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Abstract It is well-known that many unconventional reservoirs experience porosity and permeability changes with pressure change during production. In recent work, authors have incorporated geomechanical modeling into production analysis procedures to account for stress-sensitivity of permeability of unconventional gas reservoirs, such as shale gas. Such corrections are necessary for deriving both accurate estimates of reservoir and hydraulic fracture properties from rate-transient analysis and for developing accurate long-term forecasts. Some shale gas reservoirs are unique in that dynamic changes may occur in both the induced hydraulic fracture AND matrix permeability, which could have a substantial impact on shale gas productivity. Stress-dependence of shale gas permeability has been quantified in the lab by several researchers, but measurements of this kind for propped or unpropped fractures under in-situ conditions are less routinely measured. For the latter, a variety of mechanisms, caused in part or wholly by stress changes in the induced hydraulic fracture, could lead to conductivity changes. In the current work, we investigate the impact of both stress-dependent matrix permeability and fracture conductivity changes on 1) rate-transient signatures and 2) derived reservoir and hydraulic fracture properties. Stress-dependent matrix permeability is incorporated into rate-transient analysis using modified pseudopressure and pseudotime formulations, and fracture conductivity changes are approximated by applying a time-dependent (dynamic) skin effect. We demonstrate that when rate-transient analysis incorporates both matrix permeability changes and dynamic skin, the resulting rate-transient signature looks very similar to other shale plays (long-term transient linear flow). Uncorrected data appear to have a very short transient linear flow period, followed by apparent boundary-dominated flow. The impact of the applied corrections on estimates of system permeability and fracture half-length is demonstrated as is the impact on production forecasts.
Summary Straight‐line analysis (SLA) methods, which are a subgroup of model‐based techniques used for rate‐transient analysis (RTA), have proved to be immensely useful for evaluating unconventional reservoirs. Transient data can be analyzed using SLA methods to extract reservoir/hydraulic‐fracture information, whereas boundary‐dominated‐flow (BDF) data can be interpreted for fluid‐in‐place estimates. Because transient‐flow periods might 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 uses the Agarwal (2010) approach for CFIP estimation, extended to variable‐rate/pressure data for low‐permeability (unconventional) reservoirs. A log‐log plot of CFIP vs. material‐balance time (for liquids) or material‐balance pseudotime (for gas) is created, which typically exhibits power‐law behavior during transient flow, and reaches a constant value [original fluid in place (OFIP)] during BDF. Although CFIP calculations do not assume a flow geometry, the SLA method requires this to extract reservoir/fracture information. Herein, transient linear flow (TLF) 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 pseudotime = 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. The new 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 the LFP (e.g., the square‐root‐of‐time plot) and the 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 multifractured 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 hydrocarbon‐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. The method is currently limited to cases exhibiting single‐phase flow, the flow‐regime sequence of TLF to BDF, and reservoir homogeneity. In future work, these limitations will be resolved.
Summary Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-of-time plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability. In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the square-root-of-time plot to improve the overestimation of fracture halflength. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.
Abstract The industry is increasingly reliant on rate-transient analysis (RTA) to extract valuable information about the reservoir and hydraulic fractures. However, currently-available RTA models can lead to analysis errors for heterogeneous unconventional reservoirs because they largely ignore reservoir heterogeneities, and assume static reservoir properties. In this work, transient linear flow is rigorously modeled in unconventional reservoirs withpressure-dependent rock and fluid properties and both continuous and discontinuous (heterogeneous) porosity and permeability. To achieve this, pseudo-pressure, pseudo-time and pseudo-distance are introduced to reduce the temporal and spatial non-linear diffusivity equation to that with constant coefficients. Both a Laplace-domain solution and approximate analytical solution to the diffusivity equation are verified against a series of fine-grid numerical simulations for the assumption of fractal-based reservoir heterogeneity (over a wide range of stress-dependent rock and fluid properties). The results indicate that reservoir heterogeneity can result in nonlinear square-root-of-time plots. Further, rock and fluid pressure-dependencies act to decrease the slope of the square-root-of-time plot and affect reservoir/ fracture property evaluations. Two liquid-rich shale (LRS) field examples in North America are analyzed to demonstrate the practical applicability of the new RTA models. In addition to being able to estimate fracture half-length, the new RTA models and analysis workflow can also be used to quantify the non-uniform permeability distribution around the fractures. The major contribution of this work is the introduction of a new approach for evaluating the transient linear flow period for the case of reservoir heterogeneity. This new approach is particularly useful for evaluating the effectiveness of hydraulic fracturing operations by extracting the spatial variability of reservoir quality within the stimulated reservoir volume (SRV). Introduction Recent advancements in multi-stage hydraulic fracturing of horizontal wells have led to commercial development of North American low-permeability (unconventional) reservoirs, significantly impacting energy supply and markets. However, more efficient development of these resources using this technology could be achieved if heterogeneities in these reservoirs were effectively quantified. While production characteristics are affected by these heterogeneities, until now, rate-transient analysis methods, designed to quantitatively analyze production data for reservoir and/ or hydraulic fracture properties, have been limited in their capability to evaluate the distribution of reservoir properties around hydraulic fractures (e.g. permeability). This research seeks to improve RTA capabilities in this regard.
Summary The rapid pace of exploitation of unconventional gas and light oil 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 multifractured horizontal wells (MFHWs) for development. In this work, a semianalytical method (SAM) is developed to provide a solid theoretical basis for forecasting. The technique is analytical in that it uses the methods of Agarwal (2010) to calculate contacted oil in place and contacted gas in place (COIP/CGIP) from production rates, flowing pressures, and fluid properties. The rate-normalized pressure (RNP) derivative (RNP′) is a key component of the calculation; pseudopressure is used for gas cases. The technique is also empirical in that an empirical function is fitted to the resulting COIP/CGIP curve vs. 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 the extraction of RNP. The stabilized COIP/CGIP during boundary-dominated flow (BDF) must be specified for forecasting—thereafter, the method uses a material-balance simulator to model BDF. Hence, if the well is still in transient flow, a range in forecasts may be generated, depending on the assumed stabilized COIP/CGIP. The new SAM 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 ultralow-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 representing the physics better, nonetheless require additional reservoir and hydraulic-fracture data that may not be available on every well in the field. The SAM proposed herein is intended to bridge the gap between empirical and modeling-based approaches—it is more rigorous than purely empirical methods, while requiring a lesser amount of data than fully analytical techniques. The new method is tested against simulated and field cases (tight oil and shale gas). Although a simple power-law function is used in the current work to represent the COIP/OGIP curve, which appears adequate for the cases studied, one should note that wells exhibiting long transitional flow periods (e.g., elliptical/radial) will likely require a different functional form.