Program analyzes step-pressure data

I.M. Kutasov
MultiSpectrum Technologies
Santa Monica, Calif.

• Step-Pressure Equations [83,033 bytes]

During a step-pressure test, fluid is produced at two successive constant pressures. Flow rates and time data are recorded during the second constant-pressure flow period.

Fig. 1 [22,925 bytes] illustrates pressure behavior of a step-pressure test. Either a decreasing or increasing pressure sequence may be used. Similar to two-rate tests,¹ the step-pressure tests have two attractive features:

1. The tests do not require that the well be shut in if it is already producing at a constant bottom hole pressure.
2. The well bore storage effects on the test data are short-lived.²

In this article, a general equation is presented along with a computer program that can be used without any limitations for processing step-pressure test data in fractured/stimulated or damaged wells.

Equations

If one assumes that a well is producing against a constant pressure from an infinite-acting reservoir, the effective well bore radius concept can be used.3

In this case, flow rate in oil field units is defined by Equations 1 and 2 (see equation box).

The nomenclature is as follows:

The dimensionless time (tD) is based on the apparent well bore radius concept, and for fractured wells the values of tD can be very small. For large values of tD, a simple equation for the dimensionless flow rate is usually used.2 For this reason, the principle of superposition should be used very careful for approximate solutions.

A semitheoretical equation, Equation 3, can approximate the dimensionless flow rate.4

Table 1 [102,317 bytes] shows the accuracy of Equation 3. Hence, the principle of superposition can be used without any limitations for this case.

Application of the principle of superposition obtains the flow rate for the second flow period, Equation 4.

During the second flowing period, it is assumed that two flow rates were obtained, qa = q(t=ta) and qb = q(t=tb). From these two equations, one can determine the formation permeability, k, and well bore skin factor, S.

Equation 5 then can be obtained from Equation 4. From Equation 5, one can estimate dimensionless time tD1. Next, from Equation 4 (using qa or qb ), formation permeability is calculated.

Finally, the parameter tD1 is used to compute the apparent well bore radius. From Equation 2 the well bore skin factor is calculated.

Note that if N records of flow rates are available, then it is possible to obtain N x (N-1)/2 pairs of values of k and S. In this case the regression technique can be used to analyze test data.

The Fortran program STEP (see box) can simplify the calculations.

Example

It was assumed that k = 50 md, and S = 0.0. The program "STEP" was used to estimate the formation permeability and skin factor (Table 3 [56,708 bytes]).

The calculated k and S agree well with the assumed k and S. Table 4 [51,443 bytes] lists the input parameters.

References

1. Earlougher, R.C. Jr., "Advances In Well Test Analysis," SPE, Dallas, 1977.
2. Sengul, M.M., "Analysis of Step-Pressure Tests," SPE Paper No. 12175, 58th Annual Technical Conference and Exhibition, San Francisco, Oct. 5-8, 1983.
3. Uraiet, A.A., and Raghavan, R., "Unsteady Flow to a Well Producing at Constant Pressure," JPT, October 1980, pp. 1803-12.
4. Kutasov, I.M., "Dimensionless Temperature, Cumulative Heat Flow and Heat Flow Rate for a Well With a Constant Boreface Temperature," Geothermics, Vol. 16, 1987, pp. 467-72

The Author