A New Numerical Simulation Model and Upscaling Technique for Scaled Model Sand Production
Authors: Abdulraheem Abdulazeez , Awal Mohammad R. , Taher Salah F. 
Published: December 2007

Abstract
The rock mechanical behavior and failure conditions leading to sand production are better studied in scaled laboratory conditions under in situ conditions. The results can be used to validate a numerical model that simulates fluid flow and sand production in the scaled laboratory model. The simulator lends itself to field prediction after our proposed iso-flux upscaling technique is applied. The integrated approach utilizes ultrasound measurements and triaxial load frame tests for calibrating log derived rock mechanical properties which are used as input to the numerical simulator. The model is validated with cores from Central Arabian oil field.

Introduction
The petroleum industry has witnessed three trends in the development of a predictive method for the onset of sand production: empirical methods based on field observations, laboratory experiments, and theoretical modeling. The successes of the empirical methods were limited and could not be generalized. Analytical and numerical methods were either not successfully tested or reported in the open literature. The few proprietary 3-D numerical models are incapable of making great progress in the absence of field data [Veeken et al., 1991]. An alternative is obviously the simulation of a scaled laboratory model. In our knowledge, there is no such numerical model reported in the open literature. Although Tronvoll and Morita (1992) reported a similar approach, they did not design an experimental method for the in-situ conditions of pressure, temperature and stresses, nor did they present the numerical formulation. A subsequent publication by Morita (1994) again only alluded to the numerical model. A major drawback in the conventional predictive methods is the use of hypothetical failure criteria, which tell when a rock mass ‘fail’ in the rock mechanics sense. It is now common knowledge that sand production does not necessarily begin when one or all of these ‘failure criteria’ is met. Even if the rock mass is friable sand (sand grains are not cemented together), experience in the Gulf of Mexico and elsewhere (e.g., Perkins and Weingarten, 1988) as well as laboratory experiments (e.g., Bratli and Risnes, 1981) have shown that sand is not produced until the sand arches that form around the perforations fail. Predicting the failure of sand arches has been equally allusive.
We have developed an integrated approach around a scaled physical model and its numerical counterpart. To overcome the drawbacks and problems associated with the conventional hypothetical predictive methods, we have focused on simulating flow around a perforation under in-situ conditions. We reason that it is the fluid drag force which determines whether the loose sand grains, existing a priori or created under combined in-situ and fluid-flow induced stresses, would flow or not. We show that it is not necessary to evaluate the critical fluid drag force either; a mere knowledge of the interstitial velocity and routinely available is enough to compute the critical flow rate in a well. We first determine this interstitial velocity in the scaled model, then we use a new upscaling technique in order to translate the model prediction for field conditions. The rock mechanical data required to characterize the core-based model are easily and precisely available for validating the numerical model. We also use a calibration method for obtaining representative in situ rock mechanical properties using triaxial test and ultrasound measurements data and full-wave acoustic logs.

Physical Basis of the Numerical Model
Bell (1972) reported the mathematical models of flow in a perforated cylindrical core sample and a simplified downhole system. Flow into a single, isolated perforation in a cased well comes from all surrounding parts of the reservoir.
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