It is the scope of this work to present an analytical model for sand rate, and to compare its predictions to experi-mental observations as well as numerical simulations, in order to illustrate possible mechanisms involved in the sand production process. The extent to which it can be used for quantitative predictions remains to be verified. The analytical model is based on the assumption that the driving mechanism for continuous sand production is erosion from plasti-fied material in the vicinity of the production cavity. The erosion destabilizes the plastified material, which eventually collapses. The model thus includes an erosion-mechanical coupling, although in a seemingly simpler way than similar numerical models. However, the model predicts that sand is mainly produced in bursts, and that the sand production appears as continuous only on a longer time scale. This is consistent with observations during sand production tests in the laboratory. Discrete particle modeling of the sand erosion process demonstrated similar behavior. These results points towards a detailed explanation of the microscopic processes involved during sand production. The model also describes quantitatively that the sand production rate depends on: (1) how much the well pressure is reduced below the critical sand production pressure, (2) the fluid flow rate and the fluid viscosity, and (3) the cementation of the rock. In addition, the model depends on a parameter related to sand erosion, which can be obtained in a sand production test or calibrated from field data if these are available. At present, we do not know about any other ways to establish a value for this parameter; hence for field application the model needs calibration on sand production tests.
1. INTRODUCTION
There is a growing need in the petroleum industry to be able to predict not only the occurrence of sand production, but also the amount of sand that will be produced under given conditions. This shift in focus is partly driven by the progress in research on sand production topics, and partly by the growing aware-ness among hydrocarbon producers that limited amounts of sand production may in fact be manage-able and even lead to significant increase in pro-duction.
Various numerical models for prediction of sand rate have been presented. These models differ somewhat with respect to their underlying assump-tions regarding the sand production mechanisms, although the basic elements are similar. Papamichos et al. [1] assume that sand is released through an erosion process, which eventually occurs when the rock surrounding a producing cavity has suffered certain degree of plastic strain, while Chin and Ramos [2] relate the amount of produced sand di-rectly to the volumetric plastic deformation of the rock. Willson et al. [3] focus on the parameters causing the sand failure, and use a more empirical approach. An empirical approach based on physical processes observed in sand production tests and test data from a variety of sandstones has also been used by Papamichos [4] to predict the cumulative amount sand and sand rates during the production period.
