Well Performance Modeling in Unconventional Oil and Gas Wellsalrdc.org/workshops/2018... ·...

2018 Artificial Lift Strategies for

Unconventional Wells Workshop Cox Convention Center, Oklahoma City, OK

February 4 – 7, 2018

Well Performance Modeling in

Unconventional Oil and Gas

Wells

Adeoluwa Oyewole

Mohan Kelkar

Eduardo Pereyra

Cem Sarica

Outline

Introduction

Approach

Results

Conclusions

References

2 2018 Artificial Lift Strategies for Unconventional Wells Workshop

Oklahoma City, OK Feb. 4 - 7, 2018

Nodal Analysis



∆𝑞

𝑞𝑔 =703 𝑥 10−6 𝑘ℎ 𝑃𝑟

2 − 𝑃𝑤𝑓2

𝑇𝜇𝑧 𝑙𝑛𝑟𝑒𝑟𝑤− 0.75 + 𝑆

PSS IPR

Artificial Lift

Time

What is different for wells in

Unconventional Formations? …

When bottomhole pressure is altered, a new

transient is introduced to the well

performance

The well does not reach pseudo-steady

state for a long period of time

An instantaneous nodal analysis plot cannot

provide information about the future well

performance



Objective

Predict the performance – when the

operating conditions are altered by an

artificial lift system – of a producing well in

an unconventional formation

Simple, analytical solution to complex flow

behavior

Improve on the current methods which use

conventional well performance models for nodal

analysis



Approach

Assumptions

Analytical model

Pseudo-pressure transform

Well performance model



Assumptions

Prior performance of the well is available

By changing the tubing conditions, we do

not change reservoir properties

In general, when artificial lift method is

installed, the bottom hole pressure is

reduced



Assumptions …

An unconventional well is producing under

transient conditions (linear flow)

Linear flow constant-rate pressure transient

for slightly compressible flow 𝚫𝑷

𝒒= 𝒎 𝒕 + 𝚫𝑷𝑺𝑼



Assumptions …

Flow regime validation



100000

1000000

10000000

1 10 100 1000

∆m(p

)/q

G

Time, days

Assumptions …

Both the rate and pressure can vary

To account for variable rate and variable

pressure, we use the concept of superposition

time





Assumptions …

“Data Bias in Rate Transient Analysis of Shale Gas Wells” by Agnia (2012)

Superposition time on the

production rate

Analytical model

Linear flow constant-rate pressure transient

with superposition 𝚫𝑷

𝒒= 𝒎 𝒕𝒔𝒑 + 𝚫𝑷𝑺𝑼

Superposition time

𝒕𝒔𝒑 = 𝒒𝒊 − 𝒒𝒊−𝟏𝒒𝒏

𝒕 − 𝒕𝒊−𝟏

𝒏

𝒊=𝟏



Analytical model …

Non-linear change in fluid properties with

pressure

Pseudo-pressure transformation for

Gas production

Multiphase oil & gas production



Pseudo-pressure transform …

Real gas pseudo-pressure

𝒎 𝑷 = 𝟐 𝑷

𝝁𝒈𝒛

𝑷

𝟎𝒅𝒑

𝝁𝒈, 𝒛 = 𝒇(𝑷)

𝒎 𝑷 = 𝒇(𝑷)




In conventional oil wells, gas-oil-ratio (GOR)

behavior is dependent on average reservoir

pressure

For unconventional oil wells, GOR behavior

is a strong function of well flowing pressure

GOR trend also depends on flow regime,

fracture properties, and degree of under-

saturation






SPE 184397 “Producing-Gas/Oil-Ratio Behavior of Multifractured Horizontal Wells in Tight Oil Reservoirs” by R. Steven Jones Jr.


Pwf < Pb

Multiphase (oil + water + gas) flow

2-phase pseudopressure (oil + gas)

Fetkovich (1973)

𝒎 𝑷 = 𝒌𝒓𝒐(𝒑)

𝝁𝒐𝑩𝒐

𝑷𝒊𝑷𝒘𝒇

𝒅𝒑

𝒌𝒓𝒐 = 𝒇(𝑺𝒐)

𝒎 𝑷 = 𝒇(𝑷, 𝑺𝒐)






0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300 350

GO

R, S

CF

/ST

B

Time, days

0

1000

2000

3000

4000

5000

0 50 100 150 200 250 300 350

Pw

f, p

sia

Time, days

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.3 0.5 0.8 1.0

krg

kro

So

GAS/OIL

Core Rock and Fluid Properties

(Swir, Sor , Sgc , …)

Corey (1976) 2-phase relative

permeability equations

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.3 0.5 0.8 1.0

krw

kro

Sw

WATER/OIL

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.3 0.5 0.8 1.0

krw

krg

Sw

GAS/WATER

LOOK-UP TABLES




Constant Composition Expansion (CCE)

𝑘𝑟𝑔

𝑘𝑟𝑜= 𝐺𝑂𝑅 − 𝑅𝑠 ∗

𝜇𝑔𝐵𝑔

𝜇𝑜𝐵𝑜

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.3 0.5 0.8 1.0

krg

kro

So

GAS/OIL

CCE

Assumptions

Conventional Unconventional

Fixed compositon in

multiphase region Constant GOR in

transient linear flow

GOR = f(So) @

Pwf = Pavg

Pwf has greater

effect on GOR

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000

So

Pwf, psia

PRESSURE – SATURATION RELATIONSHIP


Two-phase pseudo-pressure

𝒎 𝑷 = 𝒌𝒓𝒐𝝁𝒐𝑩𝒐

𝑷𝒊

𝑷𝒘𝒇

𝒅𝒑



Pwf

BAKER (1988) 3-PHASE OIL

RELATIVE PERMEABILITY

EQUATION So kro

𝝁𝒐, 𝑩𝒐

PRESSURE-SATURATION

RELATIONSHIP

PVT CORRELATIONS

Well performance model

Model equation

𝚫𝑷

𝒒= 𝒎 𝒕𝒔𝒑 + 𝚫𝑷𝑺𝑼

𝚫𝒎(𝒑)

𝒒= 𝒎 𝒕𝒔𝒑 + 𝚫𝒎(𝒑)𝑺𝑼

Obtain coefficients defining the past well

performance Slope, m

Intercept

Match past well performance

𝚫𝒎(𝒑)

𝒒= 𝒎 𝒕𝒔𝒑 + 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕





Well performance model …

When the bottomhole pressure is changed,

the new rate is calculated by assuming a

new transient in the well is introduced

0

2500

5000

7500

10000

0 500 1000 1500 2000

q o

il o

r g

as

Time

𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛



Well performance model …

Forecast future performance

𝒒 =∆𝒎 𝒑 −𝒎( 𝒒𝒊−𝒒𝒊−𝟏 𝒕𝒏−𝒕𝒊−𝟏 − 𝒒𝒏−𝟏 𝒕𝒏−𝒕𝒏−𝟏

𝒏−𝟏𝒊=𝟏 )

𝒎 (𝒕𝒏−𝒕𝒏−𝟏)+𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕



Results

Gas well example

Oil well example



Gas well example

Initial Reservoir Pressure = 5,000 psi

Bottomhole Temperature = 160 deg. F

Gas Gravity = 0.567

0

400

800

1200

1600

2000

0

800

1600

2400

3200

0 200 400 600

qW

, b

pd

qG, M

scfD

Time, Days

qG - MscfD qW - bpd

0

2000

4000

6000

0 200 400 600 800

Pw

f, p

sia

Time, Days



Gas well example …

100000

1000000

10000000

1 10 100 1000

∆m(p

)/q

G

Time, days




0

300000

600000

900000

1200000

1500000

1800000

0 5 10 15 20 25 30 35 40 45

∆m(p

)/q

G

√tSUP

Slope, m

Intercept




𝜟𝒎(𝒑)


0

1000

2000

3000

4000

0 100 200 300 400 500 600

qG, M

scfD

Time, Days

qG - Well Data qG - Superposition Fit

0

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800 900

qG, M

scfD

Time, Days

qG - Well Data qG - Model Forecast




Artificial Lift

at ~ 780 days

𝒒 =∆𝒎 𝒑 −𝒎( 𝒒𝒊 − 𝒒𝒊−𝟏 𝒕𝒏 − 𝒕𝒊−𝟏 − 𝒒𝒏−𝟏 𝒕𝒏 − 𝒕𝒏−𝟏

𝒏−𝟏𝒊=𝟏 )

𝒎 (𝒕𝒏 − 𝒕𝒏−𝟏) + 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕





𝒏−𝟏𝒊=𝟏 )


0

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800 900

qG, M

scfD

Time, Days

qG - Well Data qG - Model Forecast



Oil well example

Initial Reservoir Pressure = 6318 psi.

Bottomhole Temperature = 207 deg. F

Gas Gravity = 0.65

Oil API = 45 deg.

0

1000

2000

3000

4000

0

400

800

1200

1600

2000

0 20 40 60

qG, M

scfD

qO, st

bD

Time, Days

qO - Well Data qG - Well Data

0

2000

4000

6000

8000

0

1000

2000

3000

4000

5000

0 10 20 30 40

Pw

f, p

sia

GO

R,

scf/

stb

Time, Days

GOR Pwf Bubble Point Pressure



Oil well example …

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

krg

kro

Sg

krg kro

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

krw

kro

Sw

kro krw

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

krw

krg

Sw

krw krg

0.0

0.3

0.5

0.8

1.0

0.0

0.3

0.5

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

krg

kro

Sg

krg kro

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000

Oil

Sa

tura

tio

n,

So

Pwf, psia




Constant Composition Expansion (CCE)

𝒌𝒓𝒈

𝒌𝒓𝒐= 𝑮𝑶𝑹− 𝑹𝒔 ∗

𝝁𝒈𝑩𝒈

𝝁𝒐𝑩𝒐




0.1

1

10

1 10 100

∆m(p

)/q

O

Time, days




0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10

∆m(p

)/q

O

√ tsup

Slope, m

Zero-Intercept




𝜟𝒎(𝒑)


0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40

qO, st

bD

Time, Days

qO - Well Data qO - Superposition Fit





𝒏−𝟏𝒊=𝟏 )


0

500

1000

1500

2000

2500

0 10 20 30 40 50 60 70 80

qO, st

bD

Time, Days

qO - Well Data qO - Model Forecast



Conclusions

Traditional nodal analysis methods do not

accurately predict the transient performance

of unconventional wells

Rigorous and simple analytical method is

proposed based on readily-available field

data using the superposition principle



Conclusions …

In summary, the developed model

Captures past well performance by

assuming the well is producing under

transient linear flow for reasonable period

Matches past well performance with

superposition to determine coefficients

used to predict the future performance

Future performance is predicted under

existing or changing conditions



References

Baker, L. E. (1988, January 1). Three-Phase Relative Permeability Correlations. Society

of Petroleum Engineers. doi:10.2118/17369-MS

Corey, A.T., Rathjens, C.H., Henderson, J.H. and Wyllie, M.R.J.: "Three-Phase Relative

Permeability," J. Pet. Tech. (Nov. 1956) 8, 63-65; Trans .• , AIME (1956) 20i, 349-351.

Fetkovich, M. J. (1973, January 1). The Isochronal Testing of Oil Wells. Society of

Petroleum Engineers. doi:10.2118/4529-MS.

Jones, R. S. (2016, August 1). Producing Gas-Oil Ratio Behavior of Tight Oil Reservoirs.

Unconventional Resources Technology Conference. doi:10.15530/URTEC-2016-

2460396

Shahamat, Mohammad Sadeq, S. Hamed Tabatabaie, Louis Mattar, and Ehsan

Motamed. "Inflow Performance Relationship for Unconventional Reservoirs (Transient

IPR)." Inflow Performance Relationship for Unconventional Reservoirs (Transient IPR) -

OnePetro. Society of Petroleum Engineers, 20 Oct. 2015.

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