• pressure drawdown;

• pressure buildup;

• multirate;

• interference;

• pulse;

• drill stem (DST);

• falloff;

• injectivity;

• step rate.

• C. S. Matthews and D. G. Russell, Pressure Buildup and Flow Test in Wells (1967);

• Energy Resources Conservation Board (ERCB), Theory and Practice of the Testing of Gas Wells (1975);

• Robert Earlougher, Advances in Well Test Analysis (1977);

• John Lee, Well Testing (1982);

• M. A. Sabet, Well Test Analysis (1991);

• Roland Horn, Modern Well Test Analysis (1995).

1.3.1 Drawdown test

A pressure drawdown test is simply a series of bottom-hole pressure measurements made during a period of flow at constant producing rate. Usually the well is shut in prior to the flow test for a period of time sufficient to allow the pressure to equalize throughout the formation, i.e., to reach static pressure. A schematic of the ideal flow rate and pressure history is shown in Figure 1.32.

The fundamental objectives of drawdown testing are to obtain the average permeability, k, of the reservoir rock within the drainage area of the well, and to assess the degree of damage of stimulation induced in the vicinity of the wellbore through drilling and completion practices. Other objectives are to determine the pore volume and to detect reservoir inhomogeneities within the drainage area of the well.

When a well is flowing at a constant rate of Qo under the unsteady-state condition, the pressure behavior of the well will act as if it exists in an infinite-size reservoir. The pressure behavior during this period is described by Equation 1.2.134 as:

where:

The above expression can be written as:

[1.3.1]

This relationship is essentially an equation of a straight line and can be expressed as:

where:

and the slope m is given by:

[1.3.2]

Equation 1.3.1 suggests that a plot of pwf versus time t on semilog graph paper would yield a straight line with a slope m in psi/cycle. This semilog straight-line portion of the drawdown data, as shown in Figure 1.33, can also be expressed in another convenient form by employing the definition of the slope:

or:

Notice that Equation 1.3.2 can also be rearranged to determine the capacity kh of the drainage area of the well. If the thickness is known, then the average permeability is given by:

where:

Clearly, kh/μ or k/μ may also be estimated.

The skin effect can be obtained by rearranging Equation 1.3.1 as:

or, more conveniently, if selecting pwf = p1hr which is found on the extension of the straight line at t = 1 hr, then:

[1.3.3]

where |m| is the absolute value of the slope m.

In Equation 1.2.3, p1hr must be obtained from the semilog straight line. If the pressure data measured at 1 hour does not fall on that line, the line must be extrapolated to 1 hour and the extrapolated value of p1hr must be used in Equation 1.3.3. This procedure is necessary to avoid calculating an incorrect skin by using a wellbore-storage-influenced pressure. Figure 1.33 illustrates the extrapolation to p1hr.

Note that the additional pressure drop due to the skin was expressed previously by Equation 1.2.130 as:

This additional pressure drop can be equivalently written in terms of the semilog straight-line slope m by combining the above expression with that of Equation 1.3.3 to give:

Another physically meaningful characterization of the skin factor is the flow coefficient E as defined by the ratio of the well actual or observed productivity index Jactual and its ideal productivity index Jideal. The ideal productivity index Jideal is the value obtained with no alternation of permeability around the wellbore. Mathematically, the flow coefficient is given by:

where is the average pressure in the well drainage...