Petroleum Engineering Handbook Vol 4 - Production Operations Engineerings

IV-2

Petroleum Engineering Handbook-Vol. IV

Fig. 1.1-Production system and associated pressure losses.1

the fluid flows from the reservoir into and through the production system, it experiences a continuous pressure drop (as Fig. 1.1 shows). The pressure begins at the average reservoir pressure and ends either at the pressure of the transfer line or near atmospheric pressure in the stock tank. In either case, a large pressure drop is experienced as the reservoir fluids are produced to the surface. It is the petroleum engineer's responsibility to use this pressure reduction in an optimal manner. The pressure reduction depends on the production rate and, at the same time, the production rate depends on the pressure change. Understanding the relationship between  pressure and production rate is important to predicting the performance of individual oil and gas wells. To design a well completion or predict the production rate properly, a systematic approach is required to integrate the production system components. Systems analysis, which allows the  petroleum engineer to both analyze production systems and design well completions, accom plishes this. This chapter focuses on the flow of reservoir fluids through the production system,  particularly inflow performance, which is the reservoir pressure-rate behavior of the individual well, and outflow performance, which is the flow of reservoir fluids through the piping system.

1.2 Reservoir Inflow Performance Mathematical models describing the flow of fluids through porous and permeable media can be developed by combining physical relationships for the conservation of mass with an equation of motion and an equation of state. This leads to the diffusivity equations, which are used in the petroleum industry to describe the flow of fluids through porous media. The diffusivity equation can be written for any geometry, but radial flow geometry is the one of most interest to the petroleum engineer dealing with single well issues. The radial diffusivity equation for a slightly compressible liquid with a constant viscosity (an undersaturated oil or water) is