MODELING PRESSURE FIELDS IN A PETROLEUM RESERVOIR TAKING INTO ACCOUNT THE CHANGE OF LIQUID LEVEL IN THE WELL

This article presents a numerical model of pressure fields during filtration of reservoir fluid, which accounts for the effect of the well. The mathematical formulation of the problem under consideration includes the equation of piezoconductivity in a cylindrical coordinate system and differs in a non-classical boundary condition obtained from the ratio of the balance of mass and momentum. The authors compare the numerical calculations and the analytical solution constructed in the Laplace — Carson image space. Den Iseger’s numerical algorithm is used to convert it to the original space. As a result of the comparison, the area of applicability of the computational experiment was determined. It is shown that in the case of a limited reservoir, the exact solution of the problem coincides with a numerical experiment over the entire domain of definition. In the case of an infinite reservoir, the numerical model is applicable only in the region of small times, the dimensions of which are determined by the values of the right boundary and the radial coordinate.

INVERSE NODAL PROBLEM FOR A CLASS OF NONLOCAL STURM‐LIOUVILLE OPERATOR

Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered. We prove that a dense subset of nodal points uniquely determine the boundary condition parameter and the potential function of the Sturm‐Liouville equation. We also provide a constructive procedure for the solution of the inverse nodal problem.

On the generalized eigenfunctions system of the Sturm–Liouville problem

In this paperwe investigate eigenfunctions and generalized eigenfunctions system of the Sturm–Liouville problem with classical boundary condition on the left boundary and nonlocal boundary conditionsof four types on the right boundary.