Geodesic
Numerical determination of pressure and optimum activities of wells for solving boundary-value problem of two-phase filtration with the use of linear programming method
Matematičeskoe modelirovanie, Tome 21 (2009) no. 11, pp. 83-98

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The numerical algorithm of calculation of pressure, bottom-hole pressures and optimum flow rates of wells of the two-phase filtration model in some water flooding element with boundary conditions I, II or mixed (boundary conditions I and II are given on separate parts of the border of an element) has been developed. For determination of pressure on the suggested algorithm, the modified simplex method with representation of Linear Programming problem matrix in a multiplicative form is used. The algorithm was tested when carrying out the computing experiments for series of homogeneous and heterogeneous seams water flooding elements with various boundary conditions. For conditions of II application limits of algorithm are shown considering the fulfillment of the balance ratio for the movement equation in the field of two-phase filtration. The flow rates of the working wells have been compared with similar flow rates, received with the use of the method of alternating directions. This comparison is true of the bottom-hole pressures. 
@article{MM_2009_21_11_a7,
     author = {V. D. Slabnov and V. V. Skvortsov},
     title = {Numerical determination of pressure and optimum activities of wells for solving boundary-value problem of two-phase filtration with the use of linear programming method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--98},
     publisher = {mathdoc},
     volume = {21},
     number = {11},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_11_a7/}
}
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V. D. Slabnov; V. V. Skvortsov. Numerical determination of pressure and optimum activities of wells for solving boundary-value problem of two-phase filtration with the use of linear programming method. Matematičeskoe modelirovanie, Tome 21 (2009) no. 11, pp. 83-98. http://geodesic.mathdoc.fr/item/MM_2009_21_11_a7/