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Deep bed filtration of carrier water with particles occurs in numerous processes of environmental, chemical, petroleum and civil engineering. For example in the petroleum industry, deep bed filtration of drilling fluid happens during well drilling; it also takes place near to injection wells during seawater injection or produced water re-injection causing in- jectivity reduction. In this work, the filtration theory and its mathematical model are given and the filtration coefficient will be discussed. Then the transition time, the time at which the initial layer of external filter cake is completely formed has been derived mathematically. The transition time can be obtained by calculating the trapping efficiency as a function of the number of previously deposited particles where very few particles can invade the rock and the external filtration begins to build. The prediction of particle capturing and particle retention by mathematical model is an essen- tial stage during planning and design of above-mentioned industrial processes.

External Cake Build Up at Surface of Porous Medim