Numerical study of porosity effect on the thermal decomposition of oil shale in underground heating with electromagnetic field

Growing energy demand result in the search of alternative energy sources. The shale can be an example for perspective employment in industry. However, the direct burning of shale is not efficient energetically and ecologically, and the employment of shale gas as the energy carrier is more perspective. There are several technologies for shale gas extraction, and the way of underground shale heating is one of them. Experimental investigation of undergound shale decomposition is very expensive and labour-consuming. The decomposition process can pass into uncontrollable regime that needs a special investigation. The mathematical modeling can help here.
In this paper, the mathematical model of oil shale degradation is suggested for the conditions of the electromagnetic field heating. It was supposed that oil shales are laminated and porous, and when the temperature reaches 250 $^{\circ}$C or higher the solid charcoal and the gas mixture consisting basically of methane form. Further this gas could be used for energy source production. The mathematical model takes into account the reaction product transport in pores, heat- and mass exchange between solid and gas phases, chemical reactions in phases, the phenomena of the heat and concentration expansion in gas phase.
The equation system comprises the heat transfer equations for solids and gas, chemical kinetics equations and the state equation for gas. The gas velocity complies with Darcy's law. It is recognized that accumulation of the solid degradation product containing carbon affects conductivity of the solids.
The heating of the shale is carried out by rod-shaped electrodes immersed into shelf deposit. Because the longitudinal conductance of the oil shale exceeds lateral conductance, the problem is two-dimensional. The solution region is a plane with uniformly located electrodes. Distances between electrodes exceed their radii that is used for energy source approximation. .
The problem is solved numerically using implicit finite-difference schemes. The heat transfer and chemical kinetics equations were solved using the coordinate-wise splitting scheme of the second approximation order by the spatial variable and the first approximation order by time. Convective summands are approximated by upstream differences. The electrical field around the electrode was approximated by some delta-shaped function.
As a result, the distributions of temperatures, flow velocity of gaseous products and the concentration's field are studied. The effect of porosity on the solid oil shale skeleton and degradation products temperature is analyzed. It is shown that the porosity value causes an insignificant impact on the skeleton temperature, however it affects significantly the formation of gaseous products. As the porosity increases, the higher average concentrations of the useful products are obtained, and their further degradation proceeds more intensively.