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Summary In this study, we provide a detailed review and comparison of the various graphical methods, available in the literature, to interpret/analyze rate‐ and pressure‐transient data acquired from multistage hydraulically fractured horizontal wells (MHFHWs) completed in unconventional gas reservoirs. The methods reviewed in this study do not address complex transport mechanisms and complex fracture networks, but do address transient matrix linear flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012a, 2012b; Chen and Raghavan 2013) and boundary‐dominated flow (BDF). The methods for BDF are the contacted‐volume methods based on the ending times of linear flow (Wattenbarger et al. 1998; Behmanesh et al. 2015) and the flowing material‐balance (FMB) methods. The Agarwal‐Gardner FMB method (Agarwal et al. 1999) and the conventional FMB method involve plotting rate‐normalized pseudopressure vs. material‐balance pseudotime. We delineate the advantages and limitations associated with each method and identify the best methods of interpretation and analysis. Three different production modes—constant rate (CR), constant bottomhole pressure (BHP) (CBHP), and variable‐rate BHP—are considered. For comparison, various synthetic test data sets generated from a high‐resolution spectral gas simulator, which treats nonlinear gas flow rigorously and accurately to simulate rate‐transient data, is used. Both synthetic noise‐free and noisy‐rate pressure‐data sets considering wide ranges of initial reservoir pressure and BHP, as well as real‐field data sets, are used to compare the methods. For linear flow, the Nobakht‐Clarkson method (Nobakht and Clarkson 2012a, 2012b) yields the best results, although its use is tedious because it requires an iterative procedure. The Chen and Raghavan (2013) method for linear flow seems to provide results that are comparable with the Nobakht‐Clarkson method (Nobakht and Clarkson 2012b) but does not require an iterative procedure. The Ibrahim‐Wattenbarger method (Ibrahim and Wattenbarger 2006) for linear‐flow analysis always overestimates flow capacity compared with the other methods. Among the methods that discuss the ending time of linear flow, it was found that the unit‐impulse method from Behmanesh et al. (2015) provides the best results for predicting gas in place. For BDF, the results show that the Agarwal‐Gardner FMB method (Agarwal et al. 1999) is quite vulnerable to the error in rate/pressure data, whereas the conventional FMB method is more robust to noise and provides more accurate estimates of gas in place.
Abstract Straight-line material-balance plots are commonly applied to analyze reservoir performance and estimate the OHIP (original-hydrocarbon-in-place). Depending on the type of the straight-line plot is applied the OHIP may be found either from the slope or the intercept of the straight line. In the case of a gas-condensate reservoir, the compositional effect and the overpressure effect must be formulated into a general material-balance equation to obtain a valid straight-line plot. For obtaining a correct OHIP a line must be both linear and having the correct slope or intercept when straight-line material-balance plots are used. Unfortunately, a quality material-balance evaluation for a gas-condensate reservoir is difficult to achieve using straight-line material-balance plots because the additional data required for calculating the compositional effect and the overpressure effect are difficult to obtain. This paper illustrates that the compositional effect and the overpressure effect can be ignored if the results obtained based on a general material-balance equation are plotted as a horizontal line. In horizontal line material-balance plot no slope or intercept is used as the condition for determining the OHIP because only a correct OHIP can give a horizontally linear material-balance plot, the only condition to meet. Horizontal-line material-balance plots simplify the evaluation procedure and improve the quality of material-balance valuations. Introduction Material-Balance (MB) allows for evaluating the original-hydrocarbon-in-place (OHIP) by analyzing the field production performance. In cases of gas-condensate reservoirs the general material-balance equation (GMBE) written for MB evaluations must be modified to account for the compositional effects as that reported by Wang. Recently, a material-balance evaluation approach that does not require any aquifer model was proposed by Hsieh et al. In that approach (Direct approach) instead of independently calculating water influx terms (Aquifer Model approaches) then substitute them into the material-balance equations, they reverse the procedure to directly calculate water influx terms from the material-balance equation assuming the OHIP is known. Such a process simplifies the material-balance evaluation significantly because calculating water influx with known (assumed) OHIP is far simpler than that of using aquifer models. When using aquifer models not only the selected aquifer model must be able to adequately represent the actual reservoir-aquifer configuration but also the properties of the aquifer must be available. Usually, a unique solution for OHIP is difficult to obtain when using aquifer models. This happens because the aquifer model approaches attempt to solve material-balance equations based on a material-imbalance procedure in that the water influx terms are independently calculated (predicted) using aquifer models that rarely represent the true and unique reservoir-aquifer system. In applying Hsieh's Direct approach, a series of water influx index values are directly calculated for a series of assumed OHIP's using only the general material-balance equation (GMBE). Therefore, in the Direct approach the materials (terms) in material-balance equation are always balanced. Once the influx terms are solved, they use horizontal plot of Water-Influx-Index vs. Time (C-T plot) instead of the traditional linear material-balance plots to determine the OHIP. That is, the assumed OHIP that yields the most horizontal line is taken as the final OHIP because each aquifer has its unique influx index (rb/d/psi) just like each reservoir has its unique productivity index. In a C-T plot a volumetric reservoir has a consistent C of zero (or small) at different time steps, otherwise, a horizontal line with C values greater than zero (positive and not negligible) appears, indicating aquifer influx. This paper shows the Direct approach is also effective for evaluating a gas-condensate reservoir. Review of Direct Approach The formulation of Hsieh's Direct approach can be briefly explained using the following equations, taken from their paper.
This paper presents the development of two material balance methods for unconventional gas reservoirs. One method is appropriate for estimating gas-in-place while the second is appropriate for making future reservoir predictions. These techniques differ from the material balance methods for conventional gas reservoirs, in that, the effects of adsorbed gas are included. Both methods are developed using the assumptions traditionally associated with the material balance approach. For estimating original gas-in-place, the additional assumption of equilibrium between the free and adsorbed gas phases is required (ie., gas desorption is assumed to be strictly pressure dependent). Simplified forms of this generalized equation corresponding to special cases (volumetric reservoirs, etc.) are also presented. No additional simplifying assumptions are required for making future reservoir predictions.
The results of both methods are compared to those of a rigorous finite-difference simulator developed specifically for unconventional gas reservoirs. These comparisons are made to determine the effects of all assumptions and the magnitude of these effects.
Due to the assumption of equilibrium, the first approach is appropriate for shut-in wells or flowing wells in reservoir undergoing rapid desorption. The assumption of rapid desorption corresponds to reservoirs with a high natural fracture density (small primary-porosity matrix blocks) or with a high diffusion coefficient.
It is believed that the techniques presented in this paper provide basic tools currently unavailable to engineers working with unconventional gas reservoirs.
The material balance equation is one of the fundamental tools used to determine the original gas-in-place and production performance of conventional gas reservoirs. For conventional gas reservoirs, the material balance equation has the form:
or, in terms of p/Z:
These equations are derived with the following assumptions:
. The gas and reservoir rock are non-reactive.
. The reservoir acts as a constant-volume tank (ie., changes in porosity with pressure decline are negligible).
Frequently, the analysis of an undersaturated waterdrive reservoir by a material balance is unsatisfactory because reservoir conditions do not reasonably satisfy the assumptions of the material-balance equation. This occurred in the case of a Devonian reservoir in West Texas which proved difficult to analyze because of a rather unusual development history. The standard material-balance analysis technique had to be modified before a satisfactory oil-in-place value could be determined. The modified technique consisted of a material-balance formulation which permitted the analysis of pressure-production data from separate portions of the reservoir with one equation; it also permitted a judicious application of the "least-squares method" to reduce the effect of inherent inaccuracies in the early data. The analysis was accomplished with the aid of an IBM 704 computer and represents a good example of the flexibility in material-balance calculations that may be obtained by computer usage.
The determination of oil in place and water-influx performance of undersaturated water-drive reservoirs, using the material-balance principle, is a well established practice. Frequently, however, the material-balance results are questionable, and the practicing engineer begins to regard such calculations as either totally unreliable or applicable only to a strange breed of reservoirs which apparently are owned only by competitors. Inconclusive or questionable results will occur when reservoir conditions do not reasonably satisfy the assumptions of the material-balance equation and when the true average reservoir pressure is not accurately represented by an average of individual well pressures. These difficulties often can be overcome by modifying the material-balance equation to introduce additional independent parameters which may be assigned various values during the calculations to determine the effects, within certain limits, of possible inaccuracies in basic assumptions. This is exemplified by the reservoir study which is the subject of this paper. The subject reservoir is a structural trap in the Devonian dolomite-limestone formation of West Texas. The initial reservoir pressure of 3,231 psi declined to about 2,250 psi during 12 years of production, but it has remained above the saturation pressure of 1,775 psi. Material-balance calculations, made early in the life of the field, indicated a much larger reservoir than had apparently been defined by the drilling of 10 producing wells and three dry holes. Although a material balance during the early life of an expansion-drive reservoir is notably unreliable, the effort proved rewarding in this case. The consistency of the calculated value of oil in place after nearly eight years of production prompted additional drilling which eventually extended the field to include a volume approximately three times that of the initial discovery and resulted in an additional 28 producing wells. Even with the additional drilling, the amount of reservoir pore volume was still questionable. Volumetric calculations indicated 40 million STB of oil in place, but very few wells had penetrated the full Devonian section; since the top of the Devonian is eroded over most of the structure, the estimated pay thickness may be considerably in error. Material-balance calculations, although not so consistent as the earlier ones, gave an oil-in-place value of about 140 million STB and no definite indication of water influx. Furthermore, data from drill-stem tests of the Devonian formation taken in dry holes in the vicinity of the reservoir indicated the possibility of a very limited aquifer. The pressure-decline curves indicated a recovery above saturation pressure much greater than normal for an expansion drive--if the amount of actual oil in place was reasonably close to the volumetric estimate.