A Predictive Model for Sand Production in Poorly Consolidated Sands
Authors: Kim Sung Hyun , Sharma Mukul Mani , Fitzpatrick Harvey J. 
Published: March 2015

Abstract
This paper presents a sand production model that predicts the stability of wellbores and perforation tunnels, as well as the mass of sand produced. Past analytical, numerical, and empirical models on material failure and erosion mechanisms were analyzed. The sand production model incorporates shear and tensile failure mechanisms. A criterion for sand erosion in failed sand was proposed based on a force-balance calculation on the sand face. It is shown that failure, post-failure sand mechanics, and flow-dominated erosion mechanisms are important in the sand production process. The model has a small number of required input parameters that can be directly measured in the laboratory and does not require the use of empirical correlations for determining sand erosion. The model was implemented in a numerical simulator. Experiments using different materials were simulated, and the results were compared to test the model. The model-generated results successfully matched the sand production profiles in experiments. When the post-failure behavior of materials was well-known, the match between the simulation and experiment was excellent. Sensitivity studies on the effect of mechanical stresses, flow rates, cohesion, and permeability showed qualitative agreement with experimental observations. In addition, the effect of two-phase flow was presented to emphasize the importance of the water-weakening of the sand. These results showed that catastrophic sand production occurs following water breakthrough.

Introduction
A conventional and conservative approach to completing a sand-prone well is to install a mechanical means of sand control, such as gravel packs, fracpacks, and screens. In some cases, sand management is practiced through oriented perforating and rate control. An openhole completion can be an alternative to a cased and perforated completion to reduce the near-perforation fluid velocity. Before deciding on how to prevent or minimize sanding, the benefits and disadvantages of sand control/management must be evaluated carefully, and the assessment of qualitative and quantitative sanding risk is crucial.
Many publications present sand failure and sand production models supported by experimental results (Hall and Harrisberger 1970). Some models deal with the problem of sand stability and failure (Bratli 1981; Risnes 1982). With the advent of numerical simulations, such as finite element modeling (FEM), sand production became a popular numerically simulated problem because of its complexity. However, most of these models rely on parameters that may or may not be experimentally measureable. In many instances, the physical significance of some of these parameters is not obvious.
While most of the research work has generated relevant insights on sand production, a comprehensive model that can adapt to different experimental settings and to the field is not available because of one of two reasons: (1) a lack of model sophistication or (2) overly complicated models with excessive input requirements. This calls for a flexible and complete model with a quick runtime and a small and measureable set of parameters that provides reasonably accurate results. The purpose of this paper is to showcase a general 3D numerical model that describes the process of sand failure, erosion, and production quantitatively(Fig. 1).The sand production model incorporates two sequential phenomena. The first one is the failure of the near-wellbore region (wellbore or perforation), which is a necessary condition for any sand production. The subsequent step for sand production is "erosion." This process refers to the removal of the sand from the failed region.
In the model, a force balance is conducted between the frictional forces mechanically holding the sand in the formation and the hydrodynamic force (exerted by the flow) that induces detachment of the disaggregated sand. Gridblocks for which the frictional force is overcome by the hydrodynamic force are removed from the simulation and are assumed to be produced into the well. The model is verifiable with distinct sets of experiments, which then could extend and offer a reasonable prediction tool for sand-production characteristics for field cases. The numerical model also obtains results that are beyond the reach of simpler analytical solutions.