A simplified model is proposed based on elastoplastic behavior of sandstones with a non-constant dilation angle. The accuracy and reliability of the proposed model is verified by comparing the model prediction with the result of hollow cylinder tests on sandstone. The possibility of using critical effective plastic strain as an indicator for onset of borehole collapse and sand production is discussed.
Sand production has been considered undesirable outcome from reservoirs, due to either an aggressive production strategy or weakly consolidated sand skeleton. Sand control strategy, effective or not, costs the industrial millions of dollars each year, particularly in off-shore operations and horizontal wells where solid production is strictly prohibited. A strategy to evaluate sanding risks in each producing well is essential to cut the cost on well completion. Accurately predicting the onset and amount of sand production obviously can allow completion engineers to decide if and when a sand control strategy is necessary.
Numerical and analytical models have been used to develop quantitative tools, but the utilization of these tools must be verified by validating the models against field or experimental data. Extensive studies have been conducted to understand stress, deformation, and final collapsing process of various rocks. These studies are normally performed through hollow cylinder tests in lab, as well-defined boundary conditions and material behaviors may be obtained. Santarelli et al. (1986) noted that a linear elastic model may overestimate the apparent hoop stress concentration on the wall of sandstone hollow cylinders. Ewy & Cook (1990) attempted to verify a hollow cylinder failure through a complete process of deformation and final collapse. Papamichos & van den Hoek (1995) emphasized the effect of borehole size on collapse strength of hollow cylinders of sandstones. Because of the nature of simplicity, elastic-perfectly-plastic model has been used to study either the stresses or deformation near a circular hole. A drawback from such a model may rise because the such a model defines a problem which is statically determined: the near-hole stresses can be calculated separately from the strains and displacemenCs (Detournay & Fairhurst, 1987). If we wish to develop a simple model based on elasto-perfectly plasticity and determine the final failure or sanding by stress/strength, as we usually do, then we are facing a great challenge: the initial plastic yielding may be too conservative to represent the onset of failure condition, as no hoop stress build up is possible after the initial yielding. Yet no hoop stress increase is permissible after the yielding, which makes final failure prediction by comparing the hoop stress with strength criterion impossible.
To determine sand production associated with fluid flow, Bratli & Risnes (1981) proposed a criterion for sanding when the effective radial stress is approaching zero. Such a criterion has been extensively adopted for sand production in the field, and there is report to support such a criterion used in gas field (Weigarten & Perkins, 1994), but their accuracy and applicability in the field are yet to be defined in a broad sense. Because most existing simplified model is solely developed based on stress distribution, the constitutive relationship may appear irrelevanto the failure and sanding process. Such an approach can lead to serious misleading conclusions and results, as a reliable model should be verified by a physical model and compatible with constitutive relationship (Detoumay, 1986; Ewy & Cook, 1990; Veeken et al., 1992).
In this paper we proposed a simplified model based on elastoplast
