Optimal Well Placement in Heterogeneous Reservoirs Via Semi-Analytic Modeling
- Randy D. Hazlett (Potential Research Solutions) | D. Krishna Babu (Potential Research Solutions)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2005
- Document Type
- Journal Paper
- 286 - 296
- 2005. Society of Petroleum Engineers
- 5.8.6 Naturally Fractured Reservoir, 2.3.4 Real-time Optimization, 4.1.5 Processing Equipment, 5.1.5 Geologic Modeling, 1.2.3 Rock properties, 5.1 Reservoir Characterisation, 5.5 Reservoir Simulation, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 4.3.4 Scale, 3.3.6 Integrated Modeling, 5.1.1 Exploration, Development, Structural Geology, 5.3.2 Multiphase Flow, 5.6.9 Production Forecasting, 5.6.4 Drillstem/Well Testing
- 4 in the last 30 days
- 1,083 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
The need for accurate well-productivity models with arbitrary welltrajectories spurred a revival in analytic solution methodology for fluidtransport problems.Analytic formulations often depict single-phase flowthroughout the reservoir.The Babu-Odeh horizontal-well solution for abox-shaped reservoir with spatially invariant properties is generalized here toallow closed-form solutions for heterogeneous media.A reservoir isdecomposed into interacting regions, each with its own reservoir properties andassociated analytic potential flow solution.Using established boundaryelement techniques, pressure and flux continuity are imposed at selectedinterface points to solve for the steady material exchange betweenregions. Constant pressure and zero flux features (fractures andbarriers) are easily entertained at region boundaries.The 2D,pseudosteady-state solution for heterogeneous media is embedded within areservoir performance feedback loop of a powerful gradient search method toproduce a robust optimal infill well placement algorithm.Utilizing thisapproach, new criteria are developed concerning optimal placement of verticalwells for primary production with respect to heterogeneity, asymmetry, andanisotropy. The semianalytic method has been extended to 3D flows to serve as acompute engine for a new generation of reservoir management and optimizationtools.
Well-placement strategy in infill programs is strongly dependent upon thereservoir development plan and the present stage in that overallplan.Often, well patterns are deployed based upon uniform permeabilitymodels; however, the role of reservoir heterogeneity can beformidable.Most wells are placed as production wells and selectivelyconverted to injectors as fields mature and interwell communication patternsbecome increasingly important.While reservoir engineers have numericalsimulation methods capable of reservoir performance feedback with regard tocandidate well placement, many of these models have inherent restrictions onthe ability to accurately model well performance.Few reservoir engineershave the luxury to discretize on the level of the wellbore radius, but ratherrely on block-centered, wellbore coupling correlations.Well productionengineers utilize models with fine-scale discretization; however, their inflowperformance predictions can be limited in reservoir scope.
|File Size||1 MB||Number of Pages||11|
1. Muskat, M.:The Flow of Homogeneous Fluids Through PorousMedia, McGraw-Hill,New York City (1937)226.
2. Babu, D.K. et al.:"TheRelation Between Wellblock and Wellbore Pressures in Numerical Simulation ofHorizontal Wells," SPERE (August 1991) 324.
3. Peaceman, D.W.:"Interpretation of Well-Block Pressuresin Numerical Reservoir Simulation," SPEJ (June 1978) 183; Trans., AIME,265.
4. Peaceman, D.W.:"Interpretation of Well-BlockPressures in Numerical Reservoir Simulation With Nonsquare Gridblocks andAnisotropic Permeability," SPEJ (June 1983) 531.
5. Babu, D.K. and Odeh, A.S.:"Productivity of a HorizontalWell," SPERE (November 1989) 417.
6. Joshi, S.D.: Horizontal Well Technology, PennWell, Tulsa (1991).
7. Ozkan, E.:"Performance of Horizontal Wells," PhD dissertation, U.of Tulsa, Tulsa, Oklahoma (1988).
8. Ding, Y.:"UsingBoundary Integral Methods To Couple a Semianalytical Reservoir Flow Model and aWellbore Flow Model,"paper SPE 51898 presented at the 1999 SPEReservoir Simulation Symposium, Houston, 14-17 February.
9. Tribe, I.R. et al.:"Precise Well Placement Using RotarySteerable Systems and LWD Measurements ," paper SPE 71396 presented at the2001 SPE Annual Technical Conference and Exhibition, New Orleans, 30September-3 October.
10. Che' Lah, M.Z. et al.:"Technology Advancements in OptimumWellbore Placement," paper SPE 64479 presented at the 2000 SPE Asia PacificOil and Gas Conference and Exhibition, Brisbane, Australia, 16-18 October.
11. Bryant, I.D. and Baygun, B.:"Reservoir Description for OptimalPlacement of Horizontal Wells," paper SPE 35521 presented at the 1996European 3D Reservoir Modelling Conference, Stavanger, 16-17 April.
12. Wagenhofer, T. and Hatzignatiou, D.G.:"Optimization of Horizontal WellPlacement," paper SPE 35714 presented at the 1997 SPE Western RegionalMeeting, Anchorage, Alaska, 22-24 May.
13. Norrena, K.P. and Deutsch, C.V.:"Automatic Determination of WellPlacement Subject to Geostatistical and Economic Constraints," paper SPE78996 presented at the 2002 SPE International Thermal Operations and Heavy OilSymposium and International Horizontal Well Technology Conference, Calgary, 4-7November.
14. Centilmen, A., Ertekin, T., and Grader, A.S.:"Applications of Neural Networks inMultiwell Field Development," paper SPE 56433 presented at the 1999 SPEAnnual Technical Conference and Exhibition, Houston, 3-6 October.
15. Pallister, I.C. and Ponting, D.K.:"Asset Optimization Using MultipleRealizations and Streamline Simulation," paper SPE 59460 presented at the2000 SPE Asia Pacific Conference on Integrated Modeling for Asset Management,Yokohoma, Japan, 25-26 April.
16. Beckner, B.L. and Song, X.:"Field Development Planning UsingSimulated Annealing—Optimal Economic Well Scheduling and Placement," paperSPE 30650 presented at the 1995 SPE Annual Technical Conference and Exhibition,Dallas, 22-25 October.
17. Güyagüler, B. and Horne, R.N.:"Uncertainty Assessment of WellPlacement Optimization," paper SPE 71625 presented at the 2001 SPE AnnualTechnical Conference and Exhibition, New Orleans, 30 September-3 October.
18. Montes, G. et al.:"The Use of Genetic Algorithms in WellPlacement Optimization," paper SPE 69439 presented at the 2001 SPE LatinAmerican and Caribbean Petroleum Engineering Conference, Buenos Aires, 25-28March.
19. Bittencourt, A.C. and Horne, R.N.:"Reservoir Development and DesignOptimization," paper SPE 38895 presented at the 1997 SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, 5-8 October.
20. Yeten, B., Durlofsky, L.J., and Aziz, K.:"Optimization of Nonconventional WellType, Location and Trajectory," paper SPE 77565 presented at the 2002 SPEAnnual Technical Conference and Exhibition, San Antonio, Texas, 29 September-2October.
21. Santellani, G., Hansen, B., and Herring, T.:"'Survival of the Fittest': anOptimized Well-Location Algorithm for Reservoir Simulation," paper SPE39754 presented at the 1998 SPE Asia Pacific Conference, Kuala Lumpur, 23-24March.
22. Dejean, J.-P. and Blanc, G.: "Managing Uncertainties on ProductionPredictions Using Integrated Statistical Methods," paper SPE 56696presented at the 1999 SPE Annual Technical Conference and Exhibition, Houston,3-6 October.
23. Kirkup, S.:"The BEM for Helmholtz Problems," http://www.boundary-element-method.com/bemhelm/manual.htm, 2001.
24. Koh, L.S. and Tiab, D.:"A Boundary-Element Algorithm forModeling 3D Horizontal Well Problems Using 2D Grids," paper SPE 26228presented at the 1993 SPE Petroleum Computer Conference, New Orleans, 11-14July.
25. Sato, K. and Horne, R.N.:"Perturbation Boundary Element Methodfor Heterogeneous Reservoirs: Part 1—Steady-State Flow Problems," SPEFE(December 1993) 306.
26. Numbere, D.T. and Tiab, D.:"An Improved Streamline-GeneratingTechnique That Uses the Boundary (Integral) Element Method," SPERE (August1988) 1061.
27. Jongkittinarukorn, K. and Tiab, D.: "Development of the Boundary ElementMethod for a Horizontal Well in Multilayer Reservoir," paper SPE 39939presented at the 1998 SPE Rocky Mountain Regional/Low-Permeability Symposium,Denver, 5-8 April.
28. Archer, R.A. and Horne, R.N.:"The Green Element Method forNumerical Well Test Analysis," paper SPE 62916 presented at the 2000 SPEAnnual Technical Conference and Exhibition, Dallas, 1-4 October.
29. Kikani, J. and Horne, R.N.:"Modeling Pressure-Transient Behaviorof Sectionally Homogeneous Reservoirs by the Boundary-Element Method,"SPEFE (June 1993) 145.
30. Masukawa, J. and Horne, R.N.:"Application of the Boundary IntegralMethod to Immiscible Displacement Problems ," SPERE (August 1988) 1069.
31. Jasti, J.K., Penmatcha, V.R., and Babu, D.K.: "Use of Analytical Solutions ToImprove Simulator Accuracy," SPEJ (March 1999)47.
32. McCann, R.C., Hazlett, R.D., and Babu, D.K.:"Highly AccurateApproximations of Green's and Neumann Functions," Proc. R. Soc. A (2001) 457,767.
33. Linton, C.M.: "Rapidly Convergent Representations for Green's Functionsfor Laplace's Equation," Proc. R. Soc. Lond. A (1999) 455, 1767.
34. Marshall, S.L.: "A Rapidly Convergent Modified Green's Function forLaplace's Equation in a Rectangular Region," Proc. R. Soc. Lond. A (1999) 455,1739.
35. Duff, G.D.F. and Naylor, D.:Differential Equations of AppliedMathematics, John Wiley & Sons, New York City (1966).
36. Stroud, A.H.: Approximate Calculation of Multiple Integrals,Prentice-Hall,Englewood Cliffs, New Jersey (1971).
37. Brown, P.N. and Hindmarsh, A.C.:"Reduced Storage Matrix Methods inStiff ODE Systems," J. Appl. Math. & Comp. (1989)31, 49.
38. Seager, M.K.: "A SLAP for the Masses," Parallel Supercomputing: Methods,Algorithms and Applications, G.F. Carey(ed.), Wiley, New York City (1989)135-155.
39. Visual Numerics: "IMSL Fortran 90 MP Library: Function Catalog," http://www.vni.com/products/imsl/docs/F90catalog.pdf.
40. Edwards, M.G., Elf, R.A., and Aziz, K.:"Quasi K-Orthogonal Streamline Grids:Gridding and Discretization," paper SPE 49072 presented at the 1998 SPEAnnual Technical Conference and Exhibition, New Orleans, 27-30 September.
41. Nakashima, T. et al.:"Effective Permeability Estimation forModeling Naturally Fractured Reservoirs ," paper SPE 68124 presented at the2001 SPE Middle East Oil Show, Bahrain, 17-20 March.
42. Lough, M.F., Lee, S.H., and Kamath, J.: "An Efficient Boundary IntegralFormulation for Flow Through Fractured Porous Media," J. Comp. Physics(1998) 143, 1.