A New Method for Modeling the Rate of Sand Production

Abstract

Sand production causes serious problems in the petroleum industry and costs billions of dollars annually. The amount of produced sand varying from a few grams per barrel to a huge amount of solid that leads to complete filling of the borehole. Therefore, it is necessary to be able to predict not only the conditions for sand onset production, but also develop a model that can be used to predict the rate of sand production. Various numerical models for determination of sand production rate have been developed, but the issue is still under progression. In this article, a hollow cylinder sample is considered and attempted to couple fluid flow, sand erosion, and mechanical deformation. The obtained system of nonlinear differential equations is solved by finite difference method. Porosity is selected as a coupling parameter, which changes with time and space until reaching a critical value, and then sand will be produced in burst. This article proposes a method for determination of this critical value, and according to this, a new model for prediction of the rate of sand production is developed.