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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 analysis (SLA) methods, which are a sub-group of model-based techniques used for rate-transient analysis (RTA), have proven to be immensely useful for evaluating unconventional reservoirs. Transient data can be analyzed using SLA methods to extract reservoir/hydraulic fracture information, while boundary-dominated flow data can be interpreted for fluid-in-place estimates. Because transient flow periods may be extensive, it is also advantageous to evaluate the volume of hydrocarbons-in-place contacted over time to assist with reserves assessment. The new SLA method introduced herein enables reservoir/fracture properties and contacted fluid-in-place (CFIP) to be estimated from the same plot, which is an advantage over traditional SLA techniques. The new SLA method utilizes the Agarwal (2010) approach for CFIP estimation, extended to variable rate/pressure data for low permeability (unconventional) reservoirs. A log-log plot of CFIP versus material balance time (for liquids) or material balance pseudo-time (for gas) is created, which typically exhibits power-law behavior during transient flow, and reaches a constant value (original fluid-in-place, OFIP) during boundary-dominated flow. Although CFIP calculations do not assume a flow geometry, the SLA method requires this to extract reservoir/fracture information. Herein, transient linear flow is assumed, and used for the SLA method derivation, which allows the linear flow parameter (LFP) to be extracted from the y-intercept (at material balance time or material balance pseudo-time= 1 day) of a straight-line fit through transient data. OFIP can also be obtained from the stabilization level of the CFIP plot. Validation of the new SLA method for an undersaturated oil case is performed through application to synthetic data generated with an analytical model. Thenew SLA results in estimates of LFP and OFIP that are in excellent agreement with model input (within 2%). Further, the results are consistent with the traditional SLA methods used to estimate LFP(e.g. the square-root of time plot) and OFIP (e.g. the flowing material balance plot). Practical application of the new SLA method is demonstrated using field cases and experimental data. Field cases studied include online oil production from a multi-fractured horizontal well (MFHW) completed in a tight oil reservoir, and flowback water production from a second MFHW, also completed in a tight oil reservoir. Experimental (gas) data generated using a recently-introduced RTA core analysis technique, were also analyzed using the new SLA method. In all cases, the new SLA method results are in excellent agreement with traditional SLA methods. The new SLA method introduced herein is an easy-to-apply, fully-analytical RTA technique that can be used for both reservoir/fracture characterization and hydrocarbons-in-place assessment. This method should provide important, complementary information to traditionally-used methods, such as square-root of time and flowing material balance plots, which are commonly used by reservoir engineers for evaluating unconventional reservoirs.
Abstract Application of superposition principle to non-linear gas governing equations has been an elusive goal in early-transient production data analysis and has been so far limited to the use of empirical and approximate methods best applicable to boundary-dominated flow conditions. This paper presents a novel and rigorous semi-analytical model that is applicable for the analysis of production data from multi-fractured horizontal gas wells (MFHWs) producing under early-transient variable rate/pressure production conditions. Nonlinear, pressure-dependent hydraulic diffusivity retained in pseudo-pressure-based gas diffusivity equation is straightforwardly and rigorously captured without approximation. The resulting formulation of superposition applied in nonlinear gas system is written in terms of the classical solution for linear PDE plus an analytical adjustment factor that quantifies the nonlinearity of the system. Numerical examples are presented to test the validity and showcase the capabilities of proposed approach. Comparisons against available empirical and approximate models are also provided for these cases.
Abstract The rapid pace of exploitation of unconventional gas and light oil (UG/ULO) plays in North America has necessitated the development of new production forecasting methodologies to aid in reserves assessment, capital planning and field optimization. The generation of defendable forecasts is challenged not only by reservoir complexities but also by the use of multi-fractured horizontal wells (MFHWs) for development. In this work, we have developed a semi-analytical method that provides a solid theoretical basis for forecasting. The technique is analytical in that it uses the methods of Agarwal (2010) to calculate contacted oil- and gas-in-place (COIP/CGIP) from production rates, flowing pressures and fluid properties. The rate-normalized pressure (for liquids) or pseudopressure (for gas) derivative (RNP') is a key component of the calculation. The technique is also empirical in that an empirical function is fit to the resulting COIP/CGIP curve versus time. Although the method is flexible enough that any equation can be used to represent the COIP/CGIP curve, and hence the sequence of flow-regimes exhibited by MFHWs, the equation must be capable of being integrated to allow extraction of rate-normalized pressure or pseudopressure (RNP). The stabilized COIP/OGIP during boundary-dominated flow must be specified for forecasting – thereafter, the method uses a material balance simulator to model boundary-dominated flow. Hence, if the well is still in transient flow, a range in forecasts may be generated, depending on the assumed stabilized COIP/OGIP. Our new semi-analytical method addresses some of the current limitations of empirical and fully analytical (modeling) approaches. Empirical methods, which have been adapted to account for long transient and transitional flow periods associated with ultra-low permeability reservoirs, lack a theoretical basis, and therefore input parameters may be difficult to constrain. However, empirical methods are simple to apply and require a minimum amount of data for forecasting. Analytical models, while better representing the physics, nonetheless require additional reservoir and hydraulic fracture data which may not be available on every well in the field. The semi-analytical method proposed herein is intended to bridge the gap between empirical and modeling-based approaches – it is more rigorous than purely empirical methods, while requiring less data than fully analytical techniques. The new method is tested against simulated and field cases (tight oil and shale gas). Although we have used a simple power-law function to represent COIP/OGIP curve, which appears adequate for the cases studied, we note that wells exhibiting long transitional (e.g. elliptical/radial) will likely require a different functional form.
Clarkson, Christopher R. (University of Calgary) | Yuan, Bin (University of Calgary) | Zhang, Zhenzihao (University of Calgary) | Tabasinejad, Farshad (University of Calgary) | Behmanesh, Hamid (NCS Multistage) | Hamdi, Hamidreza (University of Calgary) | Anderson, Dave (NCS Multistage) | Thompson, John (NCS Multistage) | Lougheed, Dylan (NCS Multistage)
Abstract The dominant transient flow regime for multi-fractured horizontal wells producing from low-permeability and shale (unconventional) reservoirs has historically been interpreted to be transient linear flow (TLF) in the framework of classical diffusion (CD). Recently, observed deviations away from this classical behavior for Permian Basin Wolfcamp shale (oil) wells have been attributed to anomalous diffusion (AD). The objective of the current study is to systematically investigate other potential causes of deviations from TLF. The conventional log-log diagnostics used to identify flow regimes do not account for reservoir complexities such as multi-phase flow and reservoir heterogeneity. Failure to correct for these effects when they are occurring may result in misdiagnosis of flow regimes. A new workflow is therefore introduced herein to improve flow regime identification when reservoir complexities are exhibited, and to provide a more confident diagnosis of AD behavior. The workflow involves the correction of log-log diagnostics for complex reservoir behavior through the use of modified pseudo-variables (pseudo-pressure and pseudo-time) after the complex reservoir behavior is identified. Although reservoir heterogeneity is an accepted cause of deviations from TLF, the impact of multi-phase flow has not been investigated in detail. Therefore, in this study, corrections to pseudo-variables for multi-phase flow, a known reservoir complexity exhibited by Wolfcamp shale wells, are presented. Pressure-dependent permeability is also accounted for in the pseudo-variable calculations, although its impact is demonstrated to be relatively minor in this study. Application of the new workflow to a simulated case and a Wolfcamp shale field case demonstrates the following: 1) multi-phase flow, and in particular the appearance of a mobile gas phase after two-phase oil and water production, results in deviations from classical TLF behavior when data is analyzed using conventional (uncorrected) diagnostics; 2) this deviation has characteristics similar to that expected for sub-diffusion; 3) application of the modified diagnostics to a simulated case that includes multi-phase flow results in the “true” flow regime signature of TLF being observed; 4) application of the modified diagnostics to a field case exhibiting evidence of multi-phase flow reduces the deviation from TLF.