Hydro-mechanical erosion models for sand production

Abstract

SUMMARYSand production is a complex physical process that depends on the external stress and flow rate conditions as well as on the state of the material. Models developed for the prediction of sand production are usually solved numerically because of the complexity of the governing equations. Testing of new sand production models can very well be performed through calibration with laboratory experiments, which by construction possess geometric symmetry facilitating explicit mathematical analysis. We introduce an erosion model that is built upon the physics (poro-mechanical coupling of the fluid-solid system) usually incorporated in erosion models for the prediction of sand production. Around this model, we set up a mathematical framework in which sand production models because of erosion can be tested and calibrated without having to resort to complex numerical work or specialised software. The model is validated by data of volumetric sand production from a hollow cylinder test on synthetic sandstone. Generalisations of the model, which are naturally incorporated in the same framework and have useful phenomenological features, are discussed. Copyright

Estimation of Sand Production Rate Using Geomechanical and Hydromechanical Models

“…(iii) The depth of plastic region Λ: the elastic and plastic regions are presented in Figure 1 according to Gravanis et al [6]. In elastic region, combining with the boundary condition elastic ( out ) = out , we have…”

“…2 is given explicitly in terms of which is solved numerically for [6]. Note that (18) are purely algebraic.…”

“…Fjaer et al [5] and Gravanis et al [6]. We use experimental data profile of Papamichos et al [3] to calibrate empirical parameters (Table 1).…”

“…In addition, it was combined with the Hydromechanical model of Fjaer et al [5] and Gravanis et al [6] to predict sand production rate; then the results of the models will be compared. After collecting and processing data by analyzing log and other parameters, input data are shown in Table 2.…”

“…Among these models, the ones of Fjaer et al [5] and Gravanis et al [6] were chosen for this study because of their Figure 1: Schematic of the hollow cylinder [6].…”