Release:
2024. Vol. 10. № 4 (40)About the authors:
Yaroslav A. Kryazhev, Postgraduate Student, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; kryazhev_yar@mail.ru, https://orcid.org/0000-0002-9382-7378Abstract:
The assessment of the stability of oil displacement front by water is necessary for design of an oil field development system while maintaining the reservoir pressure. Multidimensional dynamic models of the stability of front are probabilistic in nature, and criterion approaches have been developed only for classical problems. Gravitational forces are considered in the framework of Rapoport-Leas model only in this article. The objective of research is to develop the Saffman–Taylor approach for assessing the stability of oil displacement front, considering capillary and gravitational forces. The proposed model is based on the laws of conservation of mass for water and oil and Darcy’s laws for these phases in a one-dimensional approximation. Corey correlations for relative phase permeabilities and the equation for capillary pressure are used as additional relations. Saffman–Taylor conditions are used to assess the stability of oil displacement front. The procedure for introducing dimensionless complexes for equations used is carried out. Using an explicit finite difference scheme, the saturation of displacing liquid at the front is calculated. The critical values are determined for the introduced dimensionless complexes, in which the displacement of oil by water is still stable. The results have shown that gravitational and capillary forces can have a stabilizing effect when the mobility of displacing fluid is higher than the mobility of the displaced one. Capillary forces have a higher stabilizing effect than gravitational forces. The stability analysis performed on the model data helped to determine the oil viscosity range at which viscous forces are insufficient for the formation of viscous fingers.Keywords:
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