Method of determination of thermodynamic and filtration parameters for hydrodynamic compositional models

About the authors:

Alexander Ya. Gilmanov, Cand. Sci. (Phys.-Math.), Senior Lecturer, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.y.gilmanov@utmn.ru; ORCID: 0000-0002-7115-1629

Ivan L. Mikhaylin, Master Student, Department of Modeling of Physical Processes and Systems, Institute of Physics and Technology, University of Tyumen; rrrrr5678@list.ru

Alexander P. Shevelev, Cand. Sci. (Phys.-Math.), Associate Professor, Professor, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.p.shevelev@utmn.ru; ORCID: 0000-0003-0017-4871

Abstract:

The calculation of phase behavior is important for choosing a rational mode of development of oil and gas fields. However, solving equations of state and material balance by traditional methods is associated with difficulties: Cardano’s formula allows finding only the roots of a cubic equation, the dichotomy method requires the selection of a segment on which there is only one root. Newton’s iterative method allows finding only one root under given conditions. Another important problem in hydrodynamic simulation is the uncertainty of the relative phase permeability of oil during three-phase filtration. It is proposed for the first time to use the algorithm of sequential division of Euclidean polynomials and Sturm’s theorem to calculate phase behavior. The aim of the work is to develop a methodology for calculating phase behavior and determining the area of increased uncertainty of relative phase permeability of oil. This area is defined as a set of phase saturation values at which relative phase permeabilities of oil according to Stone 1^st and 2^d models differ by more than 10%.

The proposed methodology makes it possible to predict areas of metastable states. The possibility of calculating the roots of material balance equations that do not have physical meaning is excluded.

For a model three-phase system, an area of increased uncertainty of relative phase permeability of oil is determined.

It is shown that it is possible to determine all real roots of the equations. The proposed metho­dology makes it possible to refine forecast calculations for gas condensate fields.

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