The analysis of fluid transport in fractured reservoirs is of great concern in petroleum and environmental engineering. The objective of this work is to study mass transfer between the matrix and the fracture network in such complex formations. In this study, the impact of adsorption on mass transfer in a fractured medium with variable fracture spacing is investigated. Development of a mathematical model for mass transfer in dual porosity systems enhances predictions of the rate of mass transfer between matrix and fracture. In addition, it provides a tool for an appropriate design of advanced oil and gas recovery processes. Mass transfer is modeled based on the advective-dispersive transport with adsorption in an infinite acting dual porosity reservoir under radially divergent and continuous injection. The fracture spacing has been taken into account by including the variable rock matrix block size distribution in the developed model.

By employing this model, the effects of the adsorption rate on the mass transport in a subsurface environment are analyzed. The impact of the rate of adsorption on the accumulation of the injected tracer (catalyst) in a reservoir is investigated. An understanding of the effect of adsorption on advective-dispersive mass transport with variable fracture intensity can be a key finding to develop and design advanced oil recovery processes.

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