Stability and Failure of Sand Arches

Abstract

When producing from an unconsolidated sand, sand arches may form behind the perforation opening. On the basis of a theoretical model, we have analyzed the stresses in the sand. The effect of flowing fluids has been studied, and criteria describing the stability and failure of the sand are given.The arching phenomenon was studied in the laboratory. The experiments qualitatively reproduced the theoretical results. To the extent that comparison was possible, the quantitative agreement between theory and experiments was fairly good. Introduction Literature Survey The principle of arching, where a self-supporting structure is spanning an opening, has been known and used in manmade constructions for centuries. The first analysis of this mechanism, related to the earth sciences, was done by Terzaghi in his trapdoor experiment. He used a box filled with sand where a section of the bottom (trap door) could be removed. He observed that the sand was able to transfer the loads exerted on the trap door to its surroundings as the trap door was removed. The work was done to get a better understanding of the stress distribution around tunnels, and he concluded that arching is a real and stable phenomenon that is insensitive to flow.Paslay and Cheatham studied the stresses induced by a flowing fluid into a wellbore. Geertsma recently studied this and other rock mechanical problems related to sand-free petroleum production. These studies were based on the work Blot did on three-dimensional consolidation. Medlin and Masse recently presented a paper concerning laboratory investigation of fracturing pressures, also based on Blot's work.Hall and Harrisberger called attention to the trap-door experiment again when they studied the stability of sand arches and its relation to maximum sand-free production rate. They found that arching may be rate sensitive at low confining stress levels, while it is independent of flow rate at high confining stress levels. They did not quantify the rates at which an arch failed when it is in the rate-sensitive region.Stein and coworkers assumed that the maximum flow rate an arch can withstand is proportional to the shear modulus G for the sand, which is obtained from density and acoustic logging data. Bradley has worked out a semiempirical approach to the wellbore stability problem, discussing specially inclined boreholes. This approach is useful to predict when the limit of elastic behavior is reached; however, it gives no information on the behavior in the plastic state.At the Colorado School of Mines a program has begun laboratory studies of the arching phenomenon and its relation to flow rate and confining stress level. As this work is still in progress, no final conclusions have been drawn. However, preliminary results seem to be very similar to the observations made in our experiments. Qualitative Description of the Experiments The laboratory model used to study the arching phenomenon consisted of a steel cylinder with a central hole in the bottom to simulate a perforation. This cylinder was filled with unconsolidated sand and compressed vertically by a piston to simulate overburden. Fluid was introduced at the top beneath the piston, spread over the total area by a multiwrapped wire screen, and forced through the sandpack. SPEJ P. 236^

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A Predictive Model for Sand Production in Poorly Consolidated Sands

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