A Multiphase Flow Approach to Modeling Sand Production Using Finite Elements
Authors: Wan R.G. , Liu Y. , Wang J. 
Published: March 2010

Abstract
The paper presents the extension of a sand production model based on erosional hydrodynamics to include a gas phase. A gas phase contribution is added to the governing equations within the framework of mixture theory and multiphase flow in a four component system; namely solids, fluidized solids, oil and gas. It is known that solution gas drive effects play an active role in the physics of sand production in that gas flow tends to increase the propensity of grain particle detachment from the sand matrix and subsequent fluid transport. The finite element formulation and essential algorithmic implementations are discussed. A one-dimensional numerical example of sand production in an oil reservoir undergoing pressure drawdown is presented to provide an understanding of the role of a gas phase in sand production.

Introduction
A long-standing problem in the oil recovery industry is sand production in unconsolidated oil sands and weak sandstones. Basically, during the oil recovery process, the pumping of the fluid induces huge drag forces that dislodge sand particles from the solid skeleton as the mechanical (inter-granular) strength of the formation is exceeded. The sand fragments are carried into the wellbore where they can block the flow, damage pumps and pipes, and contaminate the produced fluid. With time, sand production creates cavities in the formation that continually increase in size and eventually lead to wellbore instability and failure. Each year, sanding issues cost the oil industry hundreds of millions of dollars to cope with well repair, pumping device replacement and environmental issues.
There have been various works on the study of sand production from both mechanistic and fluid flow standpoints(1–5). For instance, Vardoulakis et al.(1) formulated the sand production problem as an erosional process in which sand grains are dislodged from the sand matrix under the influence of hydrodynamics. In view of solving real initial boundary value problems such as petroleum reservoirs, Wan et al.(6) and Wan and Wang(7) extended the work to consider a deformable sand matrix. Also, the authors proposed a robust computational model that solves the highly non-linear governing equations dominated by large convection terms within the framework of stabilized finite elements. However, what is missing in all the above-mentioned models is probably the consideration of a gas phase, which could be a driver for sand production mechanisms. For example, the gas phase can modify the dynamics of sand production by way of gas exsolution. Due to a drop in reservoir pressure, gas comes out of the oil phase in the form of tiny gas bubbles. As a large number of these gas bubbles nucleate, there is the formation of an emulsion that increases the mobility of the oil phase. From the solid skeleton viewpoint, additional drag forces act on the sand particles, which ultimately tend to increase the propensity to sand production.
This paper extends previous work developed on coupled erosion mechanics and hydrodynamics by including the presence of a gas phase in the formulation so as to capture the physics associated with gas exsolution.