The Productivity Index of an Inclined Well in Finite-Difference Reservoir Simulation

Lee, S.H.; Milliken, William J.

doi:10.2118/25247-ms

Cited by 31 publications

(6 citation statements)

References 9 publications

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“…As pointed out by Peaceman, 2 just using the analytical solution directly in the seven-point or five-point discretization molecule, as suggested in Ref. 16, may give a wrong solution. This will indeed be the case for a slanted well in a 3D grid with anisotropy and/or aspect ratio different from unity.…”

Section: Numerical Partmentioning

confidence: 99%

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Well Index in Reservoir Simulation for Slanted and Slightly Curved Wells in 3D Grids

Aavatsmark

Klausen

2003

SPE Journal

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A new, accurate method for computing the well index (WI) for a well that is oriented in an arbitrary direction in a 3D grid is presented. The method is simple and seminumerical and takes well direction and neighboring gridblocks into account. It is assumed that the medium is homogeneous. The method can be applied for any grid or discretization. However, only Cartesian grids with a seven-point stencil are used here. Properties of the seminumerical WI are investigated for both synthetic and field examples. The investigated properties are convergence rate and dependency on well direction, well location, grid geometry, and anisotropy. The new method shows the importance of taking the neighboring gridblocks into account. Seminumerical Well IndexThe problem of finding the WI is one of finding a relation between the well pressure, the well rate and the discrete pressure value from a numerical simulation for the entire gridblock. A typical well radius is about 10 cm, while one numerical pressure value for a gridblock typically represents a volume of 100×100×1 m 3 . The well represents a sink (or source) for the pressure distribution. This means that in the wellblock there will be a huge variation in the real pressure. An illustration is given in Fig.

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Section: Numerical Partmentioning

confidence: 99%

“…In Ref. 16, slender body theory is used to find an analytical pressure drop. This is then used directly in the seven-point discretization molecule in 3D, with adjustment for anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Well Index in Reservoir Simulation for Slanted and Slightly Curved Wells in 3D Grids

Aavatsmark

Klausen

2003

SPE Journal

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“…Using slender body theory, Lee and Milliken (1993) have derived an asymptotic solution of single-phase flow around an inclined well that is applied to the determination of the productivity index. The method of reflections can account for the presence of layer boundaries through the application of image solutions.…”

Section: Introductionmentioning

confidence: 99%

Computation of Productivity Index with Capillary Pressure Included and Its Application in Interpreting Production Data from Low-Permeability Oil Reservoirs

Chen

2011

All Days

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Capillary pressure might be ignored in high permeability rocks but could not be neglected in low permeability rocks. In order to study the effect of capillary pressure on production performance in low permeability oil wells or reservoirs, the formula of calculating water cut, dimensionless total and oil productivity indices were derived by considering capillary pressure. Productivity index and water cut data were computed using the new models with capillary pressure included. The results proved that the productivity index increases with water cut in high permeability rocks but decreases with the increase in water cut within a specific range in low-permeability rocks. Water flooding experiments have then been conducted in core samples with low and high permeabilities. The experimental data also demonstrated the same relationship between productivity index and water cut as the new productivity index model foreseen. Finally the productivity index data were calculated using production data from oil wells and the results were compared with the experimental data of the productivity index determined from core flooding tests. The curves of productivity index vs. water cut obtained from the production data of oil producers were consistent with those inferred from water flooding data in core samples. Note that the core plugs were sampled from the same oil wells. The new productivity index model could be used to explain the difference in production performance between high-and low-permeability oil wells.

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“…Others followed this approach [9][10][11][12], but 3D models were developed as well [13][14][15][16][17]. A second kind of extension are the multi-layer models [18][19][20]. Lee and Milliken [18], and Kuchuk and Habashy [19] used a method of reflection and transmission, while Basquet et al [20] used a "quadrupole" method relating the pressures between the various layers.…”

Section: Introductionmentioning

confidence: 99%

“…A second kind of extension are the multi-layer models [18][19][20]. Lee and Milliken [18], and Kuchuk and Habashy [19] used a method of reflection and transmission, while Basquet et al [20] used a "quadrupole" method relating the pressures between the various layers. The multi-layer models are also, however, still limited to constantinflux or infinite-conductivity wells.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytic Calculations of Horizontal Well Productivity in Fractured Reservoirs

Fokker¹,

Verga

Egberts³

2003

Proceedings of SPE Annual Technical Conference and Exhibition

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractSimplified analytical relations derived for homogeneous formations are usually applied for the determination of the productivity of horizontal wells regardless of the presence of heterogeneities in the reservoir. Furthermore, complex well architectures and the wealth of completion options currently available can not be properly taken into account, because the well trajectory can only be schematized as a single horizontal wellbore. However, the use of numerical reservoir simulators to reliably forecast the productivity of horizontal wells draining heterogeneous reservoirs may be time-prohibitive or not feasible due to lack of sufficiently detailed information, especially during the appraisal phase or the early stages of production.A new semi-analytic technique is proposed in this paper to solve the inflow equations in an approximate yet reliable manner. The solution to 3-dimensional problems of singlephase flow into a horizontal well, taking into account friction in the wellbore, is provided for both single-layer reservoirs and reservoirs comprising two interfering layers. The method has been extended also to describe the fluid flow when the well intercepts one or more fractures. The presented technique allows very fast calculation of the well productivity in oil and gas reservoirs offering great flexibility in the placement and architecture of the wells.The method has been applied to two field cases for which the well productivity under pseudo steady-state conditions was measured. One of these is a 200-m long horizontal well draining an isotropic carbonatic reservoir and intersected by a natural low-conductivity fracture. The other is a similar well, intercepting a natural high-conductivity fault, but the oilbearing formation is anisotropic. Good correspondence was found between the actual productivity and the predictions obtained by application of the proposed semi-analytic technique.

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The Productivity Index of an Inclined Well in Finite-Difference Reservoir Simulation

Cited by 31 publications

References 9 publications

Well Index in Reservoir Simulation for Slanted and Slightly Curved Wells in 3D Grids

Well Index in Reservoir Simulation for Slanted and Slightly Curved Wells in 3D Grids

Computation of Productivity Index with Capillary Pressure Included and Its Application in Interpreting Production Data from Low-Permeability Oil Reservoirs

Semi-Analytic Calculations of Horizontal Well Productivity in Fractured Reservoirs

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