Predictive Model and Verification for Sand Particulates Migration in Gravel Packs

Abstract

Abstract A phenomenological model is presented to optimize the performance and to minimize the costs of gravel-packs, which are subjected to severe flow and pressure conditions. The theoretical basis for the development of the model equations is discussed and the equations are derived to represent the mechanisms involved in gravel-pack damage. This model is an averaged representation of the experimentally observed step-like motion of particulates, which is characteristic for particulates transport in gravel-packs. An implicit finite difference solution of the gravel-pack damage model is utilized. The identification of the model parameters is emphasized. The influence of error in the determination of parameters is estimated by performing a sensitivity analysis. Of the three parameters, namely the amount of mobile particulates, the particle deposition rate constant, and particle mobilization rate constant, the last one is found to be less important because particle mobilization is sensitive to reduced transport capacity of the clogged gravel-pack The model has been verified by data from a set of 35 experiments conducted via large scale non-Darcy flow tests with optically transparent filtration cell. The predictions of the model are found in reasonable agreement with the test results with respect to the particulates migration distance and the amount of mobile particulates. Introduction Sand production poses serious problems to tubular material, surface equipment and the stability of the well. Solid byproducts cause erosion in tubular materials and are responsible for plugging of wells, thus reducing well productivity. Moreover, when large amount of load bearing sand particulates migrate into the well, cavities form around the well and particulates settlement occurs, possibly threatening the integrity of the well. A popular method of combating sand production is using gravel-packs. Gravel-packs have a protective function to inhibit the flow of sand particulates into the well. Conventionally designed gravel-packs aim at geometric impenetrability, which implies that the gravel-to-sand size ratio should be small. However, the currently used single parameter geometrical design criteria are insufficient as shown by recent field results, and a more subtile measure which also includes self-filtration is needed. The study of more general features of gravel-packs, that is an approach which goes beyond a strict geometrical design, must include particulates transport phenomenon through porous media. In spite of sand production being a menace for well productivity, the number of gravel-pack modeling studies is surprisingly low. P. 179^