Modeling polyclonality and mutation in Microbal Enhanced Oil Recovery

MEOR is a method whitch ehance the oil recovery by changing the function or nature of micro organisms of oil reservoirs[1]. Problem faced is that the bacteria will variey in accordance with mutation occured because of outgoing longwave radiation of earth and earth s internal heat budgets and this will end up in unenhanced oil recovery[2] [3]. Modeling polyclonality and cell mutation can be extremely advantageous, for avoiding this condition. the subpopulations are not independent but are connected by mutational events transferring mutaited cells from cell population i to cell population j . Initially, let us suppose there is a source of u mutaited cells that have mutated from healthy cells and can proliferate faster then the neighboring normal cells thereby starting to form a colony. We can think of k as a measure of the probability of u mutaited cells mutating to become the rapidly diffusing tumour cell population v Introduce the nondimensional variableswhere u0 =ʃ f (x)d x, the total original cancer cell population. The parameter α = k/ρ1 < 1 is the proportion of the first subpopulation’s growth lost to mutation.Let us take the initial source of u tumour cells to be u(x, 0) = δ(x) and take v(x, 0) = 0. The v population diffuses faster than u so ν > 1. The growth rate of the u population is larger than v so β < 1. The growth rate of u is much higher than the probability of mutation so α <1. The first solution can be solved separately from the v equation and has the solution

کلیدواژه ها:

MEOR ، outgoing longwave radiation of earth ، earth s internal heat budgets