Estimating Maximum Sand-Free Production Rates From Friable Sands for Different Well Completion Geometries
Authors: Stein N. , Odeh A.S. , Jones L.G. 
Published: December 2007

Oil or gas can be produced from a friable sand without benefit of sand control. If we have sonic and density log data and know the permeability of the formation, the fluid viscosity, formation volume factor, and number of perforations, we can estimate with a simple equation the maximum possible sand-free production rate. possible sand-free production rate. Introduction
In friable formations where sand production can be a problem, it may be possible to produce oil or gas from an essentially undisturbed formation at high rates without resorting to any form of sand control measure. It has been proposed that formation stability is achieved by the establishment of sand arches around each perforation in the casing. This paper presents a technique for utilizing sonic and paper presents a technique for utilizing sonic and density log data to estimate the maximum sand-free production rate from each arch. Thus, estimates of production rate from each arch. Thus, estimates of maximum sand-free production rates from wells are independent of such completion geometry factors as the location and length of perforated interval. The technique is based on the assumption that the maximum possible pressure gradient at the arch face for possible pressure gradient at the arch face for sand-free production is proportional to the sand strength. Arch faces must remain in place if no sand production is to occur; yet they are subjected to the production is to occur; yet they are subjected to the maximum pressure gradient in the reservoir. A less specific means was previously presented for estimating the maximum sand-free production rate. That procedure contained an assumption that is correct as long as completion geometry is not substantially changed in different wells. The assumption was that the ratio between the total reservoir pressure drawdown and the pressure gradient at the face of individual sand arches was the same for all wells. With the new technique presented here, we have eliminated the necessity for including this assumption in our estimates of maximum sand-free production rates. Thus, the new technique provides an improved estimate that can be used to determine if the economics is promising for completing a well without installing any form of sand control.

Theoretical Consideration
Consider the system illustrated in Fig. 1 for a hemispherical arch formed around a perforation in the casing. When the stress at the arch face exceeds the strength of the sand, particle movement will begin. Logically, the stress at the arch face is directly related to the fluid pressure gradient, which is a critical factor in maintaining formation stability. Moreover, the maximum stress that may be applied without causing a sand problem should be proportional to the strength of the sand. Let dr be the distance between the sand/fluid interface and the outer boundary of sand layer liable to move (Fig. 1). By Darcy's law, the pressure gradient across dr isdp q B = (1) dr 1,127 x 10 (-3) kA
Darcy's law applies to laminar flow. To use Darcy's law for calculating the maximum sand-free production rate, we assume that any effects of turbulence on the maximum pressure gradients in different zones are the same.
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