A Permeability Model for Coal and Other Fractured, Sorptive-Elastic Media
- Eric P. Robertson (Idaho National Laboratory) | Richard L. Christiansen (Wind River Resources Corp)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2008
- Document Type
- Journal Paper
- 314 - 324
- 2008. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 1.2.3 Rock properties, 5.10.1 CO2 Capture and Sequestration, 4.3.1 Hydrates, 5.8.3 Coal Seam Gas, 4.3.4 Scale, 5.5 Reservoir Simulation, 4.6 Natural Gas, 4.1.5 Processing Equipment, 1.6.9 Coring, Fishing, 5.5.1 Simulator Development
- 0 in the last 30 days
- 877 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
This paper describes the derivation of a new equation that can be used to model the permeability behavior of a fractured, sorptive-elastic medium, such as coal, under variable stress conditions. The equation is applicable to confinement pressure schemes commonly used during the collection of permeability data in the laboratory. The model is derived for cubic geometry under biaxial or hydrostatic confining pressures. The model is designed to handle changes in permeability caused by adsorption and desorption of gases onto and from the matrix blocks in fractured media. The model equations can be used to calculate permeability changes caused by the production of methane (CH4) from coal as well as the injection of gases, such as carbon dioxide, for sequestration in coal. Sensitivity analysis of the model found that each of the input variables can have a significant impact on the outcome of the permeability forecast as a function of changing pore pressure; thus, accurate input data are essential. The permeability model also can be used as a tool to determine input parameters for field simulations by curve fitting laboratory-generated permeability data. The new model is compared to two other widely used coal-permeability models using a hypothetical coal with average properties.
During gas production from a coal seam, as reservoir (pore) pressure is lowered, gas molecules, such as CH4, are desorbed from the matrix and travel by diffusion to the cleat (natural-fracture) system where they are conveyed to producing wells. Fluid movement in coal is controlled by slow diffusion within the coal matrix and is described by Darcy flow within the fracture system, which is much faster than the contribution of diffusion. A coal formation typically is treated as a fractured reservoir with respect to fluid flow, meaning that the sole contributor to the overall permeability of the reservoir is the fracture system, and the contribution of diffusion through the matrix to total flow is neglected. Coalbeds are unlike other nonreactive fractured reservoirs because of their ability to adsorb (or desorb) large amounts of gas, which causes swelling (or shrinkage) of the matrix blocks.
Coalbeds have the capacity to adsorb large amounts of gases because of their typically large internal-surface areas, which can range from 30 to 300 m2/g (Berkowitz 1985). Some gases, such as carbon dioxide, have a higher affinity for the coal surfaces than others, such as nitrogen (N2). Knowledge of how the adsorption or desorption of gases affects coal permeability is important not only to operations involving the production of natural gas from coalbeds, but also to the design and operation of projects to sequester greenhouse gases in coalbeds (RECOPOL 2005). Laboratory measurements of permeability using coal samples can be used to gain insight into field-scale permeability changes and to determine key-coal-property values necessary for field-scale simulation.
A number of permeability models derived for sorptive-elastic media such as coals have been detailed in the literature and include those proposed by Gray (1987), Sawyer et al. (1990), Seidle and Huitt (1995), Palmer and Mansoori (1998), Pekot and Reeves (2003), and Shi and Durucan (2003). These models were derived to mimic field conditions, and they assume a matrix-block geometry described as a bundle of vertical matchsticks under a uniaxial stress regime (Palmer and Mansoori 1998; Seidle et al. 1992).
However, in the laboratory, permeability typically is measured by use of hydrostatic (biaxial) core holders, which apply a single confining pressure to all external points of the core inside the holder. This is obviously different from the stress conditions encountered in the field, which typically are characterized as being under uniaxial stress as noted previously. Moreover, on a laboratory scale, coal matrix blocks may be approximated better by cubic instead of matchstick geometry, as will be discussed later in this paper. A recent study (Robertson and Christiansen 2005c) compared the accuracy of three field-permeability models when applied to laboratory-generated, sorption-affected permeability data and found that none of the three was able to match the data accurately. A model specifically derived for laboratory coreflooding conditions would be expected to provide a more reasonable match of permeability results.
This paper describes the derivation of a new model that describes the permeability behavior of a fractured, sorptive-elastic medium, such as coal, under typical laboratory conditions where common radial and axial pressures are applied to a core sample during permeability measurements. The new model can be applied to fractured rock formations where the matrix blocks contribute neither to the porosity nor to the permeability of the overall system, but where adsorption and desorption of gases by the matrix blocks cause measurable swelling and shrinkage, respectively, and thus affect permeability.
|File Size||1 MB||Number of Pages||11|
Amyx, J.W., Bass, D.M. Jr., and Whiting, R.L. 1960. Petroleum ReservoirEngineering--Physical Properties, 291. Columbus, Ohio: McGraw-Hill.
Berkowitz, N. 1985. Coal Science and Technology 7--The Chemistry ofCoal, 88. Oxford, UK: Elsevier Science.
Bradley, H.B. ed. 1987. Petroleum Engineering Handbook, thirdedition, Chap. 51. Richardson, Texas: Society of Petroleum Engineers.
Carman, P.C. 1937. Fluid Flow Through Granular Beds. Trans. Inst. Chem.Eng. 15: 150-166.
Gash, B.W. 1991. Measurement of"Rock Properties" in Coal for Coalbed Methane Production. Paper SPE22909 presented at the SPE Annual Technical Conference and Exhibition, Dallas,6-9 October. doi: 10.2118/22909-MS
Gray, I. 1987. ReservoirEngineering in Coal Seams: Part 1—The Physical Process of Gas Storage andMovement in Coal Seams. SPERE 2 (1): 28-34. SPE-12514-PA doi:10.2118/12514-PA
Janna, W.S. 1983. Introduction to Fluid Mechanics, 160. Monterey,California: Brooks/Cole Engineering Division, Wadsworth Inc.
Levine, J.R. 1996. Model Study of the Influence of Matrix Shrinkage onAbsolute Permeability of Coal Bed Reservoirs. In Coalbed Methane and CoalGeology, Special Publication No. 109, ed. R. Gayer and I. Harris, 197-212.Bath, UK: Geological Society Publishing House.
McKee, C.R., Bumb, A.C., and Koenig, R.A. 1988. Stress-Dependent Permeability andPorosity of Coal and Other Geologic Formations. SPEFE 3 (1):81-91. SPE-12858-PA doi: 10.2118/12858-PA
Palmer, I. and Mansoori, J. 1998. How Permeability Depends on Stressand Pore Pressure in Coalbeds: A New Model. SPEREE 1 (6):539-544. SPE-52607-PA doi: 10.2118/52607-PA
Pekot, L.J. and Reeves, S.R. 2003. Modeling the Effects of Matrix Shrinkageand Differential Swelling on Coalbed Methane Recovery and Carbon Sequestration.Paper 0328 presented at the International Coalbed Methane Symposium,Tuscaloosa, Alabama, USA, 5-7 May.
Puri, R., Evanoff, J.C., and Brugler, M.L. 1991. Measurement of Coal Cleat Porosityand Relative Permeability. Paper SPE 21491 presented at the SPE GasTechnology Symposium, Houston, 22-24 January. doi: 10.2118/21491-MS
RECOPOL Workshop. Greenhouse Issues 78 (June 2005): 5-7. http://www.ieagreen.org.uk/june78.htm.
Reiss, L.H. 1980. The Reservoir Engineering Aspects of FracturedFormations. Houston, Texas: Gulf Publishing Company.
Robertson, E.P. 2005. Measurement and Modeling of Sorption-Induced Strainand Permeability Changes in Coal. PhD dissertation, Colorado School of Mines,Golden, Colorado.
Robertson, E.P. and Christiansen, R.L. 2004. Optically-Based StrainMeasurement of Coal Swelling and Shrinkage. Paper 0417 presented at theInternational Coalbed Methane Symposium, Tuscaloosa, Alabama, USA, 3-7 May.
Robertson, E.P. and Christiansen, R.L. 2005a. Measurement and Modeling ofSorption-Induced Coal Strain. Paper DOE/NETL 196 presented at the 4th AnnualConference on Carbon Capture and Sequestration, Alexandria, Virginia, USA, 2-5May.
Robertson, E.P. and Christiansen, R.L. 2005b. Measurement ofSorption-Induced Strain. Paper 0532 presented at the International CoalbedMethane Symposium, Tuscaloosa, Alabama, USA, May.
Robertson, E.P. and Christiansen, R.L. 2005c. Modeling Permeability in Coal UsingSorption-Induced Strain Data. Paper SPE 97068 presented at the SPE AnnualTechnical Conference and Exhibition, Dallas, 9-12 October. doi:10.2118/97068-MS
Sawyer, W.K., Paul, G.W., and Schraufnagel, R.A. 1990. Development andApplication of a 3D Coalbed Simulator. Paper CIM/SPE 90-119 presented at theCIM/SPE International Technical Meeting, Calgary, 10-13 June.
Seidle, J.P. and Huitt, L.G. 1995. Experimental Measurement of CoalMatrix Shrinkage Due to Gas Desorption and Implications for Cleat PermeabilityIncreases. Paper SPE 30010 presented at the SPE International Meeting onPetroleum Engineering, Beijing, 14-17 November. doi: 10.2118/30010-MS
Seidle, J.P., Jeansonne, M.W., and Erickson, D.J. 1992. Application of Matchstick Geometry toStress Dependent Permeability in Coals. Paper SPE 24361 presented at theSPE Rocky Mountain Regional Meeting, Casper, Wyoming, USA, 18-21 May. doi:10.2118/24361-MS
Shi, J.Q. and Durucan, S. 2003. Changes in Permeability of Coalbeds DuringPrimary Recovery--Part 1: Model Formulation and Analysis. Paper 0341 presentedat the International Coalbed Methane Symposium, Tuscaloosa, Alabama, USA, 5-7May.
Slider, H.C. 1983. Worldwide Practical Petroleum Reservoir EngineeringMethods, 117. Tulsa, Oklahoma: PennWell Publishing Company.
Walsh, J.B. 1981. Effect of pore pressureand confining pressure on fracture permeability. Intl. J. Rock Mech.Min. Sci. Geomech. Abstracts 18 (5): 429-435.doi:10.1016/0148-9062(81)90006-1.
Young G.B.C., McElhiney, J.E., Paul, G.W., and McBane, R.A. 1991. An Analysis of Fruitland CoalbedMethane Production, Cedar Hill Field, Northern San Juan Basin. Paper SPE22913 presented at the SPE Annual Technical Conference and Exhibition, Dallas,6-9 October. doi: 10.2118/22913-MS