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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.
Analytic solutions for finite-conductive vertical fractured reservoirs are developed based on bilinear and trilinear fracture flow models for constant-pressure and constant-rate cases with and without boundaries. These solutions include effects of linear skin on the fracture, fracture conductivity, fracture to formation height ratio, wellbore and fracture storage, fracture to formation hydraulic diffusivity rate, and wellbore phase segregation.
A simple method for solving these calculations is used to extend the transient fracture solutions to pseudoradial flow regime for various fracture parameters. Characteristic curves relating the effective wellbore radius for different fracture conductivities, skin and wellbore storage values are presented to facilitate the transition to the pseudoradial solutions.
The provided type curves identify fracture linear, storage linear, bilinear, formation linear, and pseudoradial flow regimes. Example problems are analyzed using type curve methods, and parameters are problems are analyzed using type curve methods, and parameters are optimized with a Levenberg-Marquarde regression technique,
More efficient analysis methods for hydraulically fractured formations are needed as is evidenced by increasing demands for energy, decreasing new domestic finds of significant size, and ever increasing use of massive hydraulic fracturing to obtain previously uneconomical hydrocarbons. The trend in the petroleum industry is to develop faster solution methods and more accurate pressure transient models which can provide descriptions of reservoir, fracture, and wellbore behaviors for hydraulically fractured wells,
Models accounting for the influence of more physical parameters for fractured reservoirs over extreme time ranges are also needed.
Cinco-Ley reported a survey on published flow models for fractured wells. The available analysis techniques for hydraulically fractured formations are either numerical, semianalytical, or asymptotic-analytical. The accuracy of the numerical method depends on the use of the appropriate reservoir simulator, block size, time step, truncation error consideration and material balance convergence. The numerical methods are rigorous; however, the wellbore effects could not be easily incorporated into the solution.
Gringarten et al developed a semianalytical model for the pressure analysis of infinite-conductive fractured wells. Cinco-Ley et al pioneered the technique for the pressure transient analysis of pioneered the technique for the pressure transient analysis of finite-conductive fractured wells. In this technique, the instantaneous Green and source functions plus the Newman product method discussed by Gringarten and Ramey were used to generate the Fredholm integral equation. The integral was discretized in time and space. The accuracy of the semianalytical method depends on the number of time intervals and the selected fracture length segments. Also, fluid flux along the fracture has a stepwise rather than a smooth uniform distribution.
Both numerical and semianalytical methods require extensive computer processing, storage and coding to generate a representative analysis technique for hydraulically fractured wells.
The analytic bilinear model of Cinco-Ley et al is applicable for early-time pressure data prior to the pressure transients being felt at the tip of the fracture. Physically, the trilinear fracture flow model of Lee and Brockenbrough approximates the flow in a fractured formation better than the bilinear flow model.
An analytic solution for finite-conductivity, vertically fractured wells is developed for both the constant-pressure and the constant-rate cases. This solution includes linear skin on the fracture, wellbore and fracture storages, wellbore phase redistribution, and fracture-to-formation height ratio. phase redistribution, and fracture-to-formation height ratio. The Laplace-space solution is direct, and no convolution is performed to include the skin, storage, and phase performed to include the skin, storage, and phase segregation effects.
This paper presents type curves and corresponding analysis techniques for constant-pressure declining rate cases. A unique asymptotic approach to pseudoradial flow is used to produce the solutions for the unbounded reservoirs. The produce the solutions for the unbounded reservoirs. The type curves provide all possible flow regimes encountered in pressure transient testing of finite-conductivity, vertically pressure transient testing of finite-conductivity, vertically fractured wells. Tabulated comparison between this analytic solution and the ones obtained with finite-difference simulator for both bounded and unbounded formations are also provided.
Hydraulic fracturing is used to enhance production of reservoirs with low permeability, wells with severe skin damage, injectivity in gas cycling, waterflood processes, and in gas storage projects.
Production allowances and well testing procedures make it a Production allowances and well testing procedures make it a common practice to test wells at constant production rate. Since marginal wells and tighter reservoirs are being exploited and produced at capacity rates, the preferred method of well testing at constant-pressure, declining rate is gaining more interest. Production following massive hydraulic fracturing of low-permeability gas reservoirs, injection projects in which the injectivity into the hydraulically fractured zone decreases with time, open flow production, production into a constant pressure separator or production, production into a constant pressure separator or pipeline, the early-time production following a hydraulically pipeline, the early-time production following a hydraulically fractured well, and steam production from geothermal wells into constant-pressure turbines are candidates for constant-pressure, well test analysis.
Traditional well testing of the aforementioned reservoirs is complicated by the difficulties involved in maintaining a constant flowrate for a sufficient period of time to satisfy test requirements. In these cases, a constant-pressure, declining rate profile is more appropriate and easier to maintain. Fracture and formation parameters for such wells can be evaluated without any need to shut in the well.
Numerous solutions are available in the literature for postfracturing analysis of hydraulically fractured wells postfracturing analysis of hydraulically fractured wells producing at constant flowrate. However, the solution and producing at constant flowrate. However, the solution and analysis for constant-pressure, well testing has not been fully exploited. The limitations and applications of the three distinct solutions of numeric, semi-analytic, and asymptotic-analytic techniques were previously discussed. In the literature, constant-pressure solutions are usually obtained by applying the superposition principle either in real-time or in Laplace-space to the three available solution techniques for constant-rate problems.
Prats et al. applied Laplace transformation to the partial Prats et al. applied Laplace transformation to the partial differential equation obtained for an elliptical coordinate system. They presented analytic solutions for both constant-rate and constant-pressure cases of hydraulically fractured wells producing from a cylindrical reservoir.
Fractal techniques are used to create networks with fracture swarm geometry that resembles that of exploratory cores recently reported in the literature. The networks have desired total pore volume, maximum and minimum fracture spacing and fractional dimension. These properties together with fracture conductivity control their hydraulic behavior. Numerical simulation of individual fragments and the addition of production to obtain total production is shown to be consistent with simulations of the entire network when fracture conductivity is high. In this case, the network exhibits sub-linear flow (pressure derivative slope between 0.5 and 1). When fracture conductivity is low, it exhibits sub-radial flow (pressure derivative slope between 0 and 0.5) at early times with transition to sub-linear or boundary dominated flow (BDF) at later times. Longer duration of sub-radial flow is achieved by reducing fracture conductivity. These types of flow behavior cover the entire range seen in unconventional wells. They show how the power-law behavior, frequently observed in diagnostic plots, can be produced by the combined effect of matrix fragments that individually can only show linear, bi-linear or BDF flow. The relatively simple geometry of fracture swarms allows calculation of properties for sub-radial flow that complement those already known for sub-linear flow. New insights into production mechanisms of unconventional wells are discussed.
The very low matrix permeability of unconventional wells causes the pressure transient response to last a long time, typically years. This makes pressure transient analysis (PTA), that relies on analysis of shut-in periods, limited in its ability to characterize flow behavior. Rate transient analysis (RTA), on the other hand, is especially suited to deal with long flowing periods. But there have been two different problems with the application of RTA to unconventional wells. The first is that the theoretical framework for RTA is not as developed as that of PTA. The second problem is that RTA responses of unconventional wells do not exhibit the familiar flow regimes (bi-linear, linear and radial) but rather power-law behavior with log-log derivative slopes different from the expected values for those flow regimes. To tackle the first problem, we developed a new theoretical framework by rewriting and solving the diffusivity equation in terms of cumulative production (Acuna, 2017). This new solution for constant pressure complies with theoretical expectations with respect to the constant flow rate solution as shown in Appendix B. It also handles all flow regimes seen in unconventional wells including the familiar ones mentioned before. To address the second problem, we proposed the simple idea that the flow behavior of an unconventional well is the result of many matrix fragments of different size acting together (Acuna, 2018a b), a concept further developed in this paper.
This paper presents results from a comprehensive investigation of the pressure transient behavior of horizontal wells with single or multiple vertical fractures. The approach used can handle fractures with radial and linear inflow to the well, with radial inflow in transverse fractures and linear inflow in longitudinal fractures. Fractures following the wellbore with communication to the well only at the center, i.e., with radial inflow, can also be handled, with these and the tranverse fractures having a circular outer boundary (truncated to the formation if necessary). The longitudinal (rectangular) fractures are assumed to have the full length perforated. Intervals between fractures are assumed not perforated.
Most of the paper is devoted to discussions of flow periods exhibited by single- and multifractured horizontal wells under various ideal conditions. Identifying these are important since the special flow periods provide data that can be analyzed by conventional methods.
At least four fundamental flow periods can be exhibited by horizontal wells with a tranverse or longitudinal fracture. For a tranverse fracture, or a radial fracture following the well, the periods are fracture radial, radial-linear, formation linear and pseudoradial for fractures fully or nearly confined to the formation. For longitudinal fractures the early flow periods are fracture linear and bilinear. For longer transverse fractures one can also have fracture linear and bilinear flow periods preceded by fracture radial flow.
Generally, the fracture radial or fracture linear flow period occurs at a time too early to be of practical use. In any case, due to the transition periods, observing more than two of the fundamental periods in real data is not likely. For highly conductive fractures the early transient behavior is likely to be dominated by formation linear flow, while for poorly conductive fractures this flow period can be absent with the early transient behavior instead dominated by radial-linear or bilinear flow during several log cycles, if not masked by wellbore storage effects. Assuming no boundaries, the pseudoradial flow period will be reached eventually independent of fracture and formation parameters. For all the four fundamental flow periods, conventional straight-line analyses based on semilog, t or 4t plots can be used to determine fracture and formation properties,.
During the early flow phase, horizontal wells with single or multiple fractures will experience the same flow periods. However, unless the individual fractures are far shorter than the distance between neighboring fractures, interference will occur before pseudoradial flow is exhibited around each fracture. Before interference occurs the individual fractures drain independent parts of the reservoir and are appropriately analyzed by assuming a single fracture and dividing the total flow rate by the number of fractures. For a multifractured horizontal well, a compound-formation linear flow period may also occur, with linear flow towards the well (as seen from above) dominating the pressure transient behavior. Eventually, provided no flow barriers are encountered, pseudoradial flow will also develop for a multifractured horizontal well. During both the compound-formation linear flow period and the pseudoradial flow period, the full flow rate must be used in the analysis of transient pressure data.