A Well-Test Analysis Method Accounting for Pre-Test Operations
- D.B. Silin (Lawrence Berkeley Natl. Laboratory) | C.-F. Tsang (Lawrence Berkeley Natl. Laboratory)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2003
- Document Type
- Journal Paper
- 22 - 32
- 2003. Society of Petroleum Engineers
- 2.2.2 Perforating, 4.3.4 Scale, 5.6.4 Drillstem/Well Testing
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In recent work, we have extended the classical radial flow model used in a standard pressure drawdown or buildup well-test analysis by incorporating an additional parameter characterizing the pumping rate prior to the test. By this means, we develop an approach for estimating the formation hydraulic properties in the vicinity of the wellbore from regular pumping rate-pumping pressure data. In this paper, the approach is established as a well-test analysis method by accomplishing two steps. First, five parameters, including the reservoir transmissivity, storativity, skin factor, and pre-test pumping rate, are determined from analysis of measured data. Second, the average reservoir pressure and drainage radius are determined from a calculation using parameters obtained in the first part.
Using a well test to estimate hydraulic formation properties in the vicinity of a well is a common practice in petroleum and environmental industries. The basic theory of well-test analysis was proposed in an early work by Theis1 and was substantially enhanced in later research. The accrued results and experience are summarized in several monographs and surveys.2-8 The traditional technique usually requires interrupting regular operations for a certain period of time. During this time, special operations are performed at the well, and the pumping rates and pressures are measured and analyzed. Such operations normally include shutting in the well and impose additional costs on the operator.
Instead of interrupting the operations, we propose to select a portion of pumping data over a certain time interval and analyze this information. Such a situation introduces new elements into analysis of the data. The pumping rate, which is usually maintained as constant in a traditional well test, can be arbitrarily varying in time. Also, the absence of a shut-in period preceding the test implies that the standard models used for data interpretation may not work. The reason for this is that traditional methods use the solution to flow equation, which is valid only if the impact of pre-test pumping can be neglected. It is usually assumed that at initial time the pressure distribution around the wellbore is uniform (see Ref. 2, page 11). However, if the well was in operation before the test, such an assumption may be incorrect. In our recent papers, 9,10 we have analyzed how the radial flow solution is affected by neglecting the nonuniform pressure distribution caused by pretest pumping. We demonstrated that the difficulties with interpreting well-test data and, in particular, the difficulty in locating a straight-line interval on a Horner plot, can be partially explained through this nonuniform initial pressure distribution. Moreover, we proposed a modified solution, which substantially decreases, and in some cases practically eliminates, the problem of straight-line data matching. Although our argument remains based on the same model and same assumptions as traditional well-test analysis, we have introduced an additional parameter for evaluating an effective pre-test pumping rate on an indefinite time interval preceding the test. This parameter, along with more traditional coefficients of transmissivity and storativity and skin factor, was used for matching the data curve. On examples, we demonstrated that the pressure curve is matched with high accuracy on a time interval larger than in traditional methods. The quality of fitting is stable with respect to the choice of data interval. Moreover, whenever information about the pre-test pumping rate was available, the recovered value of the effective rate approximated the actual pretest pumping rate remarkably well. Comparison of our conclusions with results obtained independently using traditional methods also showed that our estimates of the skin factor can be significantly different, while the transmissivity coefficient is recovered at a higher value.
In this paper, we substantially enhance our analysis performed in Refs. 9 and 10. We propose an alternative approach to account for pre-test pumping in well-test data interpretation and develop a procedure of evaluation of average reservoir pressure and drainage radius based on a simulated well test.
In pumping rate-pumping pressure data analysis, the principal consequence of pre-test operations is nonuniform pressure distribution near the wellbore at the beginning of the test. If the pumping prior to the test was performed approximately at constant rate, then it is natural to assume that the initial pressure distribution is close to a steady-state distribution. We propose to use the pumping rate corresponding to this steady-state solution as an additional fitting parameter. We demonstrate that we obtain the same modified equation as we developed earlier in Refs. 9 and 10 based on asymptotic estimates of the consequences of moving the uniform initial pressure condition indefinitely backward in time. At the same time, the new approach proposed here allows us to obtain an estimate of average reservoir pressure and the dimensionless ratio of apparent wellbore and drainage radii. In fact, the formation near the wellbore is usually heterogeneous or fractured and subject to mechanical and chemical damage (see Ref. 11). A test procedure and further analysis can recover only average, integral formation properties. Therefore, the wellbore radius appearing in our estimates can differ from the actual radius of tubing at the perforation interval.
In addition, the steady-state solution itself (see below) is expressed through a logarithmic function of the distance from the well; therefore, it is physically meaningful only within a certain limited region. Comparison between results of well tests performed at different times can provide important information about the character of changes in the formation.
An estimation algorithm based on our method has been implemented in a computer code named ODA (Operations Data Analysis). In the examples presented below, the computations were performed using this code.
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