Fig. 6–4. Predicted coal permeability decline with depletion
while minimum values, often less than 1%, are obtained by displacement of water from stressed, well-preserved samples.18 Regardless of the experimental protocol used to measure coal porosity, determination of cleat and matrix contributions to the porosity is difficult and somewhat arbitrary. Water porosity as a function of rank was discussed by Levine.19 Porosity was largest in subbituminous coals, up to 22%, then decreased to a minimum of 3% in semianthracites before increasing to 6% in anthracites.
Water can exist in coal as chemically-bound bed water, adsorbed to the surface of the coal, or as free water in the cleats. During depletion of a coal seam, bound bed water is static, changes in adsorbed water are minimal, and cleat water decreases enough to change gas and water mobilities by several orders of magnitude. Water saturation in a coal, defined as the water volume divided by the void volume, is thus more complicated than water saturation in conventional sandstone and carbonate reservoirs. A useful concept for coal gas reservoir engineering is that of mobile water porosity, which is defined as the water volume that will flow from a coal sample due to a pressure gradient. Measurement of mobile water porosity by various methods is discussed by Gash, with the most direct method being displacement of water from the sample with humidified helium.20 Note that measurement of water displaced from a coal sample during stress loading can be used to determine cleat compressibility, and mobile water porosity is determined once the sample has equilibrated under the applied stresses. Mobile water porosity is used to compute original water in place for a given coal and is relevant for estimation of water disposal volumes.
Discussing selection and preparation of coal samples for relative permeability testing, Hyman et al. noted the fragile nature of coals and recommended that care be taken to keep coal samples moist and to prevent unnecessary mechanical loading, such as flexing of the core when laying down the core barrel at the surface.21 Gash noted that many drilling mud additives can alter coal properties and recommended potassium chloride mud for coal coring operations.22 Testa and Pratt discussed coal sample preparation necessary for reliable laboratory tests and noted that low-rank coals are even more sensitive to oxidation than high-rank coals.23 Current practice for coal core dedicated to relative permeability and other laboratory flow tests dictates the core is not removed from the barrel at the wellsite but rather cut into pieces roughly 1 m in length, capped with rubber endcaps, and shipped to the laboratory. Note that some provision must be made to allow escape of desorbing methane gas from the samples during transport.
Upon arrival at the laboratory, the core is carefully removed from the core barrel, placed in formation water (or 2% KCl water), and gently cleaned of drilling mud and debris. Well-cleated samples are visually identified, wrapped in Teflon or jacketed with heat shrink tubing, and the ends trimmed square. Stabilization of samples by coating them with epoxy or other resins can alter coal properties and is therefore not recommended. Prepared samples are stored under water until insertion into the apparatus for relative permeability measurement.
Absolute coal permeability, necessary for calculation of relative permeabilities, declines with time during laboratory measurements and shows strong hysteresis effects.24 This behavior is attributed to generation and migration of coal fines and irreversible stress dependence of the fracture apertures. Consequently for permeability measurements, coal samples are slowly cycled a single time, and care is taken to acquire plentiful data. Once in the flow apparatus, single-phase water flow is established and an initial permeability determined. Measurement of fluid volume expelled as the sample is stressed to test conditions allows calculation of cleat compressibility.
Once at test conditions, flow is monitored for several days or a week until permeability stabilizes. Gas-water relative permeabilities are then determined by one of two methods.
Measurement of relative permeability with the steady-state method requires injection of the two fluids at constant rates or constant pressures until expelled fluid fractions are the same as injected fractions. Effective permeabilities are calculated from Darcy’s law, while saturations are typically determined with tracer techniques.
The low permeabilities of many coals dictate long equilibration times for this method.
The unsteady-state method for relative permeability, in which one fluid is displaced by the other, is much quicker than the steady-state method. However, it requires independent measurement of the pore volume and suffers from a lack of precision at low gas saturations, precisely the region of interest in most coal gas plays. To avoid or minimize gas sorption effects, helium or nitrogen rather than methane is employed for coal gas-water relative permeability measurements. Gash et al. suggested procedural improvements to increase accuracy of this method for low-porosity samples at low gas saturations.25 Experimental data are analyzed with the JBN method.26
As noted above, coal deposits are characterized by two sets of natural fractures, the face and butt cleats.
Vertical reach of a face cleat typically exceeds that of a butt cleat, but both are limited by bedding plane heterogeneity, often dying out in tough, shaley layers. Flow properties of this fracture network, such as absolute and relative permeabilities, are intuitively expected to be heterogeneous, but as discussed below, laboratory and field experience indicates the opposite.
Absolute and gas-water relative permeabilities were measured on a trio of well-cleated San Juan Fruitland coal samples by Gash et al.27 All three samples, carefully prepared from fresh mine samples, were 3.5 in. in diameter by 4 in. long. Absolute permeability to water was determined first, followed by unsteady-state gas- water relative permeabilities. Sample porosity averaged 0.41%, and absolute permeability declined with time, probably due primarily to coal fines. Permeability in the butt cleat direction was one-half that in the face cleat direction, and vertical permeability was two orders of magnitude less than face cleat permeability. Stabilized absolute permeabilities and porosities measured at two confining pressures obeyed the cubic relation of equation (6.6). Experimental procedures to increase the accuracy of unsteady-state relative permeability measurements at low gas saturations were presented. Gas-water relative permeabilities measured in the face cleat, butt cleat, and perpendicular to the bedding planes were essentially equal, a counterintuitive result from an anisotropic fracture network.
In evaluating pressure transient tests from San Juan Basin coal wells, Mavor and Robinson investigated applicability of algebraic equations for gas and water relative permeabilities developed for conventional reservoirs to gas-water relative permeabilities of Fruitland coal measured by Gash.28 Gas and water relative permeabilities were calculated from
(6.20)
(6.21) Sw – Siw
Sw* = ———– (6.22)
1 – Siw where
krg = gas relative permeability,
krg = gas relative permeability at irreducible water saturation, krw = water relative permeability,
λ = empirical coefficient, n΄ = empirical coefficient, Sw = water saturation, and Siw = irreducible water saturation.
Mavor and Robinson reported the best fit to the Gash San Juan gas-water relative permeability data, presented in table 6–3, was obtained using
λ = 100, Siw = 0.05, n΄ = 0.5, krg = 0.65
Table 6–3. Gas-water relative permeabilities—San Juan Basin, Fruitland coal
Sw krw krg kg/kw Sg
0.000 0.000 1.000 9999 1.00
0.050 0.000 0.835 9999 0.95
0.100 0.000 0.720 9999 0.90
0.150 0.002 0.627 314 0.85
0.200 0.007 0.537 76.7 0.80
0.250 0.015 0.465 31.0 0.75
0.300 0.024 0.401 16.7 0.70
0.350 0.035 0.342 9.77 0.65
0.400 0.049 0.295 6.02 0.60
0.450 0.067 0.253 3.78 0.55
0.500 0.088 0.216 2.45 0.50
0.550 0.116 0.180 1.55 0.45
0.600 0.154 0.147 0.955 0.40
0.650 0.200 0.118 0.590 0.35
0.700 0.250 0.090 0.360 0.30
0.750 0.312 0.070 0.224 0.25
0.800 0.392 0.051 0.130 0.20
0.850 0.490 0.033 0.067 0.15
0.900 0.601 0.018 0.030 0.10
0.950 0.731 0.007 0.010 0.05
0.975 0.814 0.004 0.004 0.025
1.000 1.000 0.000 0.000 0.000
Source: Gash, B. W. 1991.
Gas and water relative permeabilities measured by Gash are compared with those calculated from the Mavor and Robinson equations in figure 6–5.
Fig. 6–5. Measured and calculated gas-water relative permeabilities—San Juan coal29
The two sets of curves are in general agreement for high water saturations, the saturations of most importance for coal gas reservoir engineering. Below water saturations of about 20%, the measured gas relative permeability is significantly larger than the analytic value. However, this is of little practical consequence, as both measured and analytic water relative permeabilities are so low here that actual coal wells may never attain such low saturations.
Gas-water relative permeabilities of the Blue Creek coal in the Warrior Basin were measured by Gash and Conway et al.30 Gash employed a 2 in. diameter sample approximately 4 in. in length, with a base permeability of 3 md and a mobile water porosity of 1.0%. Conway et al. used a 1 in. diameter plug of unreported length and base permeability and an inferred mobile water porosity of 0.53%. Neither study reported orientation of bedding planes in the samples. Flows may have been parallel to the bedding planes (representing nominally horizontal flow in the reservoir), perpendicular to the bedding planes (representing nominally vertical flow in the coal seam), or at an angle to the bedding planes (an unlikely orientation given the difficulty in sample preparation).
The Gash and Conway et al. gas-water permeabilities, plotted in figure 6–6 and listed in tables 6–4 and 6–5, exhibit the same general shapes. The water relative permeability initially declined rapidly to a long tail, while gas relative permeability increased nearly linearly as water saturation fell.
Fig. 6–6. Measured gas-water relative permeabilities—Marylee/Blue Creek coal31
The Gash data exhibit a critical gas saturation (the lowest gas saturation of nonzero gas relative permeability) of zero, in agreement with many other naturally fractured reservoirs. Gas and water relative permeabilities cross over at a value of 0.22, corresponding to a water saturation of 77%. Irreducible water saturation (the water saturation corresponding to zero relative permeability to water) is zero, as would be expected from the definition of mobile water porosity, and gas relative permeability is 1.0. The curves of Conway et al. exhibit a critical gas saturation of 7%, crossover relative permeabilities of 0.057 at a water saturation of 82%, and an irreducible water saturation of 35%, at which time gas relative permeability has risen to 0.800. Variations in the two sets of relative permeability curves are ascribed to sample heterogeneity, flow limitations of the limited fracture networks in the small coal samples, and experimental difficulties associated with extremely small porosities.
Table 6–4. Gas-water relative permeabilities—Warrior Basin, Blue Creek coal
Sw krw krg kg/kw Sg
0.00 0.00 1.00 na 1.00
0.10 0.00 0.900 9000 0.90
0.20 0.00 0.80 444 0.80
0.30 0.00 0.70 175 0.70
0.40 0.01 0.60 70.6 0.60
0.50 0.02 0.50 23.8 0.50
0.60 0.05 0.38 7.60 0.40
0.70 0.110 0.27 2.45 0.30
0.80 0.260 0.20 0.769 0.20
0.90 0.500 0.10 0.200 0.10
0.95 0.700 0.06 0.086 0.05
0.98 0.900 0.00 0.001 0.02
1.00 1.00 0.00 0.000 0.00
na = not available Source: Gash, B. W. 1991.
Table 6–5. Gas-water relative permeabilities—Warrior Basin, Marylee/Blue Creek coal
Sw krw krg kg/kw Sg
0.350 0.000 0.800 999 0.650
0.422 0.008 0.676 90.2 0.578
0.471 0.013 0.591 47.2 0.529
0.520 0.017 0.505 30.3 0.480
0.571 0.019 0.418 21.8 0.429
0.620 0.023 0.335 14.8 0.381
0.670 0.028 0.253 9.16 0.330
0.744 0.038 0.144 3.82 0.256
0.769 0.043 0.111 2.56 0.231
0.794 0.049 0.082 1.67 0.206
0.819 0.058 0.057 0.981 0.181
0.844 0.069 0.035 0.508 0.156
0.856 0.077 0.027 0.345 0.144
0.868 0.089 0.019 0.210 0.132
0.881 0.110 0.012 0.106 0.120
0.893 0.135 0.006 0.046 0.107
0.906 0.169 0.002 0.011 0.094
0.915 0.200 0.000 0.001 0.085
0.930 0.259 0.000 0 0.070
0.943 0.325 0.000 0 0.058
0.946 0.404 0.000 0 0.054
0.968 0.510 0.000 0 0.032
0.980 0.643 0.000 0 0.020
0.991 0.831 0.000 0 0.009
1.000 1.000 0.000 0 0.000
Source: Conway, M. W., et al. 1995.
Similar to equation (6.21), Conway et al. fit their gas relative permeability data to
where
Sgc = critical gas saturation.
Note the above equation reduces to equation (6.21) for a critical gas saturation of zero. The most accurate match was obtained from
λ = 1.0, Siw = 0.35, n΄ = 1.23, krg = 0.8, Sgc = 0.085 No similar equation could be obtained for the water relative permeability.
Gas-water relative permeabilities for the Wyodak coal of the Powder River Basin were developed by Hower et al. during the history matching portion of a simulation study that included several hundred wells on the east side of the basin.32 Performance of this highly permeable, subbituminous coal was modeled using gas-water relative permeabilities of crossed, straight lines with irreducible water and critical gas saturations of zero and different endpoint permeabilities. The endpoint values, a maximum krg of 0.8 and a maximum krw of 0.5, were two of the many history match parameters. Subbituminous coals are generally more porous, more permeable, and have a more open fabric than bituminous coals. Consequently, the distinctly different gas-water relative permeability curves for the different rank coals are not unexpected.
Gas-water relative permeabilities of coals from the Sydney and Bowen basins of Australia were discussed by Meany and Paterson.33 Relative permeabilities were measured on 10 samples 2 in. in diameter and 4.75 in. long, all but one cut vertically, nominally across the bedding planes. Similar to the Warrior Basin curves discussed above, all the Australian curves exhibited crossovers at high water saturations. Meaney and Paterson attributed this behavior to viscous fingering as gas displaces water. In addition to the 10 sets of experimentally measured relative permeabilities, gas-water relative permeabilities for 6 samples were developed from history matching field performance with a reservoir simulator. Gas-water relative permeabilities were measured on two samples from the German Creek seam of the Bowen Basin. A third set was developed from history matching performance of wells draining this coal with an unspecified simulator. All three sets of gas-water relative permeabilities are plotted in figure 6–7 and collected in table 6–6.
The divergence between the three sets of German Creek curves is typical of coal seam gas-water relative permeabilities, leading to questioning the need to expend the time and money required for their laboratory measurement. For reservoir engineering purposes, this dilemma is treated two ways. First, sensitivity of a given parameter, e.g., effective permeability to water at a given saturation, can be assessed using selected sets of relative permeability curves. Secondly, gas-water relative permeability curves can be determined from simulation of well performance. Note that history-matched relative permeability curves for a coal often exhibit very different behavior from laboratory-based curves. This is because they describe not only the classical gas and water mobilities but also incorporate viscous fingering and gas buoyancy effects in this naturally fractured reservoir.
For wells completed in water-saturated coals, gas-water relative permeability curves can be approximated by first applying a decline curve to water production to determine initial water in place. Water saturation at any given time is then calculated from cumulative water and initial water in place. Absolute permeability is estimated from initial water production. Selecting times when reservoir and bottomhole flowing pressures and gas and water rates are all known, Darcy’s equation yields effective permeabilities at that time. Dividing effective permeability to gas and water by initial permeability gives the respective gas and water relative permeabilities.
The more the coal has been dewatered, of course, the larger the water saturation range of these field-derived relative permeabilities.
Fig. 6–7. Measured and history-matched gas-water relative permeabilities—Bowen Basin, Australia, German Creek seam34 Table 6–6. Gas-water relative permeabilities—Bowen Basin, Australia, German Creek seam
Sample 3d
Sw krw krg kg/kw Sg
0.568 0.000 0.133 999 0.432
0.597 0.068 0.068 1.000 0.403
0.600 0.108 0.048 0.440 0.400
0.700 0.383 0.030 0.078 0.300
0.800 0.665 0.010 0.015 0.200
0.900 0.895 0.000 0.000 0.100
0.970 1.000 0.000 0.000 0.030
1.000 1.000 0.000 0.000 0.000
Sample 3e
Sw krw krg kg/kw Sg
0.692 0.100 0.165 1.65 0.308
0.722 0.153 0.153 1.00 0.278
0.800 0.458 0.085 0.185 0.200
0.819 0.569 0.073 0.128 0.181
Simulation
Sw krw krg kg/kw Sg
0.000 0.000 1.000 999 1.000
0.200 0.000 0.878 999 0.800
0.400 0.000 0.801 999 0.600
0.500 0.000 0.768 999 0.500
0.570 0.000 0.723 999 0.430
0.600 0.024 0.693 28.9 0.400
0.677 0.043 0.607 14.1 0.323
0.800 0.290 0.328 1.13 0.200
0.900 0.684 0.164 0.240 0.100
0.990 1.000 0.000 0.000 0.010
1.000 1.000 0.000 0.000 0.000