Geomechanics and Permeability Changes Ian Palmer Higgs - - PowerPoint PPT Presentation

Geomechanics and Permeability Changes

Ian Palmer Higgs Technologies, Houston 28 October 2004

Matrix shrinkage/swelling: can think of as due to temperature change

Matrix Shrinkage/Swelling

Co bP e = -------------- (1 + bP) where e = matrix shrinkage strain (fraction), Co = strain at infinite pressure 1/b = pressure at strain of 0.5Co (psi), P = current reservoir pressure

e P Co b

Palmer-Mansoori Equation

f = 1 + Cm (P-Po) + Co (K/M-1) bP bPo (1) f o f o f o 1+ bP 1+ bPo

k/ko= (f /f o)3

(2)

Cm = 1/M - ß (K/M + f – 1)

Stress-dependent perm term perm decreases with depletion Matrix shrinkage term perm increases with depletion Based on rock mechanics

Co, b = parameters of volumetric strain change due to desorption (depletion) Co = strain at infinite pressure 1/b = pressure at strain of 0.5Co (psi)

Other Models

• Shi and Durucan:

– based on rock mechanics – same equation – only difference is in (K/M -1) term in shrinkage

• ARI:

– based on empirical shrinkage depletion coefficient, instead of rock mechanics – same equation

Contents

• Production modeling and dilemmas

(interpretation was clean 8 years ago, now messy)

• Injection modeling and results

(interpretation appears to be clean)

• Way forward

Production Dilemmas

• Perm increases in San Juan basin are very large

(by 10-100x)

• Can be matched by Palmer-Mansoori model,

but……

• Have to remove stress-dependent perm effect (a

dilemma!)

• Also, initial porosities are VERY small (=0.1%),

and at lower limit of acceptable range (another dilemma?)

• If can’t explain these dilemmas, may have to

consider alternate models for perm increases due to depletion

Summary of San Juan Fairway Data

k/ko versus Pb

0.10 1.00 10.00 100.00 500 1000 1500 2000 Pb (psi) k/ko

Zahner (1997) (PTA tests, Well B) Clarkson (2003) (history match) Mavor & Vaughan (1997) (PTA tests) Zahner (1997) (PTA tests, Well A)

Mavor & Vaughan datapoints are from 3 separate wells This line should be elevated All are absolute perms

….contd

• No perm decrease is evident in data
• Even though P-M theory generally predicts such

a decrease at early times, due to stress- dependent permeability

• Possible explanations:

– early time data missed – perm rebound point > Po (this is case for M&V data, but not rest of data) – perm decrease predicted by stress-dependent perm is inhibited by asperities (ie, roughness) in cleats, preventing cleats from closing as reservoir pressure is decreased

One Match to Zahner/Clarkson Data: blue dashes

k/ko versus Pb

0.00 0.00 0.01 0.10 1.00 10.00 100.00 500 1000 1500 2000 Pb (psi) k/ko

c/b=8 f =.0008 v=0.3 b=.0013 no stress- perm

match if stress-dependent perm included

all parameters in range

The exponential curve is telling us something important We don’t see this curve at all!

Best matches to Clarkson/Zahner Data

match quality: Zahner/Clarkson data (standard model)

5 10 15 20 25 30 0.1 0.2 0.3 0.4 0.5

phio (%) Co/b (psi)

very poor match good match

• kay match

Region of acceptable parameters Acceptable matches have f o = 0.1% (lower limit of range) Dilemma?

Dilemmas

• Majority of data are consistent with exponential

increase of permeability with depletion. No perm decreases are evident

• Cannot match exponential perm increase data of

Zahner/Clarkson using the full P-M equation (including the stress-perm effect), because prediction is too concave upwards, and abnormally strong matrix shrinkage would be required to “straighten out” the curve

• Can match the data by omitting the stress-perm effect:

this could be due to cleats unable to close during depletion, because of asperities (ie, roughness between cleat surfaces).

• Other dilemmas: initial porosities are small (=0.1%), and

at lower limit of acceptable range of 0.05 – 0.5%. Also, matrix shrinkage values are on low side of the acceptable range: b =0.0017 /psi compared with range of 0.0013 - 0.0033 /psi, and Co is low in proportion to b.

Stress-Dependent Permeability in Lab: It does Exist!

Stress-Dependent Permeability in Field: It does Exist!

• In San Juan basin, a set of cavity surges was
• bserved (delayed) at an observation well 242 ft

away

• Delay of buildup peaks was different from delay
• f blowdown troughs
• Different delays imply different permeabilities
• Buildup perms > blowdown perms
• Agrees with stress-dependent perm (but

stronger than lab measurements)

Surges at Cavity Well and Observation Well

Other Mechanisms to Explain Exponential Increase in Perm with Depletion

• Matrix shrinkage leads to a horizontal fracture, which grows with

time, and dominates gas production

• Differential depletion: need to use average perm and average

pressure (two or more seams)

• A non-Langmuir shape governs the matrix shrinkage vs pressure
• DOES NOT APPEAR to be due to rel perm changes
• CANNOT be due to concentration of CO2 increasing over time in the

produced gas stream

• CANNOT be due to new coal failure induced by matrix shrinkage, as

Mavor and Vaughan have suggested

• CANNOT be resolved by replacing stress-perm term by exponential

term, as seen in lab

Mechanism 1 (maybe)

• Matrix shrinkage tends to open up (widen)

existing vertical cleats.

• Bulk shrinkage also occurs in vertical direction,

but there are no horizontal cleats

• Vertical compaction occurs, creating an interface

crack under a rigid shale (eg, caprock)

• This acts like a horizontal fracture, and it will

grow with depletion

Interface Crack caused by Shrinkage & Compaction

coal shale Shale (rigid) horizontal shrinkage enhances perm vertical shrinkage creates crack

Mechanism 2 (less likely)

• Differential depletion: two or more coals
• Coal with higher perm will deplete faster. In the Clarkson

data, perm increase comes from average perm calculated from total production

• If two coals are contributing, this average perm should

be tied to an average of the two depleted pressures, when creating the plot of k/ko vs P. In practice, lowest reservoir pressure was used

• This will act to bend the true perm increase curve

downwards at larger depletions. This may straighten a true perm increase curve that was concave

• But the perm increase of Zahner is exponential, and

derived from PTA tests (also may be “contaminated” by rel perm effects)

• Need to evaluate this mechanism further

Mechanism 3 (unlikely)

• A non-Langmuir shape governs the matrix

shrinkage vs pressure

• Using b/2 in place of b in P-M model gives

a better match to Zahner/Clarkson exponential data than any match with the standard model

• We know of no physical justification for

this

Summary

• Majority of data are consistent with exponential

increase of permeability with depletion. No perm decreases are evident

• Cannot match exponential perm increase data of

Zahner/Clarkson using the full P-M equation (including the stress-perm effect), because prediction is too concave upwards, and abnormally strong matrix shrinkage would be required to “straighten out” the curve

• Can match the data by omitting the stress-perm effect:

this could be due to cleats unable to close during depletion, because of asperities (ie, roughness between cleat surfaces).

• Other dilemmas: initial porosities are small (=0.1%), and

at lower limit of acceptable range of 0.05 – 0.5%. Also, matrix shrinkage values are on low side of the acceptable range: b =0.0017 /psi compared with range of 0.0013 - 0.0033 /psi, and Co is low in proportion to b.

Injection vs Production

• Injection
• Reservoir pressure

rises

• Perm increases due

to stress-dependent perm

• Perm drops due to

matrix swelling

• Production
• Reservoir pressure

falls

• Perm decreases due

to stress-dependent perm (or does it?)

• Perm increases due

to matrix shrinkage

Application to Greenhouse Gas Sequestration

• Same physics of stress-dependent permeability and

matrix shrinkage should control reservoir performance during injection of gases such as CO2

• But during injection, we expect stress-perm effect to be

fully active, while during production it appears to be suppressed

• Parameters derived from our matches may be useful as

starting points for injection modeling, prediction, and history matching in San Juan basin

• Eg, initial porosities are small (=0.1%), and at lower limit
• f acceptable range of 0.05 – 0.5%.

Mavor Formulation and Application to Canada Coals

• Based on P-M equation
• Adapted to injection
• Generalized to multi-component gas

compositions, often changing with time

• Extended to rel perms
• Modeled perm changes due to injection, soak,

production

• Calibrated model using injections/falloff tests of

(1) water or WAG and (2) SAG

• Forecast injection performance for gas

sequestration

Strains Induced during Gas Fillup

Reservoir pressure Strain

Stress-perm Swelling These are modeled

Perm Change during Gas Fillup

Reservoir pressure Perm ratio K/Ko

Virgin perm This results from previous slide

Porosity Change vs Pressure and Composition

water N2 CH4 CO2

Reservoir pressure Porosity ratio

These are modeled

Constrained Axial Modulus M

• Can be found from lab testing on cores

small-scale value

• Can be found by matching model to

injection and falloff periods separately large-scale value

• Large-scale M was at low end of range of

lab values (encouraging)

Supports model!

Injectivity Changes during CO2 Injection

• Saw no injectivity loss during CO2

injection

• Agrees with stress-perm effect > swelling

effect

Supports model!

Calibrated Perm vs Pressure at FBV 4A Well

Reservoir pressure

Absolute permeability Perm before CO2 injection Perm after CO2 injection Initial res pressure

3.66 md 0.98 md

After calibrating full model to field data

How do we Know if the Formulation is Right?

• Method iterates until it converges to a solution: there are

enough knobs to always get a solution

• If the physics is wrong, the solution will be wrong
• It appears to be wrong for production: can it be that

much wrong for injection?

• Does it matter for injection? We are matching a series of

injections/falloffs/productions by a basic perm change

• equation. Then extending to a longer-term forecast of

injection performance

• It may be like history matching production in

conventional oil & gas: the rel perms can be in error, but we can get a match. Then the forecast of production may be okay in the short term, but it may err substantially in the long term

• So its important to get the physics right for long-

term forecasting of gas sequestration

What if Perm Change Prediction is Wrong?

Reservoir pressure

Absolute permeability Perm before CO2 injection Perm after CO2 injection Initial res pressure

3.66 md 0.98 md

What if its not like this? But if it is like this? Long-term forecast could have quite an error

Way Forward

• Production dilemmas need to be resolved, to boost

confidence in injection predictions (if we don’t have the physics right here, it won’t be right for injection)

• Confirm existence or suppression of stress-dependent

perm during coalbed methane production. If this exists we have to examine alternate models for perm increase during depletion

• Explore interface crack proposition during production
• Perform lab tests to confirm Palmer-Mansoori equation
• Add error bars to injection predictions, based on rock

mechanics variability (include scale-up from core to field)

• Evaluate if coal failure can occur during

injection…..could alter permeability

The End