0403

Permeability Changes in a CBM Reservoir During Production: an Update and Implications for CO2 Injection

By Ian Palmer (Higgs Technologies LLC)

Abstract: A simple analytic model, based on rock mechanics, has been published previously for how permeability changes at late times in a coalbed methane production well (the Palmer-Mansoori or P-M model). The model includes perm decrease due to stress-dependent permeability, and perm increase due to matrix shrinkage as gas desorbs from the coal during depletion. The model has previously explained perm increases measured in production wells in the field. It has also recently been used to model gas injection during CO2 sequestration studies. A new set of permeability data from the San Juan basin have been compiled. Remarkable increases in absolute permeability are observed with depletion (by 10-100 times) in the San Juan basin fairway. The data are consistent with an exponential increase of permeability with depletion. The exponentials define quite naturally a fractional increase in permeability per unit depletion increase, which ranges from 0.23 to 0.36 % /psi. We can match the new data using the P-M model, but only by omitting the stress-dependent permeability effect. This is a bit of a dilemma, although to some extent cleats may be inhibited from closing during depletion (because of asperities or roughness between cleat surfaces). If this lack of stress-perm effect cannot be rationalized, we will be forced to consider alternate models for exponential permeability increases during depletion. Possible alternate models are discussed. According to the better matches we have obtained, using all data, initial porosities are generally small (≤0.1%), and at the lower limit of the acceptable range of 0.05 – 0.5%. Again, if these porosities cannot be confirmed, we may have to consider alternate models for perm increases due to depletion. The insights gained from this work, in attempting to predict more reliably permeability increases in CBM production wells, have application to CO2 sequestration where the same physics of stress-dependent perm and matrix shrinkage is expected to control reservoir performance. Introduction: A simple analytic model, based on rock mechanics, has been published for how permeability can increase at late times in a CBM well (Palmer and Mansoori, 1998, hereinafter referred to as P-M). The model includes perm decreases due to stress-dependent permeability, and perm increases due to matrix shrinkage as gas desorbs from the coal. The model has successfully explained perm increases measured in production

wells in the field (Mavor and Vaughn, 1997). Other San Juan basin observations of perm increases have been published by Zahner (1997), and by Clarkson and McGovern (2003). In fact Clarkson (2004) reported that the P-M theory successfully explained perm increases in San Juan wells, within the ranges of parameters given with the P-M theory. The P-M theory has also been used to model gas injection during CO2 sequestration studies (Law et al, 2003; Mavor, 2004). Pekot and Reeves (2003) have compared the P-M model with their ARI model, used in the Comet simulator. The two models are essentially equivalent in saturated coals, and where the strain function is proportional to the isotherm function. For unsaturated coals, the ARI model has perm decreasing more initially, before reaching the saturation point. Qsi and Durucan (2003a,b) have followed the Palmer-Mansoori model in their formulation of porosity changes with depletion. They included both stress-dependent permeability and matrix shrinkage terms. The formulation differs from Equation (1) below only by the constant (K/M-1) in the matrix shrinkage term (they find –K/M). To reconcile this difference would require further study. The authors have matched the “boomer” fairway well presented in P-M, and obtained initial porosity of 0.085%, which is generally similar to the low porosities we find below in this paper. They have also matched the three wells of Mavor and Vaughan separately, as we have done below. They found consistency in the coal mechanical parameters between the boomer well match, and the Mavor and Vaughan matches. In addition, they elaborated the distinction that Mavor and Vaughan presented: that if initial reservoir pressure is high enough, a theoretical permeability rebound should occur, but if its not high enough a perm rebound may NOT occur, just an increase of perm with depletion right from the start. The Palmer-Mansoori theory: From Palmer and Mansoori (1998), the porosity increase is given by: φ = 1 + Cm (P-Po) + Co (K/M-1) bP bPo (1)

φo φo φo 1+ bP 1+ bPo

k/ko = (φ/φo)3 (2)

Cm = 1/M - β (K/M + f – 1)

The term with Cm is the stress-dependent permeability term. M is the constrained axial modulus, and is a function of E and v (see Palmer & Mansoori, 1998). The term with Co is the matrix shrinkage term. The meaning of the symbols is given at the end of the paper. Permeability increases in the field induced by depletion: Most of the observations are from the San Juan basin, where wells have depleted more than in other basins. However, one observation comes from the Raton basin: at a spacing hearing before the COGCC, Evergreen presented reservoir simulations of their Raton

coal wells. To match well productivity with the simulator, permeability increase with depletion was necessary (Onsager 2003). The following data points issue from the San Juan basin: Mavor and Vaughan (1997) measured perm increases by PTA in three Valencia Canyon wells, in the far north-western end of the fairway. These wells are shallower, and initial reservoir pressures are <1,000 psi. Absolute permeabilities were estimated from PBU tests after significant depletion, and these were greater than obtained from initial openhole drillstem tests (DSTs). They found a good match by the P-M theory, if they used matrix shrinkage values measured by Levine (1996). This is shown in Figure 1. The pressure ratio is just the reservoir pressure at the time the test was done, divided by the initial reservoir pressure at that well.

Figure 1: Perm increase in Valencia Canyon wells from PTA tests. Zahner (1997) discusses two PBU tests in well A at 2740 ft, where initial reservoir pressure Po = 822 psi (0.30 psi/ft). This is unusually low for the fairway, and probably represents a depleted region of the fairway, since this well was drilled in 1992. The well is in the Cedar Hill field. Initial perm was 19 md and skin of 5.8, increasing to 124 md and skin of 0.8 md after 5 years, when Po has dropped to ~300 psi. The perm has increased by a factor of 6.5 after ~522 psi of depletion. Although not stated, we assume this perm increase has been corrected for rel perm effects, as it appears from Figure 4 to

be consistent with other perm increases that represent increases in absolute perm. In addition, while the reservoir pressure falls from 822 to ~300 psi, Zahner has the water saturation Sw decreasing from 0.67 to 0.48 (see his Figure 6), and this would only give a factor of ~2 increase in gas perm based on rel perm effects (using the typical rel perm curves of Gash, 1991). The perm increase measured by PBU tests is much greater: a factor of 6.5. Zahner also includes a plot of perm increasing with depletion (Figure 2 here), where Po = 1600 psi (0.51 psi/ft) at a depth of 3166 ft. This curve appears to be mislabeled as well A in the paper, based on the pressure range of the PBU tests, but it could be well B. The perm has increased by almost 20 times after a depletion of 1200 psi. The context of the paper implies that this is an increase in absolute perm which is added as a lookup table to the reservoir simulator, not just a change due to rel perm effects.

Figure 2: Perm increasing with depletion from PBU tests in San Juan basin well (after Zahner, 1997). Clarkson and McGovern (2003) describe a perm increase with depletion, as shown by Figure 3. This is an average curve representing multiple wells in the Fruitland Coal Fairway, not a single well. The curve was started at an advanced level of depletion (600 psi), because prior to this, it was difficult to separate out the effect of relative permeability on perm growth (the well was still dewatering). The increase of effective perm to gas was actually modeled above 600 psi, but the effects of rel perm and absolute perm growth were not separated because the wells were experiencing rapid changes in water saturation (dewatering). Below 600 psia, changes in water saturation were relatively slow, and most of the perm increase can be attributed to matrix shrinkage

effects. Note: the relative permeability curves would have to be known exactly to back out absolute perm increase above 600 psi, and this is difficult. Complicating the matter further, the increases in cleat aperture would affect water saturations as well.

Figure 3: Perm increase multiplier used in history match (after Clarkson & McGovern, 2003)

k/ko versus Pb

0.10

1.00

10.00

100.00

0 500 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)

Figure 4: Examples of increasing perm from the San Juan basin, plotted against average reservoir pressure. Figure 4 summarizes all this field data. Observations that can be made from Figure 4:

Perm increases are by factors of 10-100 in the San Juan basin fairway. These are phenomenal perm increases, and have no precedent in the oil and gas industry! If perm increases like these can be forecast for prospective CBM plays, this clearly would increase their value. Permeabilities that are marginal under current economics may become Cinderellas after depletion occurs. Note that the Clarkson curve on the far left does not have k/ko starting at initial reservoir pressure (because Po in the fairway is typically >1,000 psi). This almost certainly means this curve underestimates the full perm increase, defined relative to the true initial reservoir pressure. If relative to true Po, these curves started at k/ko = 2 or 5 (instead of 1), they really should be replotted as elevated lines in Figure 4, but with their slopes unchanged (we have actually done this in Figure 5).

•

• Most of the curves in Figure 4 are linear, and are reasonably consistent. The exception is the perm increase of Mavor and Vaughan (1997). The three upper points on the Mavor and Vaughan curve bend upwards away from the linear trend. Note however that each point represents a PTA test in a different well, and Po is different for each well due to reservoir dip (Po ranges from 776 to 957 psi). In Figure 5, each well is plotted separately, using data from Tables 1, 2 of Mavor and Vaughan. If the perm increase depends on Po (as it does in the P-M theory), there is justification for this. It appears the upward bend in Figure 4 may be an artifact of fitting all 3 data points by a single curve. What is also striking in Figure 5 is that the slope in two of the wells is almost identical with the slope in Zahner well A, which in turn is consistent with the slopes in the remaining curves in

Figure 4. Note: the outlier in Figure 5 is the VC 32-1 well, where the PTA test was restricted to the intermediate seams, whereas all other tests included the basal seams. In summary, we can argue that all the results of Figures 4 and 5 are consistent with an exponential increase of perm with depletion (ie, linear on a log-linear plot).

•

•

The slopes of the straight lines in the log-linear plot of Figure 4 define quite naturally a fractional increase in permeability per unit depletion increase. These are given in Table 1, and range from 0.23 to 0.36 % /psi. No permeability decrease is evident in the data of Figure 4, even though the P-M theory generally predicts such a decrease at early times, due to stress-dependent permeability. Possible explanations are:

o The Clarkson curve begins late, after significant depletion has already occurred. Thus any perm decrease, which would show up at early times, would have been missed (some perm increase may have been missed also).

o For the Mavor & Vaughan curve, the pressure when k/ko is a minimum as predicted by the P-M theory (ie, the rebound pressure) lies ABOVE the initial reservoir pressure of 964 psi, and so the perm trend with depletion can only be upwards (as pointed out by Mavor & Vaughan, 1997). This may not be true for the Zahner and Clarkson curves, for which Po = 1450 -1600 psi.

o The perm decrease predicted by stress-dependent permeability is inhibited by asperities (ie, roughness) in cleats, preventing the cleats from closing as reservoir pressure is decreased.

o Puri and Seidle (1991) argue that the major effect of stress-dependent permeability occurs very soon after a well is brought on line, and it becomes too subtle an effect to see after that. However, it has been inferred from delays in pressure surges seen in an observation well close to a cavity well (Palmer et al, 1995)

o It cannot be due to relative permeability changes, since the measurements in Figure 4 are from PTA tests (except for the Clarkson curve), and rel perm effects have apparently been accounted for (see discussion above).

k/ko versus Pb (Mavor & Vaughan)

1

10

0 200 400 600 800 1000 1200

Pb (psi)

k/ko Zahner (1997)

Well A

Figure 5: Perm increases from 3 wells of Mavor & Vaughan (1997), plotted separately, and from Well A of Zahner (1997). Table 1: Fractional increase in permeability per psi of depletion. Data % increase in perm/psi of

depletion Initial reservoir pressure (psi)

Zahner (Well B) 0.24 1600 Clarkson (2003) 0.29 1450 Zahner (Well A) 0.36 822 Mavor & Vaughan (Well 29-4) 0.34 776 Mavor & Vaughan (Well 32-4) 0.36 930 Mavor & Vaughan (Well 32-1) 0.23 957 Comparison with the P-M model: Figure 6 is a replot of Figure 4, where we have raised the Clarkson curve upwards. This is done by boosting ko at P = 600 psi by a factor of 12. This projection is based on (1) observing that the slopes of the Clarkson curve match that of Zahner Well B, and (2) noting the new Clarkson curve extrapolates to Po ~1450 psi, which was the initial reservoir pressure in this part of the San Juan fairway (Clarkson, 2004). During the

depletion time from Po ~1450 psi to P ~600 psi, the rel perm to gas behavior was modeled by an increase from <0.1 to 1.0. This means the effective perm to gas increased by a factor of >10, for a constant absolute virgin permeability. However the virgin perm may also have increased during this depletion (eg, due to matrix shrinkage), and may be a part of the effective gas perm increase. Although it is difficult to separate these two effects, it appears the boost factor of 12 (increase in ko at 600 psi) is not out of line in Figure 6. Even though there could be a significant error bar in the upraised Clarkson curve of Figure 6, it is consistent with an extension of the Zahner data to lower reservoir pressures. The other two curves to the left in Figure 6 correspond to lower initial reservoir pressures: Po ~900 psi compared with 1450-1600 psi for Zahner Well B and Clarkson.

k/ko versus Pb

1.00

10.00

100.00

0 500 1000 1500 2000

Pb (psi)

k/ko Zahner (1997)(PTA tests, well B)

Mavor & Vaughan (1997) (PTA tests)

Clarkson: k/ko multiplied by 12

Zahner (1997) (PTA tests, well A)

Figure 6: Replot of Figure 4, with Clarkson curve projected back to initial Po, and Mavor & Vaughan curve separated into three wells. We show in Figure 7a one match by the P-M theory, superimposed on the Zahner/Clarkson data points of Figure 6. The full equation (1) gives the vertical crosses in Figure 7a, and is not a match to the data. It is impractical to match the Zahner/Clarkson data using the full equation, because the prediction tends to be concave, rather than linear, and an abnormally strong matrix shrinkage effect would be required to “straighten out” the curve. However, when the stress-perm term is omitted from equation (1), we can get a good match, as shown by the blue dashes in

Figure 7a. We have justified this by arguing above that asperities in the cleats may restrict them from closing.

k/ko versus Pb

0.00

0.00

0.01

0.10

1.00

10.00

100.00

0 500 1000 1500 2000

Pb (psi)

k/ko

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

Figure 7a: One match (see blue dashes) of Zahner/Clarkson data by P-M theory (no stress-perm effect). The match of Figure 7a is not unique. Another match is given in Figure 7b. Here we have raised the porosity, and raised Poissons ratio: to get a match, we have to increase Co/b quite a bit (Co/b = 20 compared with acceptable range of 4-13). To check the realism of all the matches we have done, we offer in Table 2 a summary of parameter ranges in the San Juan basin (see last line of table). These we view as acceptable ranges for these parameters. The Zahner range of b and Co comes from his plot of Langmuir pressure vs Langmuir volume (his Figure 1). His Langmuir pressure is simply 1/b, if we assume the matrix shrinkage change with depletion has the same shape as the isotherm. The Langmuir volume is related to Co (or ЄL) via a correlation from Pekot and Reeves (2003). All the matches to the Zahner/Clarkson data are summarized in Table A.1 of Appendix A. Figures 8 and 9 summarize the matches: the dot size is proportional to the goodness of the match (a larger dot means a better match). The black box corresponds to the ranges of parameters given in Table 2. Only the matches that fall in the black box are deemed acceptable. These figures indicate that φo and Poissons ratio, v, are at the minimum of their range (they cannot go any lower).

k/ko versus Pb

0.10

1.00

10.00

100.00

1000.00

0 500 1000 1500 2000

Pb (psi)

k/ko

c/b=20φ=.0015v=0.39b=.0016no stress-perm

c/bout ofrange

Figure 7b: Another match (see blue dashes) of Zahner/Clarkson data by P-M theory (no stress-perm effect). Table 2: Ranges of parameters for San Juan fairway coals.

0.1-0.50.30-0.46Palmer & Mansoori

7.1 (CH4)9.0 (CO2)

.0014 (CH4)

.0026 (CO2)Levine

7.9.0016.0460.21Mavor & Vaughan

.681.35

.002

.002Seidle & Huitt;Harpalani

Chosen range

Zahner

Source

3.9 – 13.3.0013 -.00330.05 - 0.50.30-0.46

3.9 – 13.3.0013 -.00330.1-0.5

Co/b (psi)b (/psi)Φo (%)Poissonsratio, v

0.1-0.50.30-0.46Palmer & Mansoori

7.1 (CH4)9.0 (CO2)

.0014 (CH4)

.0026 (CO2)Levine

7.9.0016.0460.21Mavor & Vaughan

.681.35

.002

.002Seidle & Huitt;Harpalani

Chosen range

Zahner

Source

3.9 – 13.3.0013 -.00330.05 - 0.50.30-0.46

3.9 – 13.3.0013 -.00330.1-0.5

Co/b (psi)b (/psi)Φo (%)Poissonsratio, v

match quality: Zahner/Clarkson data(standard model)

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5

phio (%)

Co/

b (p

si)

very poor match

good match

okay match

Figure 8: Summary of φo and Co/b matches to Zahner/Clarkson data.

match quality: Zahner/Clarkson data (standard model)

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

b (/psi)

Pois

sons

rat

io, v

very poor matchgood match

okay match

Figure 9: Summary of b and v matches to Zahner/Clarkson data. We turn now to matches of the Mavor/Vaughan data in Figure 6. Note that even though only two data points define the trend in each of these wells, we have assumed the trend is exponential, as it appears to be in the Zahner and Clarkson data. And so we have tried to match the exponential trend. Figure 10 shows a good match, with parameters that honor the match by Mavor and Vaughan (1997), except for Poissons ratio, v. Here, v = 0.44, and is much greater than v = 0.21 used by M&V. Note: the usual range of v = 0.3 – 0.46,

see Table 2, so the value used by Mavor and Vaughan was abnormally low. We may conclude that we can match the M&V data, without the stress-perm effect, and honor their original parameters, but only if we invoke a much higher value for Poissons ratio (but now within the acceptable range).

k/ko versus Pb

0.1

1

10

100

0 200 400 600 800 1000 1200

Pb (psi)

k/ko

c/b=8φ=.00045v=0.44b=.0016no stress-perm

No parameters

out ofrange

Figure 10: One match (see blue dashes) of Mavor/Vaughan VC 32-4 well by P-M theory (no stress-perm effect). In Figure 11, we have pushed Poissons ratio down, to see if we can still get a match. We can, but Co/b has to be quite small (2.5) and is out-of-range. So this is not an acceptable match.

k/ko versus Pb

0.1

1

10

100

0 200 400 600 800 1000 1200

Pb (psi)

k/ko

c/b=2.5φ=.00045v=0.30b=.0013no stress-perm

c/b is out ofrange

Figure 11: One match (see blue dashes) of Mavor/Vaughan VC 32-1 well by P-M theory (no stress-perm effect). Once again, the matches of Figures 10 and 11 are not unique. A summary of the matches is given in Table A.2 of Appendix A. Figures 12 and 13 summarize the matches we have obtained to the Mavor/Vaughan data (both wells). Again, the black box corresponds to the ranges of parameters given in Table 2, and only the matches that fall in the black box are deemed acceptable. These figures indicate that φo and b are now at the minimum of their range (they cannot go any lower). To summarize the matches of both data sets: according to the better matches we have obtained, initial porosities are generally small (≤0.1%), and at the lower limit of the acceptable range of 0.05 – 0.5%. Also, matrix shrinkage values are on the low side of the acceptable range: b ≤0.0017 /psi, compared with the range of 0.0013 - 0.0033 /psi, and Co/b ≤8 compared with the range of 4 – 13. The low porosity matches are a little worrying, since the majority of reservoir simulations in San Juan basin find porosities in the range 0.1-0.5%. For example, both Zahner and Palmer-Mansoori in Table 2 argue that φo = 0.1-0.5 % in the San Juan basin. Yet Figures 8 and 12 both reveal acceptable matches ONLY for φo ≤0.1%. Such low porosities need to be confirmed by history matching production data. If they are not acceptable, then perhaps alternate mechanisms for perm increases need to be investigated.

match quality: Mavor/Vaughan data(standard model)

0

2

4

6

8

10

12

14

16

18

0 0.1 0.2 0.3 0.4 0.5

phio (%)

Co/

b (p

si)

all good matches

Figure 12: Summary of φo and Co/b matches to Mavor/Vaughan wells 32-4 and 32-1.

match quality: Mavor/Vaughan data (standard model)

0

0.1

0.2

0.3

0.4

0.5

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

b (/psi)

Pois

sons

rat

io, v

all good matches

Figure 13: Summary of b and v matches to Mavor/Vaughan wells 32-4 and 32-1.

match quality: Zahner/Clarkson data (alternate models)

0

2

4

6

8

10

12

14

16

18

0 0.1 0.2 0.3 0.4 0.5

phio (%)

Co/

b (p

si)

good match

very good match

n=2

n=2d<b

d<b

Figure 14: Summary of φo and Co/b matches to Zahner/Clarkson data (alternate models). To see if we can avoid the low porosities of the matches, we have investigated two alternate models (actually two variants of the basic P-M model):

1. Permeability is given by k/ko = (φ/φo)2 instead of (φ/φo)3. 2. The matrix shrinkage term in Equation (1) is rewritten as

bP bPo --------- - ---------- (3) (1 + dP) (1 + dPo)

where the parameter d alters the shape of the strain vs pressure curve, so that it is no longer a Langmuir-isotherm shape.

The match results to the Zahner/Clarkson data are in Table A.3 in Appendix A, but are summarized here in Figure 14. All the matches are good to very good. The two dots on the left correspond to model 1., while the two dots on the right are for model 2. For k/ko = (φ/φo)2 , we can get a good match, but φo has to be very low, Co/b has to be high, and v has to be low (all three near their limits). This weaker dependence of perm on porosity helps to straighten out the curve, and gives better matches, but seems a bit forced since three parameters are all at their limits. An example of a match for the non-Langmuir model 2., using d = b/2, is given in Figure 15. This reveals a VERY close fit to the data, with no parameters out-of-range. However, we also find that if d = 0, then the theory prediction is too convex to match the straight line trend. On the other hand, if d = 2b the prediction is too concave. Altogether, this argues that d ≈ b, and this is consistent with lab measurements of matrix shrinkage which more-or-less follow the isotherm shape.

k/ko versus Pb

1.00

10.00

100.00

0 500 1000 1500 2000

Pb (psi)

k/ko

d= .0008c/b=10.5φ=.0015v=0.39b=.0016no stress-perm

Figure 15: One match (see blue dashes) of Zahner/Clarkson data by P-M theory with d = b/2 (alternate model with no stress-perm effect). Implications of exponential increase of perm with depletion: The linear trends of data in Figure 4 represent an exponential increase in perm with depletion. This appears to mean the stress-perm term in Equation (1) is suppressed during gas production, as when we include it we CANNOT match the Zahner/Clarkson data in Figure 4 (using parameters in the accepted ranges). If we include the stress-perm term, the perm increase is always concave, and never linear, on log-linear plots like Figure 4. An example is given in Figure 16. The match is very poor, and is unacceptable anyway since Co/b is way out of range: Co/b = 40 compared with the acceptable range of 4 – 13. In general, to get a match when stress-perm is included, we have to increase φo and E, and reduce v, in order to lessen the stress-perm behavior (eg, see U-shaped curve of vertical crosses in Figures 7 and 10). And then we have to raise b and Co/b to bring the curve up higher (ie, we need a relatively strong matrix shrinkage to compensate for the perm reduction by the stress-perm effect). For now, we are faced with accepting that some mechanism is suppressing the stress-dependent permeability. This is a bit of a dilemma, since stress-dependent permeability is a sacred tenet of naturally fractured reservoirs, which includes coal. One explanation for the suppression of the stress-perm effect is that cleat closing is inhibited by asperities (roughness) of the cleats. That is, stress-dependent permeability can act fully when pore pressure rises and cleats open up, but cannot act fully when pore pressure falls due to depletion. There is some support for this in the general observation that Youngs modulus,

E, increases when confining pressure (ie, stress) applied to a core is initially increased….the standard interpretation is that minor flaws and fractures are closing, and thereby making the bulk rock more rigid. This could be incorporated in the P-M model by making E and therefore M and Cm in Equation (1) to be functions of pressure (ie, depletion). However, it is still hard to accept that there is no stress-perm behavior in the field, especially after reviewing the lab tests of Seidle et al (1992). Another interpretation that may be hard to refute is one occasion when pressure surges in a cavity well were also recorded in a nearby observation well. The time delay was different for pressure blowdown and for pressure buildup, and this asymmetry has been explained by the average interwell permeability being pressure-dependent.

k/ko versus Pb

1.00

10.00

100.00

1000.00

0 500 1000 1500 2000

Pb (psi)

k/ko

c/b=40φ=.004v=0.3b=.0023no stress-perm

c/b is way out ofrange

Stress-perm included

Figure 16: One attempted match (see vertical crosses) of Zahner/Clarkson data by P-M theory with stress-perm effect included. Note: the exponential increase in perm with depletion CANNOT be due to the concentration of CO2 increasing over time in the produced gas stream. As relatively more CO2 desorbs from the coal, compared with methane, the matrix shrinkage effect becomes relatively greater (b and Co/b become greater), and the perm increase should become greater than for a fixed composition of methane and CO2. This would cause perm increase curves, such as in Figure 4, to bend upwards more at larger depletion (ie, more concave). The exponential increase in perm with depletion also CANNOT be due to new coal failure induced by matrix shrinkage, as Mavor and Vaughan have suggested, because the k/ko trend from P-M would be magnified with depletion, ie, the curve would again bend up more (more concave), and this is the wrong trend.

If it can be shown that the stress-perm effect is NOT suppressed in Equation (1), but does in fact occur during depletion, then we would be forced to seek some other mechanism to explain the exponential increase in perm with depletion. Three possibilities are:

• Differential depletion: the coal with higher perm will deplete faster. In the case of the Clarkson data, the perm increases apparently come from average perms calculated from total production data. If there are two coals contributing, this average perm should be assigned to an average of the two depleted pressures, when creating the plot of k/ko vs P. In practice, the lowest reservoir pressure was used (Clarkson & McGovern, 2004). This will act to bend the true perm increase curve downwards at higher depletions. In essence, this may have straightened a true perm increase curve that was concave. If the exponential perm increase curve of Clarkson (Figure 4) has been straightened by this effect, the true perm increase curve might not be consistent with the Zahner data, which is also exponential, and derived from PTA tests. More analysis needs to be done in this area, to see if differential depletion has altered the true perm increase significantly.

• A non-Langmuir shape governs the matrix shrinkage vs pressure, as described above. Although we know of no physical justification for this, we note that using d = b/2 in the P-M model gives a BETTER match to the Zahner/Clarkson exponential data than any match with d = b (ie, the standard model). One of these matches is shown in Figure 15.

• Matrix shrinkage tends to open up (widen) the existing cleats. Since normally there are no horizontal cleats, bulk shrinkage may imply vertical compaction, and may lead to subsidence if the coal is bounded by a strong caprock (as appears to be the case in San Juan fairway coals). That is, an interface crack may develop under the caprock, and act rather like a horizontal hydraulic fracture to increase the productivity of a well. As depletion proceeds, the interface crack may grow longer, and the well PI may continue to increase over time. This may contribute to an increasing back-pressure coefficient, Cp, or an increase in effective permeability.

In summary, in view of the importance of validating the P-M theory, there needs to be more investigation of this whole subject of the existence or suppression of stress-dependent permeability during coalbed methane production. One final consequence of all this is that the back-pressure coefficient, Cp, measured from well performance in the field, will also increase approximately exponentially with depletion. Cp will approximately follow the k/ko trend, since Cp is proportional to k(av): 0.703 k(av) h

Cp = ------------------------------- (4) µZT [ln(Re/Rw) – 0.75 + S] The relationship is approximate, and not exact, since k(av) is the volumetric average of k(r), and depends on wellbore pressure as well as reservoir pressure. Although the pressure drop near the wellbore, due to drawdown, generally has only a small effect on k(av), sudden changes in drawdown can make a significant change to k(av) and thus to Cp. Such a situation may occur when a compressor is hooked up, for example.

Application to greenhouse gas sequestration: The same physics of stress-dependent permeability and matrix shrinkage is expected to control reservoir performance during injection of gases such as CO2. But during injection, we expect the stress-perm effect to be fully active, whereas during production it appears to be suppressed, as we have discussed. Obviously, injection will lead to swelling of coal, rather than shrinkage, and would reduce the permeability if acting alone. The other finding from this study is that initial porosities are small (≤0.1%), and at the lower limit of the acceptable range of 0.05 – 0.5%. Also, matrix shrinkage values are on the low side of the acceptable range: b ≤0.0017 /psi compared with the range of 0.0013 - 0.0033 /psi, and Co/b ≤8 compared with the range of 4 – 13. The parameters derived from our matches may be useful as starting points for injection modeling, prediction, and history matching in the San Juan basin. Finally, if Cp increases derived from gas production reveal exponential increases with depletion that are steeper than those compiled here (0.23 – 0.36 %/psi), these could possibly be matched by similar low initial porosities ~0.1%, but stronger matrix shrinkage values: b >0.0017 /psi, and Co/b > 8. Conclusions:

• Remarkable increases in absolute permeability are observed with depletion (by 10-100 times) in the San Juan basin fairway, and have no precedent in the oil and gas industry! If perm increases like these can be forecast for prospective CBM plays, this clearly would increase their value. Permeabilities that are marginal under current economics may become Cinderellas as the reservoir depletes.

• A majority of the data are consistent with an exponential increase of permeability with depletion. No perm decreases are evident. The data of Mavor and Vaughan, initially represented as stronger than exponential, may actually be exponential.

• When these exponentials are plotted on a log-linear plot, the slopes of the straight lines define quite naturally a fractional increase in permeability per unit depletion increase. These range from 0.23 to 0.36 % /psi.

• It is not viable to match the exponential perm increase data of Zahner/Clarkson using the full P-M equation (including the stress-perm effect), because the prediction tends to be concave, rather than linear (on a log-linear plot), and an abnormally strong matrix shrinkage effect would be required to “straighten out” the curve.

• However, we have successfully matched 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).

• For now, we are faced with accepting that some mechanism is suppressing the stress-dependent permeability. This is a bit of a dilemma, since stress-dependent permeability is a sacred tenet of naturally fractured reservoirs, which includes coal. In view of the importance of validating the P-M theory, there needs to be more investigation of the subject of the existence or suppression of stress-dependent permeability during coalbed methane production. If stress-dependent perm is proven to occur during depletion, then we will be forced to examine alternate models for perm increase during depletion, as mentioned below.

• We can also match the Mavor and Vaughan data, without the stress-perm effect, and honor their original parameters, but only if we invoke a much higher value for Poissons ratio (but now within the acceptable range).

• The exponential increase in perm with depletion CANNOT be due to the concentration of CO2 increasing over time in the produced gas stream.

• The exponential increase in perm with depletion CANNOT be due to new coal failure induced by matrix shrinkage.

• According to the better matches we have obtained, from all data, initial porosities are generally small (≤0.1%), and at the lower limit of the acceptable range of 0.05 – 0.5%. Also, matrix shrinkage values are on the low side of the acceptable range: b ≤0.0017 /psi, compared with the range of 0.0013 - 0.0033 /psi, and Co/b ≤8 compared with the range of 4 – 13. The better matches require lower porosity and lower b values to reduce the curvature, to match the exponential data. The low porosity matches are a little worrying, since the majority of reservoir simulations in San Juan basin find porosities in the range 0.1-0.5%. Such low porosities need to be confirmed by history matching production data. If they are not acceptable, or if the stress-perm effect is proven to occur during depletion, then perhaps alternate models for perm increases with depletion need to be investigated.

• One alternate model is that a non-Langmuir shape governs the matrix shrinkage vs pressure. Although we know of no physical justification for this, we note that using d = b/2 in the P-M model gives a BETTER match to the Zahner/Clarkson exponential data than any match with d = b (ie, the standard model). Note, however, that d must lie between 0 and 2b, because these two limits do not allow a match to the data.

• A second alternate model has k/ko ~ (φ/φo)2. This weaker dependence of perm on porosity helps to straighten out the curve, and gives better matches, but seems a bit forced since three parameters are all at their limits.

• A third alternate model is differential depletion between two or more coal seams. This may alter the true perm increase significantly, and needs to be investigated.

• A fourth alternate model is that matrix shrinkage could imply vertical compaction, since normally there are no horizontal cleats, and this could lead to a horizontal interface crack under a strong caprock. This crack would lengthen as depletion proceeds, and might contribute to an increasing effective permeability over time.

• Porosity changes are > 30% in the matches we have demonstrated here. Although this violates the linear elastic assumption behind the P-M theory, we assume the theory still gives the trend. But this needs to be investigated more.

• Back-pressure coefficients derived from gas production should in general follow the trend of perm increase with depletion. If back-pressure increases reveal exponential increases with depletion that are steeper than those considered here (0.23 – 0.36 %/psi), these could possibly be matched by low initial porosities ~0.1%, but stronger matrix shrinkage values: b >0.0017 /psi, and Co/b > 8.

• The parameters derived from our matches may be useful as starting points for sequestration (injection) modeling, prediction, and history matching in the San Juan basin.

Acknowledgements:

For insightful comments on this paper, we are indebted to Chris Clarkson. Matt Mavor and John Seidle also provided helpful direction. Symbols: E = Youngs modulus (psi) v = Poissons ratio M = constrained axial modulus (psi) K = bulk modulus (psi) f = fraction 0 1 β = grain compressibility (/psi) 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) φ = porosity φo = initial porosity P = reservoir pressure (psi) Po = initial reservoir pressure (psi) k = permeability (md) ko = initial permeability (md) k(av) = permeability averaged over reservoir (md) µ = gas viscosity (cp) Z = gas compressibility factor T = reservoir temperature (R degrees) Re = equivalent radius of well acreage (ft) Rw = wellbore radius (ft) S = skin factor References:

1. Palmer, I.D. and Mansoori, J. “How permeability depends on stress and pore pressure in coalbeds: a new model”, SPE Res. Eval. and Eng., p 539, Dec 1998.

2. Mavor, M., and Vaughn, J. “Increasing permeability in the San Juan basin Fruitland formation”, Procs. 1997 Intl. CBM Symp., Tuscaloosa, Alabama, May 1997.

3. Law, D. H. et al, “Comparison of numerical simulators for greenhouse gas sequestration in coalbeds, Part 3: More complex problems”, Procs. NETL's Second National Conference on Carbon Sequestration, Alexandria, VA, May 5-8, 2003.

4. Mavor, M. J. and Gunter, W. D. “Secondary porosity and permeability of coal vs. gas composition and pressure”, Intl. CBM Symp., Tuscaloosa, AL, May 2004.

5. Pekot, L. J. and Reeves, S. R. “Modeling the effects of matrix shrinkage and differential swelling on coalbed methane recovery and carbon sequestration”, Paper 0328, Intl. CBM Symp., Tuscaloosa, AL, May 2003.

6. Shi, J. Q. and Durucan, S. “Changes in permeability of coalbeds during primary recovery – Part 1: model formulation and analysis”, Paper 0341, Intl. CBM Symp., Tuscaloosa, AL, May 2003.

7. Shi, J. Q. and Durucan, S. “Changes in permeability of coalbeds during primary recovery – Part 2: model formulation and analysis”, Paper 0342, Intl. CBM Symp., Tuscaloosa, AL, May 2003.

8. Zahner, R “Application of material balance to determine ultimate recovery of a San Juan Fruitland coal well”, SPE 38858, SPE Ann. Tech. Mtg., San Antonio, TX, October 1997.

9. Clarkson, C. R. and McGovern, J.M. “A new tool for unconventional reservoir exploration and development applications”, Paper 0336, Intl. Coalbed Methane Symp., Tuscaloosa, AL, May 2003.

10. Clarkson, C. and McGovern, M., personal communication, 2004. 11. Onsager, P., personal communication, 2004 12. Levine, J. “Model study of the influence of matrix shrinkage on absolute

permeability of coal bed reservoirs.” In Gayer, R. and Harris, I. (eds): Coalbed Methane and Coal Geology, Geological Society Special Publication No. 109, pp 197-212, 1996.

13. Seidle, J.P., Jeansonne, M.W., Ericson, D.J. “Application of matchstick geometry to stress dependent permeability in coals”, SPE 24361, Rocky Mtn. Reg. Mtg., Caspar, WY, May 1992.

14. Seidle, J.P. and Huitt, L.G. “Experimental measurement of coal matrix shrinkage due to gas desorption and implications for cleat permeability increases”, SPE 30010, SPE Intl. Mtg. Petr. Eng., Beijing, China, November 1995.

15. Puri, R. and Seidle, J.P. “Measurement of stress dependent permeability in coal and its influence on coalbed methane production”, 1991 CBM Symp., Tuscaloosa, AL, May 1991.

16. Palmer, I.D. et al, “Completions and stimulations for coalbed methane wells”, SPE 30012, Intl. Mtg. Petr. Eng., Beijing, China, November 1995.

17. Gash, B.W. “Measurement of rock properties in coal for coalbed methane production”, SPE 22909, 66th Ann. Tech. Conf., Dallas, TX, October 1991.

Appendix A: Summary of matches to perm increase data. A summary of matches that have been made by the standard model (minus stress-dependent permeability) to the Zahner/Clarkson data is given in Table A.1. This includes parameters that are beyond the acceptable range of Table 2 in the main text, which also corresponds to the black boxes in the figures (eg, Figures 8, 9). We note that if the stress-perm term in Equation (1) were included, the best match parameters would be even further out of range!

nonen=30.3.001660.07okay

nonen=30.3.0023120.2poor

n=3

n=3

n=3

n=3

n=3

(Φ/Φo)^n

none0.3.001380.08good

Co/b.39.0016200.15okay

Co/b0.3.0016170.2okay

none0.3.00270.1okay

Co/b0.3.0016250.3okay

out of range

νb (/psi)Co/b(psi)

Φo (%)match

nonen=30.3.001660.07okay

nonen=30.3.0023120.2poor

n=3

n=3

n=3

n=3

n=3

(Φ/Φo)^n

none0.3.001380.08good

Co/b.39.0016200.15okay

Co/b0.3.0016170.2okay

none0.3.00270.1okay

Co/b0.3.0016250.3okay

out of range

νb (/psi)Co/b(psi)

Φo (%)match

Table A.1: Summary of matches to Zahner/Clarkson data (standard model, but no stress-perm) A summary of matches that have been made by two alternate models (again minus stress-dependent permeability) to the Zahner/Clarkson data is given in Table A.2.

out of range

(Φ/Φo)^nνb (/psi)

Co/b(psi)

Φo (%)

match

d=.00065n=30.3.001380.14best

d=.0008n=30.39.001610.50.15best

nonen=20.3.002110.08good

Co/bn=20.3.0016140.08best

out of range

(Φ/Φo)^nνb (/psi)

Co/b(psi)

Φo (%)

match

d=.00065n=30.3.001380.14best

d=.0008n=30.39.001610.50.15best

nonen=20.3.002110.08good

Co/bn=20.3.0016140.08best

Table A.2: Summary of matches to Zahner/Clarkson data (alternate models, but no stress-perm) A summary of matches that have been made by the standard model (minus stress-dependent permeability) to the Mavor/Vaughan data is given in Table A.3. Two wells only are matched, since the third well, VC 29-4, is quite similar to VC 32-4. Note that even though only two data points define the trend in each of these wells, we have

assumed the trend is exponential, as it appears to be in the Zahner and Clarkson data. And so we have tried to match the exponential trend (see for example Figures 10 and 11).

nonen=20.39.001340.045good

nonen=20.34.001680.1good

nonen=20.44.001680.045good

n=2

n=2

n=2

n=2

(Φ/Φo)^n

Co/b0.30.00132.50.045good

none0.41.001680.1good

none0.46.001680.045good

none0.30.001340.045good

out of range

νb (/psi)Co/b(psi)

Φo (%)match

nonen=20.39.001340.045good

nonen=20.34.001680.1good

nonen=20.44.001680.045good

n=2

n=2

n=2

n=2

(Φ/Φo)^n

Co/b0.30.00132.50.045good

none0.41.001680.1good

none0.46.001680.045good

none0.30.001340.045good

out of range

νb (/psi)Co/b(psi)

Φo (%)match

Acceptable matches to well VC 32-4 with Po = 930 psi

Acceptable matches to well VC 32-1 with Po = 957 psi

Table A.3: Summary of matches to Mavor/Vaughan data (standard model, but no stress-perm)