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Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. Fig 1 illustrates a flow-after-flow test.
The major objective of this paper is to identify the most generally applicable method to analyze pressure transient tests in coalbed methane reservoirs. The desired methodology should allow us to analyze short term pressure tests and long term performance data consistently and in a way that can lead to an adequate reservoir description. An important part of this work was the evaluation of the methods currently proposed in the literature for estimating properties of coalbed methane reservoirs. The paper identifies the assumptions and data requirements for the conventional (i.e. Perrine-Martin) method and pseudopressure method of Kamal and Six along with their potential range of applicability in coalbed methane reservoirs. The paper compares the results using the analytical solution methods to the results obtained with a 2-phase, 3-dimensional, finite difference simulator. We show that oversimplifying or neglecting desorption of methane from the coalbed methane reservoir matrix as is done in the analytical methods can lead to inaccurate estimates of permeability. Thus, we concluded that the only generally trustworthy method of analysis of transient and longer-term production data is to use a coalbed methane simulator which includes diffusion and desorption.
Another objective of the paper is to validate the method chosen for estimating permeability in a coalbed methane reservoir at a specific geologic location using actual field data. We developed a coalbed methane reservoir description by history matching actual production and pressure data. We compared the permeability values from the simulator to those estimated from the analytical solution methods and found that the analytical methods do not provide accurate estimates of permeability for this field example. The oversimplified assumptions used in the development of the conventional and pseudopressure methods have a significant influence on the permeability estimates and cause inaccurate results.
The value of coal seam permeability is obviously a critical parameter when evaluating the productivity of a coal seam and estimating this property can be difficult. Normally, estimates of reservoir permeability are obtained from the analysis of single or multi-well pressure transient tests; however, in coalbed methane reservoirs, the analyses of these data are complicated by two-phase flow in the fracture system and the effects of gas desorption. The petroleum industry has been testing coalbed methane wells by (1) a series of water pump-in and falloff tests upon completing the wells to ensure a single-phase system or (2) running conventional pressure buildup tests and using pseudopressure or multi-phase potential analysis methods to account for the two-phase flow.
Several methods are available to analyze pressure transient data for an estimate of permeability from coalbed methane wells. Conventional analysis, pseudopressure analysis and reservoir simulation are the most common methods. Conventional well test analysis uses well pressures and single-phase flow rates to evaluate the reservoir around the well. Martin presented a formal proof of a method developed by Perrine for the analysis of data from multi-phase flow tests.
This paper presents analysis techniques for post-transient gas flow at a constant flowing bottomhole pressure. Reservoir parameters can be estimated from production decline curve analysis using analytical solutions which are formulated in terms of real gas pseudopressure analysis.
These techniques were applied to a field study of two small, low productivity gas reservoirs in Northern Tennessee. The productivity data for this field study was analyzed using decline curve analysis. The types of decline curve analysis used were: rate-time graphical, rate-time and cumulative-time non-linear least squares. Decline curve analysis by the use of type curves was attempted, but data scatter caused significant deviation of results when compared to the other types of decline curve analysis.
The decline curve analysis results were then interpreted using an analytic reservoir model which did include pseudopressure analysis. This analysis was verified by a simulated real gas example which attempted to model producing conditions similar to those encountered in the field. The overall objective of the field study was to find correlations of reservoir parameters to measured production data. Several rate-reserve, rate-permeability/porosity-area , and rate-permeability-thickness (kh) correlations were obtained from the results of the decline curve analysis. The best correlations were based on an average rate, calculated from a well's first three months of production.
The purpose of this paper is to present a straightforward approach for obtaining reservoir parameters from production decline curve. This approach could be used for single well analysis or it could, as to be shown in this work, be extended to a field study of several reservoirs.
Without this type of analysis we would be forced to use more tedious material balance methods which would require average reservoir pressure estimates as a function of time. This would be virtually impossible for the small operator and it could be quite unprofitable for a major operator since a well has to be shut-in for extended periods to obtain average reservoir pressures. Therefore, the ability to estimate reservoir parameters from production data is needed.
The first approach used to analyze production decline curves was to fit the production data with some empirical model such as an exponential or hyperbolic equation and to extrapolate that equation to some economic limit. Nind gives a thorough development of these empirical relations, which are summarized in Table 1. Recently, Fetkovich has developed a type curve for analyzing production decline curve data. The transient portion of the type curve is based on analytical model while the depletion or post-transient portion of the type curve has an analytic exponential stem and several empirical hyperbolic stems. This is a sound approach for analyzing production data, but since our rate data are quite scattered, non-unique matches were obtained when this method was applied.
Since type curve matching could not be used, we chose to use the data fitting techniques. A very efficient solution algorithm proposed by More, et al., was chosen to solve the data fitting problem in a non-linear least squares sense.