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 e b Co bP Co e = -------------- (1 + bP) P where e = matrix shrinkage strain (fraction), Co = strain at infinite pressure 1/b = pressure at strain of 0.5Co (psi), P = current reservoir pressure
Palmer-Mansoori Equation Based on rock mechanics f = 1 + Cm (P-Po) + Co (K/M-1) bP bPo (1) f o f o f o 1+ bP 1+ bPo Stress-dependent Matrix shrinkage term perm term � perm increases � perm decreases with depletion with depletion (2) k/ko= (f /f o) 3 Cm = 1/M - ß (K/M + f – 1) 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 All are absolute k/ko versus Pb perms Mavor & Vaughan 100.00 datapoints are Mavor & Vaughan (1997) from 3 separate (PTA tests) wells 10.00 Zahner (1997) (PTA tests, Well B) k/ko 1.00 This line should 0 500 1000 1500 2000 be elevated Clarkson (2003) Zahner (1997) (history match) (PTA tests, Well A) 0.10 Pb (psi)
….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 The exponential curve is telling us something k/ko versus Pb important c/b=8 f =.0008 all parameters v=0.3 100.00 b=.0013 in range no stress- 10.00 perm 1.00 0 500 1000 1500 2000 k/ko 0.10 0.01 match if stress-dependent perm included We don’t see 0.00 this curve at all! 0.00 Pb (psi)
Best matches to Clarkson/Zahner Data match quality: Zahner/Clarkson data (standard model) 30 Region of 25 acceptable 20 Co/b (psi) parameters good match 15 very poor match 10 okay match 5 0 0 0.1 0.2 0.3 0.4 0.5 phio (%) Acceptable matches Dilemma? have f o = 0.1% (lower limit of range)
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 observed (delayed) at an observation well 242 ft away • Delay of buildup peaks was different from delay of 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 Shale (rigid) vertical shrinkage creates crack coal horizontal shrinkage enhances perm shale
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 • Production • Reservoir pressure • Reservoir pressure rises falls • Perm increases due • Perm decreases due to stress-dependent to stress-dependent perm perm (or does it?) • Perm drops due to • Perm increases due matrix swelling 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 of 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 Strain Stress-perm These are modeled Swelling Reservoir pressure �
Perm Change during Gas Fillup Perm ratio This results from K/Ko previous slide Virgin perm Reservoir pressure �
Porosity Change vs Pressure and Composition Porosity water ratio N2 These are modeled CH4 CO2 Reservoir pressure �
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