Mathematical modeling of injectivity damage with oil droplets in the waste produced water re-injection of the linear flow

.The formation damage issue is considered as the substantial phenomenon in petroleum industries when the produced water re-injection (PWRI) taken into the operational performance. Due to the current complexities of the interaction between the mechanical and petrophysical properties, and water quality is of importance. Regarding the previous research articles which clearly shown that only a little amount of oil droplets in the injected water would cause severe potential damages. However, there are several experimental evaluations are taken into the report to emphasize the importance of this issue, the objective of this paper to propose an analytical and mathematical model to predict the injectivity decline behavior which is in good agreement with the experimental data. To do this, two types of experimental data from Ottawa and SiC sandpack are used to model a time-dependent progression of water permeability decrease in the linear flow. As a result, the increase of captured oil saturation, the amount of permeability has reduced regarding the relationship of relative permeability drainage. Furthermore, this reduction would be stabilized when the equilibrium oil saturation was controlled by the injection velocity and the size of oil droplets.