Analysis of Uncertainty Introduced by Scaleup of Reservoir Attributes and Flow Response in Heterogeneous Reservoirs
- Juliana Y. Leung (University of Alberta) | Sanjay Srinivasan (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2011
- Document Type
- Journal Paper
- 713 - 724
- 2011. Society of Petroleum Engineers
- 5.7.2 Recovery Factors, 5.8.7 Carbonate Reservoir, 5.1.1 Exploration, Development, Structural Geology, 4.3.4 Scale, 5.5 Reservoir Simulation, 1.6.9 Coring, Fishing
- scaling methods, volume averaging, reservoir heterogeneities, scale-up, sub-scale variability
- 3 in the last 30 days
- 540 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Reservoir heterogeneities occur over a wide range of length scales, and their interaction with various transport mechanisms controls the performance of subsurface flow and transport processes. Modeling these processes at large scales requires proper scaleup of petrophysical properties that are autocorrelated or heterogeneously distributed in space, and analyzing their interaction with underlying transport mechanisms.
A method is proposed to investigate and quantify the uncertainty in reservoir models introduced by scaleup. It is demonstrated that when the volume support of the measurement is smaller than the representative elementary volume (REV) scale of the attribute to be modeled, there is uncertainty in the conditioning data because of scaleup and that uncertainty has to be propagated to spatial models for the attribute. This important consideration is demonstrated for mapping total porosity for a carbonate reservoir in the Gulf of Mexico. The results demonstrate that in most cases, the uncertainty distributions obtained by accounting for the scaleup procedure successfully characterize the variability in the actual core and log data observed along new wells. Conventional reservoir models considering the well data as "hard" conditioning data fail to predict the "true" values.
Following this discussion on scaling of reservoir attributes, a conceptual understanding of the scaling characteristics of flow responses such as recovery factor (RF) is provided, in terms of the mean and variance of RF at different length scales. Finally, a new technique is presented to systematically quantify the scaling characteristics of transport processes by accounting for subscale heterogeneities and their interaction with various transport mechanisms based on the volume averaging approach. The objective is to provide a tool for understanding the scaling relationships for RF using detailed fine-scale compositional reservoir simulations over a subdomain of the reservoir.
|File Size||987 KB||Number of Pages||12|
Bear, J. 1972. Dynamics of Fluids in Porous Media. Oxford, UK:Environmental Science Series, Elsevier.
Corbett, P.W.M., Jensen J.L., and Sorbie, K.S. 1998. A review of up-scalingand cross-scaling issues in core and log data interpretation and prediction.Geological Society, London, Special Publications 136 (1):9-16. doi:10.1144/GSL.SP.1998.136.01.02.
Coutelieris, F.A., Kainourgiakis, M.E., Stubos, A.K., Kikkinides, E.S., andYortsos, Y.C. 2006. Multiphase mass transport with partitioning and inter-phasetransport in porous media. Chemical Engineering Science 61(14): 4650-4661. doi:10.1016/j.ces.2006.02.037.
Cushman, J.H. 1982. Proofs of the volume averaging theorems for multiphaseflow. Advances in Water Resources 5 (4): 248-253. doi:10.1016/0309-1708(82)90009-4.
Gelhar, L.W., Welty, C., and Rehfeldt, K.R. 1992. A Critical Review of Dataon Field-Scale Dispersion in Aquifers. Water Resour. Res. 28 (7): 1955-1974. doi:10.1029/92WR00607.
Howes, F.A. and Whitaker, S. 1985. The spatial averaging theorem revisited.Chemical Engineering Science 40 (8): 1387-1392. doi:10.1016/0009-2509(85)80078-6.
Journel, A.G. and Huijbregts, C.J. 1978. Mining Geostatistics.London: Academic Press Limited.
Kechagia, P.E., Tsimpanogiannis, I.N., Yortsos, Y.C., and Lichtner, P.C.2002. On the upscaling of reaction-transport processes in porous media withfast or finite kinetics. Chemical Engineering Science 57 (13):2565-2577. doi:10.1016/S0009-2509(02)00124-0.
Kelkar, M. and Perez, G. 2002. Applied Geostatistics for ReservoirCharacterization. Richardson, Texas: SPE.
Lake, L.W. 1989. Enhanced Oil Recovery. Englewood Cliffs, New Jersey:Prentice Hall.
Lake, L.W. and Srinivasan, S. 2004. Statistical scale-up of reservoirproperties: concepts and applications. J. Pet. Sci. Eng. 44(1-2): 27-39. doi:10.1016/j.petrol.2004.02.003.
Lake, L.W., Srinivasan, S., and John, A. 2005. Statistical scale-up:concepts and application to reservoir flow simulation practice. InGeostatistics Banff 2004, ed. O. Leuangthong and C.V. Deutsch, Vol. 1,681-690. Dordrecht, The Netherlands: Quantitative Geology and Geostatistics,Springer.
Leung, J.Y. 2009. Reservoir modeling accounting for scale-up ofheterogeneity and transport processes. PhD dissertation, University of Texas atAustin, Austin, Texas.
Leung, J.Y. and Srinivasan, S. 2008. Analysis of uncertainty introduced byscale-up of log-derived porosity in carbonate settings. Proc., EighthInternational Geostatistics Congress, Santiago, Chile, 1-5 December, Vol. 2,1059-1064.
Leung, J.Y. and Srinivasan, S. 2009. Scale-up of hydrocarbons recoveryprocesses in heterogeneous reservoirs. Paper presented at the InternationalAssociation of Mathematical Geology Annual Meeting, Stanford, California, USA,23-28 August.
Li, D. and Lake, L.W. 1995. Scaling Fluid Flow Through HeterogeneousPermeable Media. SPE Advanced Technology Series 3 (1):188-197. SPE-26648-PA. doi:10.2118/26648-PA.
Neuman, S.P. 1994. Generalized scaling of permeabilities: Validation andeffect of support scale. Geophysical Research Letters 21(5): 349-352. doi:10.1029/94GL00308.
Plumb, O.A. and Whitaker, S. 1988. Dispersion in heterogeneous porous media:1. Local volume averaging and large-scale averaging. Water ResourcesResearch 24 (7): 913-926. doi:10.1029/WR024i007p00913.
Quintard, M. and Whitaker, S. 1988. Two-phase flow in heterogeneous porousmedia: The method of large-scale averaging. Transport in Porous Media 3 (4): 357-413. doi:10.1007/BF00233177.
Quintard, M. and Whitaker, S. 1998. Transport in chemically and mechanicallyheterogeneous porous media--III: Large-scale mechanical equilibrium and theregional form of Darcy's law. Advances in Water Resources 21 (7): 617-629. doi:10.1016/S0309-1708(97)00015-8.
Quintard, M. and Whittaker, S. 1994. Transport in ordered and disorderedporous media: I. The cellular average and the use of weighing functions.Transport in Porous Media 14 (2): 163-170. doi:10.1007/BF00615199.
Quintard, M. and Whittaker, S. 1996. Transport in chemically andmechanically heterogeneous porous media. I: Theoretical development ofregion-averaged equations for slightly compressible single-phase flow.Advances in Water Resources 19 (1): 29-47. doi:10.1016/0309-1708(95)00023-C.
Rovey, C.W. II and Cherkauer, D.S. 1995. Scale Dependency of HydraulicConductivity Measurements. Ground Water 33 (5): 769-780. doi:10.1111/j.1745-6584.1995.tb00023.x.
Sharma, A., Leung, J., Srinivasan, S., and Kim, Y. 2008. An IntegratedApproach to Reservoir Uncertainty Assessment: Case Study of a Gulf of MexicoReservoir. Paper SPE 116351 presented at the SPE Annual Technical Conferenceand Exhibition, Denver, 21-24 September. doi: 10.2118/116351-MS.
Shook, M., Li, D., and Lake, L.W. 1992. Scaling immiscible flow throughpermeable media by inspectional analysis. In Situ 16 (4):311-349. doi:10.1016/0148-9062(93)91860-L.
Soga, K., Page, J.W.E., and Illangasekare, T.H. 2004. A review of NAPLsource zone remediation efficiency and the mass flux approach. Journal ofHazardous Materials 110 (1-3): 13-27. doi:10.1016/j.jhazmat.2004.02.034.
Vereecken, H., Kasteel, R., Vanderborght, J., and Harter, T. 2007. UpscalingHydraulic Properties and Soil Water Flow Processes in Heterogeneous Soils.Vadose Zone Journal 6 (1): 1-28. doi:10.2136/vzj2006.0055.
Whitaker, S. 1999. The Method of Volume Averaging. Dordrecht, TheNetherlands: Theory and Applications of Transport in Porous Media, KluwerAcademic Publishers.
Wood, D.J., Lake, L.W., Johns, R.T., and Nunez, V. 2008. A Screening Modelfor CO2 Flooding and Storage in Gulf Coast Reservoir Based on DimensionlessGroups. SPE Res Eval & Eng 11 (3): 513-520.SPE-100021-PA. doi:10.2118/100021-PA.
Zanotti, F. and Carbonell, R.G. 1984. Development of transport equations formultiphase system--I: General Development for two phase system. ChemicalEngineering Science 39 (2): 263-278. doi:10.1016/0009-2509(84)80026-3.