The boundary element method in two-phase Stefan problems

Abstract The presented paper is devoted to the development and testing of a computational tool for assessment of the reservoir pressure and prompt generation of the pressure maps of collectors. The tool is based on a proxy model that allows to solve the two-dimensional diffusion equation for unsteady liquid filtration using the boundary element method. To expand the applicability of the proxy model, an algorithm for automated parameter adaptation was developed. This algorithm allows to exclude knowingly unreliable data or low-quality data from modeling. This is achieved due to analyzing the correlation between the injection, production and bottom-hole pressures for the entire well stock over the history of the reservoir development. In addition, this paper describes an approach to modeling two-phase oil and gas filtration based on the use of pseudofunctions. This approach considers the influence of gas on the oil filtration process. The use of pseudofunctions allows us to linearize the diffusion equation for two-phase filtration and to solve it using the boundary element method in the same manner as for the case of oil filtration without gas. To demonstrate the results of the proxy model validation, examples of its use for generating the pore pressure maps for two real collectors are given. The average values of the reservoir pressure at the wells calculated using the proxy model are compared with the results of the corresponding well tests and with the traditional isobar maps. The analysis showed that the average deviation of the proxy model from the real reservoir pressures is less than 10%.

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Toward Large Scale Simulations of Emulsion Flows in Microchannels Using Fast Multipole and Graphics Processor Accelerated Boundary Element Method

Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D ◽

10.1115/imece2012-86238 ◽

2012 ◽

Cited By ~ 2

Author(s):

Yulia A. Itkulova ◽

Olga A. Solnyshkina ◽

Nail A. Gumerov

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Large Scale ◽

Experimental Studies ◽

Three Dimensions ◽

Graphics Processors ◽

Fast Multipole ◽

Two Phase ◽

Droplet Dynamics ◽

Element Method

Several interesting effects discovered recently, such as “dynamic blocking” and “jamming” of emulsion flows in microchannels require in depth theoretical, computational, and experimental studies. The present study is dedicated to development of efficient computational methods and tools to understand the behavior of complex two-phase Stokesian flows. Application of the conventional boundary element method is frequently limited by the computational and memory complexity. The fast multipole methods provide O(N) type algorithms, which can further be accelerated by utilization of graphics processors. We developed efficient codes, which enable direct simulation of systems of tens of thousands of deformable droplets in three dimensions or several droplets with very high discretization of the interface. Such codes can be used for detailed visualization and studies of the structure of droplet flows in channels. Example computations include droplet dynamics in shear flows and in microchannels. We discuss results of simulations and details of the algorithm. We also consider that the present work is a step towards more realistic modeling of the microchannel dispersed flows as further development of the model is required to account for properties of thin films between the droplets, processes of coalescence, etc.

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