Digital cluster model of pore space at flow of three-phase flow in porous medium

About the authors:

Aleksandr B. Shabarov, Dr. Sci. (Tech.), Professor, Honored Scientist of the Russian Federation, Professor, Department of Applied and Technical Physics, School of Natural Science, University of Tyumen, Tyumen, Russia; a.b.shabarov@utmn.ru, https://orcid.org/0000-0002-5374-8704
Dmitry E. Igoshin, Cand. Sci. (Phys.-Math.), Head of the Reservoir Physics Laboratory, Corporate Center for the Study of Reservoir Systems (Core and Fluids), Gazprom VNIIGAZ (Moscow); Associate Professor, Department of Fundamental Mathematics, Institute of Physics and Technology, University of Tyumen; d.e.igoshin@utmn.ru

Polina M. Rostenko, Postgraduate Student, Department of Applied and Technical Physics, Institute of Physics and Technology, University of Tyumen; stud003991636@study.utmn.ru

Anastasia P. Sadykova, Postgraduate Student, Department of Applied and Technical Physics, Institute of Physics and Technology, University of Tyumen; stud0000217819@study.utmn.ru

Abstract:

The work is devoted to one of the urgent problems of the oil and gas industry — the study of three-phase filtration. The creation of pore space models is an important stage in the study of the flow of oil and gas mixtures for the subsequent determination of the filtration and reservoir properties of reservoir rocks. The aim of the study is to develop a physical and mathematical model of a porous medium on the scale of a core sample. A digital cluster model for calculating the geometric parameters of the pore space is presented. The structure of the pore space of the cluster model is based on the distribution of pores by diameters obtained from capillary pressure curves (KCD). The core contains clusters consisting of a big channel (B) through which oil, water and gas move in a clear mode, average channels (A) with moving water and gas and small channels (S) with moving gas, as well as bridges between these channels. The division of the pore diameter distribution function into regions related to big, average and small channels is based on empirically determined relationships between the numbers of channels through which fluids move in the pore space in the above combinations. At the same time, the transition from the physical core model to the digital cluster model is carried out with the preservation of porosity, absolute permeability and taking into account the tortuosity of the channels. The dependence of the tortuosity of channels on their diameter is assumed according to a decreasing power law. The model presented in this paper is tested on two examples at different values of effective porosity and the number of intervals of the pore distribution function by diameter. The model has the potential for further development and calculation of the filtration flow of a three-phase mixture (oil, gas and water) on the scale of a core sample.

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