Simulation of Sand Transport in a Horizontal Well
Authors: Doan Q. , Ali S.M. Farouq , George A.E. , Oguztoreli M. 
Published: December 2007

Abstract
An important application of horizontal well technology in Canada is recovering oil from marginal heavy oil reservoirs in Saskatchewan and Alberta. These reservoirs are often poorly consolidated; as a result, recovery operations are susceptible to sand production which potentially poses a serious problem as the sand particles deposit and partially block the horizontal well. This work presents a mathematical treatment of the transport process of oil and sand particles inside a horizontal well.
In particular, the model described in this paper formulates the transport process mechanistically. Equations of mass and momentum conservation for the solid phase (sand particles) and the fluid phase (oil) are formulated. The oil is assumed to be Newtonian, and the sand particles are assumed to be spherical in shape and uniform in size. In addition, the model incorporates empirical correlations to describe the interaction between the two phases. The system of equations is solved numerically to determine the distribution of sand particles and oil, their pressure and velocity distributions as a result of the presence of a constriction inside the horizontal well.
Simulation results obtained provide insight into the mechanisms involved in the transport process, thus enhance the understanding of the flow of sand and oil inside a horizontal well. This, in turn, yields some guidelines for production operations involving horizontal wells in unconsolidated and poorly consolidated reservoirs.

Introduction
One of the most common applications of horizontal well technology in Canada is to recover oil from heavy oil reservoirs in Saskatchewan and Alberta. In heavy oil reservoirs underlain with bottom-water, the use of horizontal wells has been found to improve primary recovery performance prior to water coning - recovering up to 15% of the initial oil in place (in shorter time, also), compared with only 5% for a vertical well. Horizontal wells have also been successfully used for increasing steamflood recovery. However, recovery operations in these heavy oil reservoirs are usually susceptible to sand production due to their unconsolidated nature. Sand production potentially poses a serious problem in horizontal wells, as the sand particles settle and accumulate at different positions along the well, reducing the cross-sectional area of the wellbore open to flow (Figure 1). The ultimate effect of sand deposition could be the partitioning of the horizontal well into several segments, leading to a loss of production and a negation of the principal advantage of horizontal wells (large contact area with the reservoir). This problem is investigated in the following study. Specifically the study examines through numerical simulation, the transport and distribution of sand particles, pressure, and velocity distributions in a horizontal well. A special feature of the physical model is the presence of a constriction inside the horizontal well.
Solid-fluid multiphase flow encompasses many different areas of science and engineering, ranging from the transport of colloids in rain water, sediment transport in river streams, bed fluidization to slurry pipeline transportation, drill cuttings removal, and transport of fracture proppant, etc. The large number of independent variables involved in these transport processes, coupled with the complex interaction between these variables have resulted in a large number of empirical investigations over the years, with only a few studies attempting to understand the transport processes mechanistically. A majority of these studies focus on the interaction between a single solid particle and the surrounding fluids, cloud of solid particles with fluids, transport of suspensions in pipe etc. P. 581