In evaluating well performance, the standard usually referred to is the productivity index of an open hole that completely penetrates a circular formation normal to the strata and in which no alteration in permeability has occurred in the vicinity of the wellbore. Substituting Eq. (8.47) into Eq. (8.49), we get The productivity ratio (PR) then… Continue reading Productivity Ratio (PR)

The ratio of the rate of production, expressed in STB/day for liquid flow, to the pressure drawdown at the midpoint of the producing interval, is called the productivity index, symbol J. The productivity index (PI) is a measure of the well potential, or the ability of the well to produce, and is a commonly measured well property.… Continue reading Productivity Index (PI)

The differential equation for the flow of compressible fluids in terms of the real gas pseudopressure was derived in Eq. (8.42). When the appropriate boundary conditions are applied to Eq. (8.42), the pseudosteady-state solution rearranged and solved for q yields Eq. (8.48):

Once the pressure disturbance has been felt throughout the reservoir including at the boundary, the reservoir can no longer be considered as being infinite in size and the flow is not in the transient regime. This situation necessitates another solution to Eq. (8.38), using a different boundary condition at the outer boundary. The initial condition… Continue reading Radial Flow of Slightly Compressible Fluids, Pseudosteady-State Flow

For the transient flow cases that were considered in the previous section, the well was assumed to be located in a very large reservoir. This assumption was made so that the flow from or to the well would not be affected by boundaries that would inhibit the flow. Obviously, the time that this assumption can… Continue reading Pseudosteady-State Flow

Eq. (8.35) was developed to describe the flow of any fluid flowing in a radial geometry in porous media. To develop a solution to Eq. (8.35) for the compressible fluid, or gas, case, two additional equations are required: (1) an equation of state, usually the real gas law, which is Eq. (2.8), and (2) Eq.… Continue reading Radial Flow of Compressible Fluids, Transient Flow

If Eq. (8.2) is expressed in terms of density, ρ, which is the inverse of specific volume, then the following is obtained: where pR is some reference pressure and ρR is the density at that reference pressure. Inherent in this equation is the assumption that the compressibility of the fluid is constant. This is nearly always a good assumption over… Continue reading Radial Flow of Slightly Compressible Fluids, Transient Flow

By applying appropriate boundary and initial conditions, particular solutions to the differential equation derived in the preceding section can be discussed. The solutions obtained pertain to the transient and pseudosteady-state flow periods for both slightly compressible and compressible fluids. Since the incompressible fluid does not exist, solutions involving this type of fluid are not discussed. Only… Continue reading Transient Flow

The radial diffusivity equation, which is the general differential equation used to model time-dependent flow systems, is now developed. Consider the volume element shown in Fig. 8.12. The element has a thickness Δr and is located r distance from the center of the well. Mass is allowed to flow into and out of the volume element during a period… Continue reading Development of the Radial Diffusivity Equation

Many producing formations are composed of strata or stringers that may vary widely in permeability and thickness, as illustrated in Fig. 8.10. If these strata are producing fluid to a common wellbore under the same drawdown and from the same drainage radius, then Figure 8.10 Radial flow in parallel beds. Then, canceling, This equation is the same… Continue reading Permeability Averages for Radial Flow