NONLINEAR FLOW COMPUTATION USING TOTAL-VARIATION REGULARIZATION

Many researchers note the nonlinearity of flow in tight rocks. This manifests itself in the form of a decrease in effective permeability with a decrease in flow rate. For low-permeable rocks, the estimation of reservoir permeability without taking into account the nonlinearity of the flow can yield significant errors. Accounting for non-linear flow can also lower the estimate of reservoir productivity and lead to an increase in stationary oil zone estimation. Regular methods of studying fluid flows in porous rocks are poorly suited to study their permeability when approaching to zero fluxes. Previously, we described a method for laboratory testing of non-linear flow in low-permeability rock samples, based on measuring flux during a slow decline in the pore pressure gradient. A feature of the described technique is that the flow rate of the liquid is measured by its continuous weighing. This method of measurement allows us to study very slow flows, but it requires a special approach to calculating the flow rate from mass change data. One of these approaches is the TotalVariation Regularization method, which is often used in the problems of filtering noise in images. We investigated the possibility of using this method to analyze the results of measuring infinitesimal flow rates based on the mass change. As a result, it was shown that this method has a number of advantages, and in combination with the proposed modification of the quality functional, it allows processing significantly irregular data. The method proposed by us can be used in research work for a more accurate assessment of the permeability of dense rocks, the filtration properties of which can be significantly non-linear.