Author: haroonkhan

Earlougher and others have discussed the application of the principle of superposition to fluid flow in reservoirs.3,12,13,14 This principle allows the use of the constant rate, single-well equations that have been developed earlier in this applies them to a variety of other cases. To illustrate the application, the solution to Eq. (8.38), which is a linear,…

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…

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.…

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…

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…

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.…

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…

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…

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…