We present a mathematical model for simulating petroleum particle flow for petroleum reservoir characterization, near the Lamu Basin of the Kenyan coast using the equations governing fluid flow. The petroleum particle flow near Lamu basin reservoir is pressure dependent, decreasing with decreasing pressure in time. In this numerical model, the partial differential equation was discretised using integrated finite difference method (IFDM) and approximated by an algebraic equation which was valid in a small sub-region for a particular time. A number of such equations were written for all the sub-regions into which the entire domain of study was suitably divided. The discretised mathematical pro
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