Markov Process Describes Dispersion Phenomena In Porous Medium

This paper has researched dispersion phenomenon that exists in miscible-phase displacement and chemical flood to enhance oil recovery further. Owing to concentration difference between injected solution and formation fluid and the randomness of pore channels, it obtains that solute motion in pores is the combined action of molecules diffusion and convection dispersion. Analyzing this process, it considers that the displacement of solute particles in pores is markov process. Assumed that cores are homogeneous, based on diffusion process in random process, and considered that solute is not adsorped and deposited in pores, it derives one-dimensional convection dispersion equation, translates it into dimensionless equation, and computes numerical solution using implicit difference scheme of Crank-Nicolson type.In this paper, it solves analysis of transition probability of which solute particles move in an infinite reservoir; obtains concentration distribution curves at different time in an infinite reservoir with the help of numerical method. It analyzes the effect of different dispersion coefficients and flow velocity on con- centration history and breakthrough curve in a semi-infinite reservoir. The effect contributes to the influ- ence of dimensionless dispersion rate on dispersion phenomenon. It resolves the conditions of continuous injection and slug injection in limited cores, and analyzes different consequences of different dimensionless dispersion rate to concentration curves and breakthrough curves. It can be seen from these curves that, the higher the dimensionless dispersion rate, the stronger the dispersion. As dimensionless dispersion rate is under a certain value, concentration curve and breakthrough curve don't change.In this paper it introduces the method of determining dispersion coefficient, and make a experimental study of dispersion phenomenon in cores, obtained data agree with computed data. Show that it is feasible that this paper establish convection dispersion equation, and use solution. This paper bring forward a method that establish convection dispersion equation, this has instructed significance to study convection dispersion phenomenon. The results obtained in study is in conformity with computational data, which confirms that diffusion-dispersion equation established and method adopted in this paper is available. The method of establishing diffusion-dispersion equation has guiding significance of studying diffusion-dispersion phenomenon.