METHOD OF SIMULATION OF TEMPERATURE FRONT MOVEMENT DURING NON-ISOTHERMAL FILTRATION

Abstract

The dynamics of objects with distributed parameters is described by differential equations in partial derivatives of the parabolic type, which with boundary conditions are mathematical models of many nonstationary nonlinear processes. Mathematical models of heat and mass transfer are systems of equations of parabolic type with the same boundary conditions. All real processes are usually nonlinear. The choice of the optimal method for solving a problem of field theory and technical means for its implementation is a difficult question. At this time, the most widespread in the mathematical modeling of complex objects with distributed parameters are methods of discretization of the mathematical model by space-temporal quantization. The representation of a mathematical model of objects with distributed parameters by systems of ordinary differential or algebraic equations allows to model them on analog and digital computers. Let’s assume that the operating time of the circulation system is limited by the time of reaching the temperature front of the production well. Studies [1] have shown that the heat flow from the surrounding massif in real formation conditions does not show a significant effect on the operation of the circulating system at a constant temperature. Therefore, in the calculations of heat flow is neglected. In the production of geothermal energy there is a pressure filtration, in which the value of μ has a value of about 10-6 m-2. In this regard, the system goes into steady state for a short time compared to the time of its operation. A method is proposed in this article for modeling the motion of a temperature front using a differential model with a transition to finite-difference model. After calculating the first approximation of the value of the speed of cold water, this value is refined using iterations for different parameters of the model.