Modelling Sand Production Within a Continuum Mechanics Framework

Abstract The paper presents a continuum mechanics framework in which sand production can be modelled on the basis of an erosional mechanism. A representative elementary volume, comprised of three constituents namely solid, fluid, and fluidized solids, is chosen upon which mass balance and particle transport equations are written. The erosional process is described by a particle generation constitutive law. The coupled non-linear governing equations are finally solved using the finite element technique with a Newton-Raphson scheme. In order to illustrate the capabilities of the model, the evolution of controlling field variables, such as porosity, fluidized sand concentration, and pressure, are computed for a wellbore subjected to a pressure gradient corresponding to fluid draw down during pumping. In the case of anisotropic permeability conditions, sand production is at its peak value at different points around the wellbore, and there is a time lag between the times at which each point reaches its peak. This is due to the averaged fluid and fluidized sand fluxes being non-radial. Sand production from unconsolidated formations occurs when the well fluid being produced under a high pumping rate dislodges a portion of the formation solids, leading to a continuous flux of formation solids. In Alberta, the formation from which the fluid (hydrocarbon) is being produced is oil sand, while the solids comingout with the fluid is sand, although solids can be produced from a variety of other formation types, such as sandstones. Sand in the well fluid can erode casing, pipes, and pumps, or plug the well if sufficient quantities are produced. The distinct periods of sand production in the well and reservoir life as pressure is being depleted were discussed by Morita et al.(1) Introduction There are a number of schemes to address sand production. Exclusion schemes involve the installation of gravel packs or screen filters in order to catch the sand as it enters the well. However, by doing so, the flow rate of heavy oil in the well can drastically fall from 7 – 15 m3/day to maybe 0.5 – 5 m3/day. On the other hand, avoidance schemes include pressure and fluid rate control, selective perforations, and resin injection to coat the sand. As operators are following more aggressive production schedules, this has led to a demand for understanding the phenomenon of sand production mechanisms so that correct predictions of the anticipated amount of produced sand as a function of time, applied stress, and fluid flow rates can be made. The challenge is to develop a mathematical tool with a predictive capability that will allow oil operators to devise pumping schemes that produce hydrocarbons at a flow rate just below one that will produce sand. The physics of sand production is not clearly understood. However, oil rate enhancement is often linked to solution gas effects, sand movement, and growth of large high permeability regions or cavities known as wormholes(2).

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