Mathematical Description of the Flow Dynamics of Sand, Crude Oil and Water in an Oil Well

The flow of particulates and fluids from a reservoir has been described using different models. However, obtaining one model that has the capacity to simulate all the phenomena existing in a horizontal oil well may be very difficult. The model described here is very flexible and has the capacity to integrate the essential parameters necessary to give a detailed description of the flow phenomenon. Furthermore, clear descriptions of the flow dynamics, threshold and critical velocity estimation of the components that make up the phases have been attempted in this paper. Within the model's high level of accuracy, the unsafe limits for incipient sand deposition and bed load transport were estimated to be drag forces of 8.938* (10-8-10-10 kgm/s2) as well as threshold and critical velocities of 0.0445 and 0.0134 m/s respectively for Reynolds number in the region of 300-1000. The findings of this study will aid upstream petroleum engineers in avoiding situations that will lead to critical/laminar flows which can in turn cause sand bed formation or bed load transport which can in turn lead to pipeline blockage and loss of productivity.