(2019) Diffusion Model with Memory. Accounting for Special Properties of Reservoir During Oil Production

Project Type: Work project, Mathematical Modeling, Academic Research
Programming Language: Maple 18, Python 3
Project Сode: Non-steady Equation, Steady Equation
Project Full Description: About Conference Presentation.pdf
Company: math. model. lab. GAMMETT

I. Motivation

Diffusion models are used in a wide range of applications, such as market forecasting or oil production forecasting. Models with memory have appeared relatively recently and are used in a wide range of tasks. The combination of these approaches makes it possible to carry out a forecast taking into account nonlocality in coordinates.

II. Problem

The main purpose of this work is derivation and debugging of a computational algorithm for a new diffusion model. The main difficulty is the presence of a singularity in the operator.

III. Key Results

A computational method for a new predictive model of hydrodynamics with memory has been developed and implemented. The computational problem of the model and the solution method are highlighted.

• Numerical scheme is constructed for the steady case;
• Explicit numerical scheme for non-steady equation is constructed.

III. Content

Radial steady-state fluid flow model for porous media with the Riesz potential is considered. A numerical scheme for model with one-dimensional representation of the Riesz potential is presented. Regularity and monotonicity of solution of the Dirichlet boundary value problem corresponding to the constant pressure in the bottomhole zone are discussed.

The project code contains 2 scripts:

1. Non-steady Equation;
2. Steady Equation.