Equivalent Wellblock Radius for Partially Perforated Vertical Wells--Part I: Anisotropic Reservoirs With Uniform Grids
- Ali H. Dogru (Saudi Arabian Oil Company)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2010
- Document Type
- Journal Paper
- 1,028 - 1,037
- 2010. Society of Petroleum Engineers
- 5.1.1 Exploration, Development, Structural Geology, 5.1.5 Geologic Modeling, 2.2.2 Perforating, 5.5 Reservoir Simulation
- equivalent wellblock radius, well modeling, numerical reservoir simulation, reservoir simulation, reservoir modeling
- 4 in the last 30 days
- 559 since 2007
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The well index in a numerical reservoir simulator relates the flow rate to the difference between well flowing pressure and simulator gridblock pressure. The standard method for computing well index, Peaceman's formula (Peaceman 1978), requires an equivalent wellblock radius at which the gridblock pressure is equal to the pressure from an analytical solution for steady-state single-phase flow. Although Peaceman?s formula is accurate for fully penetrating vertical wells, it fails to account for the effect of vertical flow in partially penetrating wells.
In this paper, we present a new analytical expression for the equivalent wellblock radius in a homogeneous, anisotropic reservoir with a uniform square grid around the well path. The new equation has the same structure as Peaceman's equation but adds one new parameter to account for partial penetration and for vertical flow. The new formula reduces to Peaceman's formula when the well is fully penetrating. Model simulation study showed that the new method reduced the error in the calculated flow rates from 30% to less than 1% at minimal cost.
|File Size||564 KB||Number of Pages||10|
Aavatsmark, I. and Klausen, R.A. 2003. Well Index in Reservoir Simulationfor Slanted and Slightly Curved Wells in 3D Grids. SPE J. 8 (1): 41-48. SPE-75275-PA. doi: 10.2118/75275-PA.
Aziz, K. and Settari, A. 1979. Petroleum Reservoir Simulation. Essex,UK: Elsevier Applied Science Publishers.
Babu, D.K. and Odeh, A.S. 1989. Productivity of a HorizontalWell. SPE Res Eng 4 (4): 417-421. SPE-18298-PA. doi:10.2118/18298-PA.
Brons, F. and Marting, V.E. 1961. The Effect of Restricted Fluid Entry onWell Productivity. J Pet Technol 13 (2): 172-174;Trans., AIME, 222. SPE-1322-G. doi: 10.2118/1322-G.
Craft, B.C. and Hawkins, M.F. 1959. Petroleum Reservoir Engineering.Upper Saddle River, New Jersey: Prentice Hall Press.
Ding, Y. 1995. Scaling-up inthe Vicinity of Wells in Heterogeneous Field. Paper SPE 29137 presented atthe SPE Reservoir Simulation Symposium, San Antonio, Texas, USA, 12-15February. doi: 10.2118/29137-MS.
Dogru, A.H., Sunaidi, H.A., Fung, L.S., Habiballah, W.A., Al-Zamel, N., andLi, K.G. 2002. A ParallelReservoir Simulator for Large-Scale Reservoir Simulation. SPE Res Eval& Eng 5 (1): 11-23. SPE-75805-PA. doi:10.2118/75805-PA.
Donnez, P. 2007. Essentials of Reservoir Engineering, 201-205. Paris:Editions TECHNIP.
Kozeny, J. 1953. Hydraulik: Ihre Grundlagen und Praktische Anvendung.Vienna, Austria: Springler-Verlag.
Lin, C.Y. 1995. New Well Modelsfor Partially Penetrating Wells in Heterogeneous Reservoirs Using Non-Uniformgrids. Paper SPE 29122 presented at the SPE Reservoir Simulation Symposium,San Antonio, Texas, USA, 12-15 February. doi: 10.2118/29122-MS.
Muggeridge, A.H., Cuypers, M., Bacquet, C., and Barker, J.W. 2002. Scale-upof well performance for reservoir flow simulation. Petroleum Geoscience 8 (2): 133-139.
Muskat M. 1949. Physical Principles of Oil Production. New York:International Series in Pure Applied Physics, McGraw-Hill Book Co.
Muskat, M. 1937. The Flow of Homogeneous Fluids Through Porous Media.New York: McGraw-Hill Book Co.
Odeh, A. 1980. An Equation forCalculating Skin Factor Due to Restricted Entry. J Pet Technol 32 (6): 964-965. SPE-8879-PA. doi: 10.2118/8879-PA.
Peaceman, D.W. 1978. Interpretation of Well-Block Pressuresin Numerical Reservoir Simulation. SPE J. 18 (3):183-194; Trans., AIME, 265. SPE-6893-PA. doi:10.2118/6893-PA.
Peaceman, D.W. 1983. Interpretation of Well-BlockPressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks andAnisotropic Permeability. SPE J. 23 (3): 531-543;Trans., AIME, 275. SPE-10528-PA. doi: 10.2118/10528-PA.
Wolfsteiner, C., Durlofsky, L.J., and Aziz, K. 2000. Approximate Model for Productivity ofNonconventional Wells in Heterogeneous Reservoirs. SPE J. 5 (2): 218-226. SPE-56754-PA. doi: 10.2118/62812-PA.