The eight seminar of the Web-laboratory of Continuum Mechanics was held 12 March 2019 in the Institute for System Programming of the RAS.

### The topic of the seminar:

Mathematical modeling of the thermogas enhanced oil recovery method.

### Presenter:

Daria Romanova (Moscow State University)

### Abstract:

The thermogas oil displacement method considered in this paper is one of enhanced oil recovery methods. This method is characterized by injecting into the reservoir a heated mixture of gas and water as a displacing agent. The gas is a mixture of oxygen and nitrogen. Heated oxygen reacts with the hydrocarbon, in result the hydrocarbon is oxidizing with the release of heat. The fluid temperature rises and the viscosity decreases, as a result the process of oil displacement from the formation is accelerated. A three-phase fluid model is used to describe the displacement process. The gaseous phase consists of four components: nitrogen, oxygen, carbon dioxide and water vapor, for which their concentration in the flow is calculated. The movement of fluid in a porous medium is called filtration and is described by the Darcy equations. The skeleton has a temperature different from the fluid, and thus the model is two-temperature. The mathematical model of the problem consists of ten equations: three phases mass balance equations, four gas phases mass balance equations, equation for pressure, energy balance equations for fluid and skeleton. The system of equations is closed by the following equations of state: Darcy equations determining phase velocities, algebraic relations determining relative phase permeabilities, viscosity, thermal conductivity of a fluid and its components, phase density, as well as kinetics of chemical reactions. A numerical simulation of the first year of thermogas displacement of oil from the reservoir in a two-dimensional setting was carried out. As a result, the following processes were calculated: interphase mass transfer due to a chemical reaction, energy release during a chemical reaction, thermal conductivity, heat transfer between the skeleton and fluid, convective heat influx, dynamics of phase displacement. The fields of the studied quantities were obtained (fluid saturation with water, fluid saturation with oil, gas saturation, nitrogen concentration in the gas phase, oxygen concentration in the gas phase, carbon dioxide concentration in the gas phase, water vapor concentration in the gas phase, pressure, fluid temperature, skeleton temperature ), and a graph of the rate of oil displacement along the line from the injection well to the producing well, and a graph of the production rate of the producing wells. A similar calculation was carried out for simple displacement with water, displacement with hot steam, as well as displacement with a cold mixture of air and water; a comparison of the results was made and an increase of the oil recovery factor was obtained.