Analysis of Parallel Algorithm Efficiency for Numerical Solution of Mass Transfer Problem in Fractured-Porous Reservoir

Uzyanbaev, R. M.; Poveschenko, Yuri Andreevich; Подрыга, В. О.; Polyakov, Sergey V.; Bobreneva, Yuliya Olegovna; Gubaydullin, I. M.

doi:10.1007/978-3-031-22941-1_3

Cited by 4 publications

(3 citation statements)

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“…A one-dimensional statement of Problems ( 1)-( 7) is considered. An implicit finite-difference scheme on a uniform grid is used to solve partial differential equations [15,19,20]. Note that the approach presented below will be the basis for the problem in the multidimensional case.…”

Section: Difference Scheme Constructionmentioning

confidence: 99%

“…To solve a short problem, all MPI processes carry out a collective exchange of coefficients; the details of the algorithm are presented in [15]. This algorithm is implemented using the MPI_Allreduce function, the parameters of which are presented below.…”

Section: Matrix Sweepmentioning

confidence: 99%

“…In our previous works [14,15], the isothermal process of mass transfer of a two-phase fluid in a fractured-porous reservoir was considered in a one-dimensional setting. An original implicit finite-difference scheme on a non-uniform spatial grid and a parallel algorithm for solving the problem were proposed.…”

Section: Introductionmentioning

confidence: 99%

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One Approach to Numerical Modeling of the Heat and Mass Transfers of Two-Phase Fluids in Fractured-Porous Reservoirs

Bobreneva,

Poveshchenko,

Podryga

et al. 2023

Mathematics

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The work is devoted to numerical modeling of the processes of heat and mass transfer of a two-phase fluid in the environment of a production well, which is necessary for monitoring the development of fractured-porous reservoirs. This work proposes an efficient approach to constructing a solution to the problem. To solve the problem, a model of the “double medium” type is used, where the pore part of the reservoir is considered as the first medium, and the system of natural fractures is considered as the second medium. For the resulting mathematical model, the difference schemes with time weights are constructed based on the algorithm of splitting by physical processes, which ensure the correctness and consistency of fluxes in the fracture system and the pore reservoir. In the numerical solution, the approximations of differential operators obtained in the framework of the finite difference method are used. For the parallel implementation of the developed numerical approach, the domain decomposition method and the matrix sweep algorithm are chosen. The program implementation is made using the MPI standard. Computational experiments are carried out, the results of which confirm the effectiveness of the developed numerical algorithm and its parallel implementation. In numerical experiments, the distributions of pressure and temperature near an operating production well are obtained, on the basis of which it is possible to adjust the operation of wells in order to increase production.

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Section: Difference Scheme Constructionmentioning

confidence: 99%

Section: Matrix Sweepmentioning

confidence: 99%