Analytical Solutions for Multiple Matrix in Fractured Reservoirs: Application to Conventional and Unconventional Reservoirs
- Mehmet A. Torcuk (Colorado School of Mines) | Basak Kurtoglu (Marathon Oil Company) | Najeeb Alharthy (Colorado School of Mines) | Hossein Kazemi (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2013
- Document Type
- Journal Paper
- 969 - 981
- 2013. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 4.1.2 Separation and Treating
- 4 in the last 30 days
- 758 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
In this paper, we present a new method to model heterogeneity and flowchanneling in petroleum reservoirs--especially reservoirs containinginterconnected microfractures. The method is applicable to both conventionaland unconventional reservoirs where the interconnected microfractures form themajor flow path. The flow equations, which could include flow contributionsfrom matrix blocks of various size, permeability, and porosities, are solved bythe Laplace-transform analytical solutions and finite- difference numericalsolutions. The accuracy of flow from and into nanodarcy matrix blocks is ofgreat interest to those dealing with unconventional reservoirs; thus, matrixflow equations are solved by use of both pseudosteady-state (PSS) andunsteadystate (USS) formulations and the results are compared. The matrixblocks can be of different size and properties within the representativeelementary volume (REV) in the analytical solutions, and within each controlvolume (CV) in the numerical solutions. Although the analytical solutions weredeveloped for slightly compressible rock/fluid linear systems, the numericalsolutions are general and can be used for nonlinear, multiphase, multicomponentflow problems. The mathematical solutions were used to analyze the longterm andshort-term performances of two separate wells in an unconventional reservoir.It is concluded that matrix contribution to flow is very slow in a typicallow-permeability unconventional reservoir and much of the enhanced productionis from the fluids contained in the microfractures rather than in the matrix.In addition to field applications, the mathematical formulations and solutionmethods are presented in a transparent fashion to allow easy usage of thetechniques for reservoir and engineering applications.
|File Size||1 MB||Number of Pages||13|
Al-Ajimi, N. M., Kazemi, H. and Ozkan, E. 2008. Estimation of StorativityRatio in a Layered Reservoir with Crossflow. SPE Res Eval & Eng 11 (2): 267-279. http://dx.doi.org/10.2118/84294-PA.
Alamdari, B. B., Kiani, M. and Kazemi, H. 2012. Experimental and NumericalSimulation Of Surfactant-Assisted Oil Recovery In Tight Fractured CarbonateReservoir Cores. Paper SPE 153902 presented at the SPE Improved Oil RecoverySymposium, Tulsa, Oklahoma, 14-18 April. http://dx.doi.org/10.2118/153902-MS.
Alharthy, N., Kobaisi, M. A., Torcuk, M. A., et al. 2012. Physics andModeling of Gas Flow in Shale Reservoirs. Paper SPE 161893 presented at the AbuDhabi International Petroleum Conference and Exhibition, Abu Dhabi, United ArabEmirates, 11-14 November. http://dx.doi.org/10.2118/161893-MS.
Barenblatt, G. I., Zeltov, Y. P. and Kochina, I. 1960. Basic Concepts in theTheory of Seepage of Homogeneous Liquids in Fissured Rocks. Prikl. Mat.Mekh. 24 (5): 1286-1303.
Carslaw, H.S. and Jaeger, J.C. 1959. Conduction of Heat in Solids,second edition. New York City, New York: Oxford University Press.
de Swaan-O, A. 1976. Analytic Solutions for Determining Naturally FracturedReservoir Properties by Well Testing. SPE J. 16 (3):117-122. http://dx.doi.org/10.2118/5346-PA.
de Swaan-O, A. 1978. Theory of Waterflooding in Fractured Reservoirs. SPEJ. 18 (2): 117-122. http://dx.doi.org/10.2118/5892-PA.
Du, K. and Stewart, G., 1992. Transient Pressure Response of HorizontalWells in Layered and Naturally Fractured Reservoirs with Dual-PorosityBehavior. Paper SPE 24682 presented at the SPE Annual Technical Conference andExhibition, Washington, D.C., 4-7 October. http://dx.doi.org/10.2118/24682-MS.
Du, K. and Stewart, G., 1995. Bilinear Flow Regime Occurring in HorizontalWells and Other Geological Models. Paper SPE 29960 presented at theInternational Meeting on Petroleum Engineering, Beijing, China, 14-17 November.http://dx.doi.org/10.2118/29960-MS.
Erdélyi, A. ed. 1953. Higher Transcendental Functions, Volume II.New York City, New York: McGraw-Hill Book Company, Inc.
Erdélyi, A. ed. 1954. Tables of Integral Transforms, Volume 1. NewYork City, New York: McGraw-Hill Book Company, Inc.
Kazemi, H. 1969. Pressure Transient Analysis of Naturally FracturedReservoirs with Uniform Fracture Distribution. SPE J. 9(4): 451-462. http://dx.doi.org/10.2118/2156-A.
Kazemi, H., Gilman, J. R. and Elsharkawy, A. M. 1992. Analytical andNumerical Solution of Oil Recovery from Fractured Reservoirs with EmpiricalTransfer Functions. SPE Res Eval & Eng 7 (2): 219-227.http://dx.doi.org/10.2118/19849-PA.
Kazemi, H. and Gilman, J. R. 1993. Multiphase Flow in Fractured PetroleumReservoirs. In Flow and Contaminant Transport in Fractured Rocks, eds.J. Bear, C-F. Tsang, and G. De Marsily, 267-323. San Diego, California:Academic Press, Inc.
Kurtoglu, B., Torcuk, M. A. and Kazemi, H. 2012a. Pressure TransientAnalyses of Short and Long Duration Well Tests in Unconventional Reservoirs.Paper SPE 162473 presented at the SPE Canadian Unconventional ResourcesConference, Calgary, Alberta, Canada, 30 October-1 November. http://dx.doi.org/10.2118/162473-MS.
Kurtoglu, B. and Kazemi, H., 2012b. Evaluation of Bakken Performance UsingCoreflooding, Well Testing, and Reservoir Simulation. Paper SPE 155655presented at the SPE Annual Technical Conference and Exhibition, San Antonio,Texas, 8-10 October. http://dx.doi.org/10.2118/155655-MS.
Najurieta, H. L. 1980. A Theory for Pressure Transient Analysis in NaturallyFractured Reservoirs. J. Pet Tech 32 (7): 1241-1250. http://dx.doi.org/10.2118/6017-PA.
Nobakht, M. and Mattar, L. 2010. Analyzing Production Data FromUnconventional Gas Reservoirs with Linear Flow and Apparent Skin. Paper SPE137454 presented at the Canadian Unconventional Resources and InternationalPetroleum Conference, Calgary, Alberta, Canada, 19-21 October. http://dx.doi.org/10.2118/137454-MS.
Pruess, K. and Narasimhan, T. H. 1985. A Practical Method for Modeling Fluidand Heat Flow in Fractured Porous Media. SPE J. 25 (1):14-26. http://dx.doi.org/10.2118/10509-PA.
Stehfest, H., 1970. Numerical Inversion of Laplace Transforms. Commun.ACM 13 (1): 47-49. http://dx.doi.org/10.1145/361953.361969.
van Everdingen, A. and Hurst, W. 1949. The Application of the LaplaceTransformation to Flow Problems in Reservoirs. J. Pet Tech 1 (12): 305-324. http://dx.doi.org/10.2118/949305-G.
Warren, J. E. and Root, P. J. 1963. The Behavior of Naturally FracturedReservoirs. SPE J. 3 (3): 245-255. http://dx.doi.org/10.2118/426-PA.