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-linear filtration models and the effect of nonlinearity parameters on flow rates in low-permeability reservoirs

Filtration of oil in low-permeable reservoirs is considered. The experimental data of dependence of filtration velocity on pressure gradient are analysed. It is shown that the filtration law in low-permeability reservoirs differs from the linear Darcy’s law and from the non-linear law with an initial pressure gradient. The power law of filtration in low-permeability reservoirs is experimentally substantiated. Models of nonlinear filtration influence on flow rate are proposed. The analysis of influence of nonlinear filtration parameters on flow rate in technogenically modified near-wellbore zone is carried out.

Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory

This paper is devoted to the study of the Cauchy problem for a system of differential equations describing the unsteady flow of a compressible fluid in a homogeneous and inhomogeneous porous medium with a general nonlinear filtration law in three-dimensional space. In the work using the methods of four-dimensional mathematics, a special four-dimensional space of space and time coordinates was developed, as well as a functional space of regular functions, and analytical conditions were obtained on the general form of the nonlinear filtration law for which the Cauchy problem has a solution.

Inverse Problem For A Linear Filtration Function

The article is devoted to an important task of underground hydro-mechanics-filtration of suspension in a porous medium. One-dimensional long-term deep filtration of a monodisperse suspension in a homogeneous porous medium is considered. For a one-dimensional macroscopic model with a linear filtration function, an asymptotic solution is constructed near the concentration front of suspended and retained particles. On the basis of explicit asymptotic formulas, the inverse filtration problem is studied : finding the filtration function for a given concentration of suspended particles at the outlet of a porous medium. It is revealed that the least squares method is an effective way to determine the model parameters. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the numerical solution. The proposed numerical - asymptotic method makes it possible to calculate the linear filtration function using laboratory experiments and adjust the model to specific field conditions. It is concluded that the next stage in solving the inverse filtration problem is to determine unknown parameters of a nonlinear filtration function that depends on three or more constants. To do this, it is needed to modify the methods presented in this paper.

Application of generalized method of least modules in problems of processing and analysing images

The article describes the use of nonlinear smoothing filter for image processing and analysis. Description of the model of the smoothing filter based on the generalized method of the least absolute values is given. The filter constructed on the basis of the offered model efficiently reduces the noise on brightness difference. Along with noise reduction in the contrast images, this method can be used for the solving problems of machine vision, medical diagnostics, etc. It has been found that nonlinear filtration on the basis of the generalized method of the least modules allows to solve such problems as clarification of the boundaries of contrast objects and segmentation of the image. There has been shown the possibility of recovering the boundaries of the images in which the contrast borders were blurry. X-ray image of an animal hand with defocusing was used as an example. After filtering, the contrast boundary was restored to the place where it was originally located. When processing a fluorography image, the filter removed various artifacts from the image and increased the contrast. Removal of artifacts along with the recoveries of the boundaries of contrast objects improves the overall “readability” of the fluorography image and also allows seeing earlier not distinguishable details on the image. Examples of the filter application in the clustering problem using the k-means algorithm are given. Due to the lack of this algorithm, applying it directly to the image does not give an acceptable result. However, after processing the original image with a nonlinear filter, the application of the k-means algorithm yields the desired result.