Flow In a Constricted Horizontal Well
Authors: Doan Q.T. , Ali S.M. Farouq , Oguztoreli M. , George A.E. 
Published: March 2010

Abstract
Horizontal wells have been used successfully in Canada to recover oil from marginal heavy oil reservoirs in Saskatchewan and Alberta. These reservoirs are often poorly consolidated; recovery operations in these reservoirs are, therefore, usually susceptible to sand production. A horizontal well could be partially blocked due to the deposition and accumulation of sand particles inside the wellbore. This study presents a mathematical treatment of the transport process of oil and sand particles inside a constricted horizontal well.
The model described in this paper formulates the transport process mechanistically. Continuum assumption is made for the fluid phase (oil) as well as the solid phase (sand particles). Equations of mass and momentum conservation for the solid phase and the fluid phase are formulated. The oil is assumed to be Newtonian, and the sand particles are assumed to be spherical in shape and uniform in size. The model incorporates empirical correlations to describe the interaction between the two phases. The system of equations is solved numerically to determine the transient distribution of sand particles and oil, and their pressure and velocity distributions as a result of an expanding constriction inside the horizontal well.
Numerical simulation results provided insight into the mechanisms involved in the transport process, thus enhancing the understanding of the flow of sand and oil inside a horizontal well.

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 compared with only 5% for a vertical well(1). The recovery rate is also increased. Horizontal wells have also been successfully used for increasing steamflood recovery(2, 3). However, recovery operations in these heavy oil reservoirs are usually susceptible to sand production due to their unconsolidated nature. The produced sand could give rise to production problems, as the sand fill up the wellbore, prevent the operations of downhole pumps, etc.(4). In the case of horizontal wells, sand production potentially poses an even more serious problem, due to the settlement and accumulation of sand particles at different positions along the well, leading to the reduction of 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). The study reported here investigates this problem. Specifically the study examines, through numerical simulation, the transport and distribution of sand particles, and pressure, and velocity distributions in a horizontal well. A special feature of the model is the presence of a constriction inside the horizontal well.