Numerical Identification of the Filtration Capacitive Parameters in Two-Phase Petroleum Reservoirs

We study initial and boundary value problem for nonlinear three dimensional two phase nonlinear filtration problem in three dimensional bounded regions. The reservoir is a two phase and three dimensional oil-water system that is been implemented with typical parallelepiped model. The reservoir constructed with different number of grid blocks in x, y and z directions and initialized with initial pressure, water saturation, corresponding fluid and rock properties in every grid block. To find approximate solution of the above mentioned problem we use finite difference method. We form solution’s algorithm of inverse problem for numerical parameter identification of the petroleum reservoir.

Non-Field Analytical Method for Filtration of Slightly Compressible Fluid through Porous Media with Stagnation Areas

In this study the method of Kulish has been used to derive a non-field solution of the equation, which models the process of unsteady filtration of a slightly compressible fluid within a domain consisting of both flow and stagnation areas under the influence of some pressure distribution at the boundary. The solution relates the local values of pressure and the corresponding pressure gradient and is valid everywhere within the domain including the boundary. The solution thus obtained is in the form of a series with respect to generalised differ-integral operators of fractional orders. The solution has been compared with the know solution of the filtration problem with no stagnation areas. Finally, an integral equation to estimate the pressure evolution at the boundary for a given filtration speed has been proposed.

Mathematical modelling of carbonate reservoir dissolution and prediction of the controlled hydrochloric acid treatment efficiency

The article presents the theoretical studies results of hydrochloric acid compositions filtration in carbonate collectors porous media saturated with two-phase formation liquid. Solution of filtration problem in the process of carbonate rock leaching with possible regulation of process by hydrocarbon solvents is considered. Numerical algorithm of acid effect on oil-saturated formation is proposed and tested, which allows to determine the following parameters of filtration flow: concentration of hydrochloric acid, distribution of water saturation, pressure and other parameters. A mathematical model of the carbonate collector dissolution process using composite solvents has been developed, which allows predicting technological indicators of acid impact efficiency.

ASYMPTOTICS OF THE FILTRATION PROBLEM WITH ALMOST CONSTANT COEFFICIENTS

During the construction of hydraulic and underground structures, a grout solution is pumped into the ground to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through the pores of a rock. For a one-dimensional filtration problem in a homogeneous porous medium with almost constant coefficients, an asymptotic solution is constructed. The asymptotics is compared with the numerical solution.

An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media

In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards equation. To approximate fractures we use the Discrete Fracture Model (DFM). Complex geometric features of the computational domain requires the construction of a fine grid that explicitly resolves the heterogeneities such as fractures. This approach leads to systems with a large number of unknowns, which require large computational costs. In order to develop a more efficient numerical scheme, we propose a model reduction procedure based on the Generalized Multiscale Finite element method (GMsFEM). The GMsFEM allows solving such problems on a very coarse grid using basis functions that can capture heterogeneities. In the GMsFEM, there are offline and online stages. In the offline stage, we construct snapshot spaces and solve local spectral problems to obtain multiscale basis functions. These spectral problems are defined in the snapshot space in each local domain. To improve the accuracy of the method, we add online basis functions in the online stage. The construction of the online basis functions is based on the local residuals. The use of online bases will allow us to get a significant improvement in the accuracy of the method. We present results with different number of offline and online multisacle basis functions. We compare all results with reference solution. Our results show that the proposed method is able to achieve high accuracy with a small computational cost.

Multiparameter mathematical models of the filtration problem of unstructured and structured fluids

The article is devoted to constructing a generalized mathematical model and the method of their solution of the process of filtration of fluids with various linear and nonlinear characteristics. The multiparameter model contains 13 mathematical models developed in due time by scientific research and included new mathematical models. The classification of these models is carried out in accordance with the laws of filtration, and they are confirmed by the results of numerical solutions. For unknown boundaries of disturbances, the application of the "shuttle" iteration method made it possible to reduce the number of iterations.

DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution