EU

R (

bcf)


30 Year20 Year


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


EU

R (

bcf)


30 Year

Max EUR (30 y) = 2 bcf


20 Year

0.02 md reservoir,

fractured

(~10 bcf / section)

Example – South Texas, Deep

Gas Well

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

10-9

10-8

7

9

2

3

4

5

7

2

3

AG Typecurve Match

Fracture Model

Sqrt k X xf = 155

Min OGIP = 4.2 bcf

Example – South Texas, Deep

Gas WellRecovery Plot - Linear System

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600

ROI (acres)

EU

R (

bcf)

Minimum EUR = 3.5 bcf

Maximum EUR = 6.7 bcf

Recovery period = 30 years

sqrt k X xf = 155

pi = 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


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.


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


Pseudo Steady-State Model- EquationsThe Fetkovich water influx equation for a finite aquifer is:

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:

/

1

ieii

i

eie

WtJpe-pp

p

WW Initial encroachable water

Aquifer transfer coefficient

Reservoir boundary pressure

/

1 1

D

i

nn

ei

na

i

eie

WtJpep-p

p

WW

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

1

1

1

1

D

ei

n

j

ej

ia

W

W

ppn

(1)


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

G

BW

G

G

z

p

z

p

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 G

BW

G

G

z

p

z

pnn

Equations 1 and 2 are now solved simultaneously at each timestep, to obtain a discretized

reservoir pressure and water influx profile through time.

Cumulative Production

FVF at initial conditions

Gas-in-place


Transient ModelsTransient 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 plot

typecurves 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)


Definitions

Model Type: Radial Composite (two zones);

outer zone is of infinite extent

Reservoir Aquifer

aq

res

res

aq

res

aq

k

k

M

MM

Mobility Ratio (M):


Diagnostics

Increasing Aquifer Mobility

(M)

M=0 (Volumetric Depletion)

M=10 (Constant Pressure System

(approx))

Decreasing reD value


Diagnostics

M=10 (Constant Pressure System

(approx))

M=0 (Volumetric Depletion)

Decreasing reD value

Increasing Aquifer Mobility

(M)


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 discretizing the 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-Leverett equations.

Water Drive (Aquifer) Models: 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

5

6

8

2

3

4

5

6

8

2

3

4

5

6

8

No

rmal

ized

Rat

e

Blasingame Typecurve AnalysisExample F

-Boundary dominated

-Pressure support evident

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

2002 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

Pre

ssu

re,

psi

Data ChartExample F

LegendPressure

Actual Gas Data

-Gulf coast gas

condensate reservoir

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

5

6

8

2

3

4

5

6

8

2

3

4

5

6

8

No

rmalized

R

ate

, D

eri

vati

ve

Agarwal Gardner Rate vs Time Typecurve AnalysisExample F

k = 8.5 md

s = 0

OGIP = 12 bcf

M = 0.001

Transient Water Drive

Model

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

5

6

8

2

3

4

5

6

8

2

3

4

5

6

8

No

rmalized

R

ate

Blasingame Typecurve AnalysisExample F

k = 3.1 md

s = -4

OGIP = 13.5 bcf

IWIP = 47 MMbbl

PI (aq) = 0.59 bbl/d/psi

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

Well A Well B

Rate is adjusted at Well A

q

Q Q

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/Dp)

tce= (QB +QA)/qA

log(tc) 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 2002

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

Oil / W

ate

r R

ate

s,

bb

l/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

Pre

ssu

re,

psi

Data ChartWell 1

LegendPressure

Actual Gas Data

Pool Production

Water 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 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

5

7

2

3

4

5

7

2

3

4

5

7

No

rmalized

R

ate

Blasingame Typecurve AnalysisWell 1

“Leaky reservoir” diagnostic

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

5

7

2

3

4

5

7

2

3

4

5

7

No

rmalized

R

ate

Blasingame Typecurve AnalysisWell 1

Corrected using multi-well model

Total 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 Line

Flowing 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 Line

Flowing 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)

Co

mp

ressib

ilit

y (

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 dt

q c c p p

*

11

1 ( )

1

i

i

p

f i

p

p p G

zz c p p OGIP

p p G

zz OGIP

Flowing MB

Typecurves

Geomechanical Model – Corrects

Well Productivity

D

4

3ln

*6417.1

)(

2 **

wa

e

i

a

iit

ip

r

r

hk

Tqet

GZc

qpp

Dpi

pwfi

p

z

pdppk

kp

)(2*

t

ti

ita

c

dtk

k

ct

0

* )(

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

5

6

8

2

3

4

5

6

8

2

3

4

5

6

8

No

rmalized

R

ate


Gulf Coast, deep gas condensate reservoir

Boundary dominated flow

OGIP = 17 bcf


Example

June July August September October

2003

0

10

20

30

40

50

60

70

80

Rat

e,

MM

scfd

2000

4000

6000

8000

10000

12000

14000

16000

18000

Pressu

re, p

si

History Match

Radial Model218 Prod and Pressure Data

Good flowing pressure match,

Poor shut-in pressure match

OGIP = 17 bcf


Example

June July August September October

2003

0

10

20

30

40

50

60

70

80

Rat

e,

MM

scfd

2000

4000

6000

8000

10000

12000

14000

16000

18000

Pressu

re, p

si

History Match

Radial Model218 Prod and Pressure Data

Good flowing pressure match,

Good shut-in pressure match

OGIP = 29 bcf


Example

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) Permeability218 Prod and Pressure Data

LegendDefault

Custom

Interpolation

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

Where is the square root of the anisotropic ratio:

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:

L

rr

wawD

2

h

LLD

2

v

h

k

k

The characteristic dimensionless parameter for each suite of horizontal typecurves is defined as follows:

For an input value of “L”,

L

2xe

rwa h

Plan

Cross Section

L

2xe

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

3

4

6

8

2

3

4

6

8

2

3

4

6

8

2

3

4

6

8

No

rmalized

R

ate

Blasingame Typecurve AnalysisUnnamed Well

L/2xe = 1

rwD = 2e-3

Ld = 5

Le = 1,968 ft

k (hz) = 0.18 md

k (v) = 0.011 md

OGIP = 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 effects

Include 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 Oct

2001 2002

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

Liq

uid

Rate

s,

bb

l/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

Pre

ssu

re,

psi

Data Chartexample7

LegendPressure

Actual Gas Data

Oil Production

Water Production- Pumping oil well

- Assumed to be pumped offProducing 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

4

5

6

8

2

3

4

5

6

8

2

3

4

5

6

8

No

rmalized

R

ate

Blasingame Typecurve Analysisexample7

k = 1.4 md

s = -3

OOIP = 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 2022

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

Oil R

ate

, b

bl/d

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

Pre

ssu

re,

psi

Numerical Radial Model - Production Forecastexample7

LegendHistory Oil Rate

Flow Press

Syn Rate

History Reservoir Press

Forecasted Press

Forecasted Reservoir Press

Forecasted Rate

240 month forecast

EUR = 265 Mbbls

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