WELL TESTING ANALYSIS CONCEPTS

PRIMARY RESERVOIR CHARACTERISTICS. Flow in porous media is a very complex phenomenon and cannot be described as explicitly as flow through pipes or conduits. It is rather easy to measure the length and diameter of a pipe and compute its flow capacity as a function of pressure; however, in porous media flow is different in that there are no clear-cut flow paths which lend themselves to measurement.

The analysis of fluid flow in porous media has evolved throughout the years along two fronts:

the experimental and the analytical. Physicists, engineers, hydrologists, and the like have examined experimentally the behavior of various fluids as they flow through porous media ranging from sand packs to fused Pyrex glass. On the basis of their analyses, they have attempted to formulate laws and correlations that can then be utilized to make analytical predictions for similar systems. The mathematical forms of these relationships will vary depending upon the characteristics of the reservoir. These primary reservoir characteristics that must be considered include:

• types of fluids in the reservoir.
• Flow regimes.
• Reservoir geometry.
• Number of flowing fluids in the reservoir.

TYPES OF FLUIDS IN THE RESERVOIR

The isothermal compressibility coefficient is essentially the controlling factor in identifying the type of the reservoir fluid. In general, reservoir fluids are classified into three groups:

• Incompressible fluids.
• Slightly compressible fluids.
• Compressible fluids.

FLOW REGIMES

There are basically three types of flow regimes that must be recognized in order to describe the fluid flow behavior and reservoir pressure distribution as a function of time. These three flow regimes are:

• Steady-State flow.
• Unsteady-State flow.
• Pseudosteady-State flow.

Steady-State Flow:

The flow regime is identified as a steady-state flow if the pressure at every location in the reservoir remains constant, i.e., does not change with time. This equation states that the rate of change of pressure p with respect to time t at any location i is zero. In reservoirs, the steady-state flow condition can only occur when the reservoir is completely recharged and supported by strong aquifer or pressure maintenance operations.

Unsteady-State Flow:

Unsteady-state flow (frequently called transient flow) is defined as the fluid flowing condition at which the rate ofchange of pressure with respect to time at any position in the reservoir is not zero or constant. This definition suggests that the pressure derivative with respect to time is essentially a function of both position i and time t.

Pseudosteady-State Flow:

When the pressure at different locations in the reservoiris declining linearly as a function of time, i.e., at a constant declining rate, the flowing condition is characterized as pseudosteady-state flow. Mathematically, this definition states that the rate of change of It should be pointed out that pseudosteady-state flow is commonly referred to as semisteady-state flow and quasisteadystate flow. pressure with respect to time at every position is constant.

RESERVOIR GEOMETRY

The shape of a reservoir has a significant effect on its flow behavior. Most reservoirs have irregular boundaries and a rigorous mathematical description of their geometry is often possible only with the use of numerical simulators. However, for many engineering purposes, the actual flow geometry may be represented by one of the following flow geometries:

• Radial Flow.
• Linear Flow.
• Spherical Flow and Hemispherical Flow.

Radial Flow:

In the absence of severe reservoir heterogeneities, flow into or away from wellbore will follow radial

flow lines a substantial distance from the wellbore. Because fluids move toward the well from all directions and coverage at the wellbore, the term radial flow is used to characterize the flow of fluid into the wellbore.

Linear Flow:

Linear flow occurs when flow paths are parallel and the fluid flows in a single direction. In addition, the cross-sectional area to flow must be constant. A common application of linear flowequations is the fluid flow into vertical hydraulic fractures.

Spherical and Hemispherical Flow:

Depending upon the type of wellbore completion configuration, it is possible to have spherical or hemispherical flow near the wellbore. A well with a limited perforated interval could result in spherical flow in the vicinity of the perforations. A well which only partially penetrates the pay zone,  could result in hemispherical flow. The condition could arise where coning of bottom water is important.

NUMBER OF FLOWING FLUIDS IN THE RESERVOIR

The mathematical expressions that are used to predict the volumetric performance and pressure behavior of a reservoir vary in form and complexity depending upon the number of mobile fluids in the reservoir.

There are generally three cases of flowing system:

• Single-phase flow (oil, water, or gas).
• Two-phase flow (oil–water, oil–gas, or gas–water).
• Three-phase flow (oil, water, and gas).

The description of fluid flow and subsequent analysis of pressure data becomes more difficult as the number of mobile fluids increases.