Mathematical modeling of geomechanical behavior of tarmat during the depletion of giant oil reservoir-aquifer systems

In this work, deformation and failure behavior of tarmat layers during depletion of a giant reservoir–aquifer system has been studied. Deformation response of the tarmat to increasing pressure differential caused by continuous depletion of reservoir is examined and a mathematical model is developed for the study of this type of composite systems. The geomechanical failure that takes place when the pressure differential reaches a critical value is also evaluated, along with the characterization of the resulting fracture. Plate theory, maximum shear stress failure criterion, conventional well test model, Perkins–Kern–Nordgren (PKN) and Khristianovic–Geertsma–de Klerk (KGD) models and flow through fractures models are used. The developed sensitivity analysis proposes the proper protocol to be followed in order to undertake production design in such composite systems. The methodology presented in this paper, ultimately, predicts fracture width and fracture permeability that would be developed in a system with a tarmat layer having a certain thickness and a reservoir being produced at a certain production rate and total depletion time.