Finite-conductivity Hydraulic Fractures Research Articles

Performance evaluation of analytical methods in linear flow data for hydraulically-fractured gas wells

Hydraulically fractured wells drilled in unconventional gas reservoirs are often produced with significantly high fixed drawdown to increase production. However, such unconventional gas wells exhibit extended periods of linear flow regime which could last for several years. Linear flow regime results from the fluid flow throughout Infinite-Conductivity Hydraulic Fractures (ICHFs) and Finite-Conductivity Hydraulic Fractures (FCHFs). This makes the analysis of linear flow regime of great importance to estimate parameters like fracture half-length, fracture width, fracture permeability and other parameters. Since the fracture half-length is an essential parameter for history matching and forecasting, it should be properly estimated and predicted. In this study, two analytical methods for analyzing linear flow were used to estimate the fracture half-length in hydraulically fractured gas wells producing from ICHFs and FCHFs under constant pressure conditions (fixed drawdown). The analytical methods compared are square root time and inverse production method. The investigated two analytical methods were compared along with the use of five different correction methods. The correction methods applied on the analytical solutions are those proposed by Ibrahim and Wattenbarger (2006), Nobakht and Clarkson (2012), Behmanesh et al. (2017), Chen and Raghavan (2013) and mean pressure. The comparison was done by conducting sensitivity analysis in term of initial pressure, flowing bottom hole pressure, reservoir temperature, permeability and dimensionless fracture conductivity. The study demonstrated that for ICHFs, both analytical methods provide close estimates of fracture half-length with the best results coming from the use of correction techniques of Nobakht and Clarkson (2012) and Behmanesh et al. (2017). For FCHFs, the inverse production method performed better than the square root time technique with the use of Chen and Raghavan (2013) and Ibrahim and Wattenbarger (2006) corrections. However, the inverse production methodology seems to be more sensitive than square root time to the change level in initial pressure and permeability. Moreover, it is shown that the square root time methodology generally overestimates the value of fracture half-length for FCHFs except some of the cases where the mean pressure is used. The results of this study provide general guidelines on the most accurate methods with their correction ways that can help to better analyze linear flow data in fractured gas wells. Also, this research can serve as selection criteria to choose the best analytical production methods to evaluate the performance of hydraulic fractures according to the well and reservoir properties. • This study showed that the square root time methodology can be used for both ICHF and FCHF. • Behmanesh et al. (2017) correction method was recommended due to its straight forward application. • If the inverse solution method is used, Behmanesh et al. (2017) correction is recommended for the ICHF cases. • Chen and Raghavan (2013) correction should be applied for the FCHF cases if the inverse solution method is used. • The square root time method tends to overestimate the value of fracture half-length in some conditions.

Matrix permeability and flow-derived DFN constrain reactivated natural fracture rupture area and stress drop — Marcellus Shale microseismic example

Microseismic events associated with shale reservoir hydraulic fracturing stimulation (HFS) are interpreted to be reactivations of ubiquitous natural fractures (NFs). Despite adoption of discrete fracture network (DFN) models, accounting for NFs in fluid flow within shale reservoirs has remained a challenge. For an explicit account of NFs, this study introduced the use of seismology-based relations linking seismic moment, moment magnitude, fault rupture area, and stress drop. Microseismic data from HFS monitoring of Marcellus Shale horizontal wells had been used to derive planar hydraulic fracture geometry and source properties. The former was integrated with associated well production data found to exhibit transient linear flow. Analytical solutions led to linear flow parameters (LFPs) and system permeability for scenarios depicting flow through infinite and finite conductivity hydraulic fractures. Published core plug permeability was stress-corrected for in-situ conditions to estimate average matrix permeability. For comparison, the burial and thermal history for the study area was used in 1D Darcy-based modeling of steady and episodic expulsion of petroleum to account for geologic timescale persistence of abnormal pore pressure. Both evaluations resulted in matrix permeability in the same picodarcy (pD) range. Coupled with LFPs, reactivated NF surface area for stochastic DFNs was estimated. Subsequently, the aforementioned seismology-based relations were used for determining average stress drops needed to estimate NF rupture area matching flow-based DFN surface areas. Stress drops, comparable to values for tectonic events, were excluded. One of the determined values matched stress drops for HFS operations in past and recent seismological studies. In addition, calculated changes in pore pressure matched estimates in the aforementioned studies. This study unlocked the full potential of microseismic data beyond extraction of planar geometry attributes and stimulated reservoir volume (SRV). Here, microseismic events were explicitly used in the quantitative account of NFs in fluid flow within shale reservoirs.

Transient pressure behavior for unconventional gas wells with finite-conductivity fractures

Horizontal wells and hydraulic fracturing technologies are the only way that makes commercial production from the low and ultra-low permeability unconventional plays possible. The development of analytical and semi-analytical tools to analyze transient behavior of multi-fractured horizontal gas wells have been largely biased towards solving the simplified problem of one-dimensional (1D) Cartesian gas flow in matrix domain, which are only applicable to the production from infinite-conductivity fractures. This study presents a novel semi-analytical method for transient behavior analysis of horizontal gas wells producing from finite-conductivity fractures. Unlike the available transient analysis tools for finite-conductivity fractures which are developed based on empirical and approximate solution, the proposed solution is rigorously derived by solving the governing gas diffusivity equations written for gas flow in two contiguous regions of matrix and fracture simultaneously. Nonlinear, pressure-dependent gas properties remaining in pseudopressure-based diffusivity equations—namely viscosity and compressibility—are rigorously and straightforwardly captured in both fracture and matrix systems. The validity of proposed solution is verified against commercial numerical simulator (COMSOL Multiphysics®) for a series of synthetic cases considering constant and variable -rate production constraints. The case studies presented in this paper also showcase the applicability of proposed solution to the analysis of transient behavior of multi-fractured horizontal gas wells in shale plays under the following two state-of-the-art interpretations: 1) production from finite-conductivity hydraulic fractures in a single-porosity matrix; and 2) production from infinite-conductivity hydraulic fractures in a naturally-fractured matrix.

Transient pressure analysis of a volume fracturing well in fractured tight oil reservoirs

This paper presents a semi-analytical model to simulate transient pressure curves for a vertical well with a reconstructed fracture network in fractured tight oil reservoirs. In the proposed model, the reservoir is a composite system and contains two regions. The inner region is described as a formation with a finite conductivity hydraulic fracture network and the flow in the fracture is assumed to be linear, while the outer region is modeled using the classical Warren–Root model where radial flow is applied. The transient pressure curves of a vertical well in the proposed reservoir model are calculated semi-analytically using the Laplace transform and Stehfest numerical inversion. As shown in the type curves, the flow is divided into several regimes: (a) linear flow in artificial main fractures; (b) coupled boundary flow; (c) early linear flow in a fractured formation; (d) mid radial flow in the semi-fractures of the formation; (e) mid radial flow or pseudo steady flow; (f) mid cross-flow; (g) closed boundary flow. Based on our newly proposed model, the effects of some sensitive parameters, such as elastic storativity ratio, cross-flow coefficient, fracture conductivity and skin factor, on the type curves were also analyzed extensively. The simulated type curves show that for a vertical fractured well in a tight reservoir, the elastic storativity ratios and crossflow coefficients affect the time and the degree of crossflow respectively. The pressure loss increases with an increase in the fracture conductivity. To a certain extent, the effect of the fracture conductivity is more obvious than that of the half length of the fracture on improving the production effect. With an increase in the wellbore storage coefficient, the fluid compressibility is so large that it might cover the early stage fracturing characteristics. Linear or bilinear flow may not be recognized, and the pressure and pressure derivative gradually shift to the right. With an increase in the skin effect, the pressure loss increases gradually.

Productivity Analysis of Volume Fractured Vertical Well Model in Tight Oil Reservoirs

This paper presents a semianalytical model to simulate the productivity of a volume fractured vertical well in tight oil reservoirs. In the proposed model, the reservoir is a composite system which contains two regions. The inner region is described as formation with finite conductivity hydraulic fracture network and the flow in fracture is assumed to be linear, while the outer region is simulated by the classical Warren-Root model where radial flow is applied. The transient rate is calculated, and flow patterns and characteristic flowing periods caused by volume fractured vertical well are analyzed. Combining the calculated results with actual production data at the decline stage shows a good fitting performance. Finally, the effects of some sensitive parameters on the type curves are also analyzed extensively. The results demonstrate that the effect of fracture length is more obvious than that of fracture conductivity on improving production in tight oil reservoirs. When the length and conductivity of main fracture are constant, the contribution of stimulated reservoir volume (SRV) to the cumulative oil production is not obvious. When the SRV is constant, the length of fracture should also be increased so as to improve the fracture penetration and well production.

Production performance analysis of multiple fractured horizontal wells with finite-conductivity fractures in shale gas reservoirs

Shale gas flow is controlled by multiple mechanisms and multi-stage hydraulic fracturing often creates complex fracture geometry. It is very challenging to incorporate various transport mechanisms of shale gas and evaluate production performance of the multiple fractured horizontal well (MFHW) in shale gas reservoirs. This paper presented a new semi-analytical model to study the pressure behavior and production performance of MFHWs with finite conductivity fractures in shale gas reservoirs. Multiple mechanisms were considered, which contained diffusion in kerogen bulk, desorption from the surface of organic matters and clay minerals, slippage flow in matrix pores, transient-state inter-porosity flow and Darcy flow in natural fractures. Finite-conductivity hydraulic fractures, stress sensitivity effect and inclination angles were also taken into account. Line source function, Laplace transformation, perturbation technique, numerical discrete method, Gauss elimination method and Stehfest inversion algorithm were employed to calculate the pressure responses. A field case from Barnett Shale was used to illustrate the validity of this model. Type curves were plotted and flow regimes were identified. A synthetic case was used to study the effects of hydraulic fracture conductivity, inclination angle, permeability modulus, kerogen content, clay minerals content, solubility coefficient, diffusion coefficient, Langmuir pressure and Langmuir volume on well production performance. By performing sensitivity analysis of key factors, we come to some conclusions that hydraulic fracture conductivity has an optimal value for shale gas development; a small inclination angle and a large permeability modulus have a negative effect on well performance while a large Langmuir pressure and Langmuir volume have a positive effect; both clay minerals and organic matters contribute to shale gas production; dissolved gas stored in kerogen bulk should be considered and a larger diffusion coefficient is beneficial for dissolved gas to release. With its rapid computational speed, this semi-analytical approach will serve as an efficient tool to evaluate well productivity and provide critical insights into development optimization of shale gas reservoirs.

Pressure transient analysis of multistage fracturing horizontal wells with finite fracture conductivity in shale gas reservoirs

A new analytical solution of pressure transient analysis is proposed for multistage fracturing horizontal well (MFHW) with finite-conductivity transverse hydraulic fractures in shale gas reservoirs. The effects of absorption, diffusion, viscous flowing, stress sensitivity, flow convergence, skin damage and wellbore storage are simultaneously considered as well in this paper. Laplace transformation, source sink function, perturbation method and superposition principle are, respectively, employed to solve related mathematical models of reservoir system and hydraulic fracture system. And then boundary element method (BEM) is applied to couple reservoir system and hydraulic fracture system. The transient pressure is inverted from Laplace space into real time space with Stehfest numerical inversion algorithm. Based on this new solution, the distribution of transient pseudo-pressure for MFHW with multiple finite-conductivity transverse hydraulic fractures is obtained. Different flowing regimes are identified, and the effects of relevant parameters are analyzed as well. The essence of this paper is considering the effects of transient gas flowing occurrence in finite-conductivity hydraulic fractures with BEM. Compared with some existing models and numerical simulation model of shale gas reservoirs, this proposed new model can provide a relative more accurate analysis of the relevant parameters, especially for the fracture conductivity. In conclusion, this new model provides the relative accurate and comprehensive evaluation results for multistage fracturing horizontal technology.

Transient linear flow analysis of constant-pressure wells with finite conductivity hydraulic fractures in tight/shale reservoirs

Abstract Transient linear flow is the dominant flow regime in many multi-fractured horizontal wells completed in very low permeability reservoirs. Therefore, development of reliable methods for analyzing production data from this flow regime is of great value. The common methodology for production analysis of this flow period is use of square-root-time plot in which normalized pressure (or pseudopressure for gas) is plotted vs. square-root-time. This method has been proved to be acceptable for systems with infinite conductivity hydraulic fractures. The square-root-time plots for such systems exhibit a zero intercept. When analyzing production histories of real examples, we observe cases for which the square-root-time plot exhibits a straight-line trend with a positive intercept. We demonstrate that this behavior can be attributed to systems with finite conductivity hydraulic fractures. For constant-pressure systems with finite conductivity hydraulic fractures, the square-root-time plot methodology overestimates fracture half-length. This has been shown using synthetic examples. To solve this problem, we have developed a new inverse solution methodology which is based on an analytical formulation. We have defined new plotting functions and illustrated that a plot of these functions against each other in the formation linear flow period exhibits a linear trend. From the slope of this plot, the true value of fracture half-length can be estimated. Also, fracture conductivity can be determined from the intercept. The proposed methodology has been verified using synthetic tight oil examples. We have also applied it for several tight gas examples. We have analyzed production data for two field examples using the conventional square-root-time plot methodology and the new inverse solution methodology. Our analysis reveals that the square-root-time plot methodology considerably overestimates the fracture half-length for these examples.

Sensitivity analysis of geometry for multi-stage fractured horizontal wells with consideration of finite-conductivity fractures in shale gas reservoirs

A new analytical solution of pressure and rate transient analysis is proposed for MFHW with finite-conductivity transverse hydraulic fractures in shale gas reservoirs. Meanwhile, desorption, adsorption, viscous flow, stress sensitivity of natural fractures, skin damage and wellbore storage are simultaneously considered as well in this paper. Laplace transformation, line source function, perturbation method, and superposition principle are employed to solve this new model. The pressure and rate transient responses are inverted into real time space with stehfest numerical inversion algorithm. Based on this new solution, the transient pressure distribution of MFHW with multiple finite-conductivity transverse hydraulic fractures was obtained, type curves are plotted, and different flow regimes in shale gas reservoirs are identified, the effects of relevant parameters are analyzed as well. The innovation and essence of this paper is combining transient gas flow in finite-conductivity hydraulic fractures, the geometry of hydraulic fractures and dual-porosity character of shale gas reservoirs. Compared with some existing models for shale gas reservoirs, this new model is more comprehensive and can provide a relative practical analysis of the relevant parameters. Besides, the conclusions involving in the geometry of hydraulic fractures can greatly match with the previous conclusions from numerical simulation and are more persuasive than that. To sum up, this new model provides some relative real evaluation results for multi-stage fracturing horizontal well technology in shale gas reservoirs.

Transient Pressure Analysis of Wells Intercepted by Partially Penetrating Finite Conductivity Hydraulic Fractures

Most current pressure transient analysis techniques of hydraulically fractured wells are based on the fully penetrating assumption, which assumes equal thickness of hydraulic fracture and the formation. However, field application show that the fractures thickness can be shorter than the thickness of formation, which leads to vertical flow into the fracture. Thus applying the thickness equality assumption of current well test models to a partial penetrating fracture may give contradictory result. Further, there are very few studies concerning pressure transient analysis of partial penetrated wells. So it is important to develop analysis model and procedure to this type of fracture. In this paper, we presented an analytical model for partially penetrating hydraulic fracture in isotropic systems, along with the assumption that fracture is finite conductive. This model is then applied in the analysis of field production data, which verified validity of this new model.

Modeling of Interference Test in Two Wells with Finite-Conductivity Hydraulic Fractures

In the paper we study pressure behavior in a system with two wells with finite-conductivity hydraulic fractures in a low permeability formation. We present numerical solution of the problem, sensitivity analysis for the system parameters, our model using by modeling interference test. The numerical model is used to interpret field measured data and to determine the system parameters.

Analysis of pressure derivative data of hydraulically fractured wells by the Tiab's Direct Synthesis technique

This paper extends Tiab's Direct Synthesis ( TDS) technique for interpreting the behavior of the pressure and pressure derivative data of a well intersected by a finite conductivity hydraulic fracture. In this technique log–log plots of pressure and pressure derivative data of a pressure drawdown or pressure buildup test are analyzed without using the type-curve matching or regression procedures. A log–log plot of pressure and pressure derivative versus test time for a fractured well in a closed system may reveal the presence of several straight lines corresponding to different flow regimes; bilinear flow, linear flow, infinite-acting radial flow, and pseudosteady state flow. The slopes and points of intersection of these straight lines are unique and therefore can be used to calculate several well, reservoir and fracture parameters: permeability, skin factor, wellbore storage coefficient, fracture conductivity, half-fracture length, and drainage area. Equations corresponding to the points of intersection are very useful in checking on the parameters obtained from the slopes, when the pressure derivative curve is not smooth. A new equation is derived for calculating (a) the half-fracture length in the absence of the linear flow regime straight line of slope 0.5 such as in the case of low conductivity fracture, (b) the fracture conductivity in the absence of the bi-linear flow line of slope 0.25, and (c) the skin factor in the absence of the infinite acting radial flow line such as in the case of a short test.

Analysis and evaluation of gas well tests for wells intersected by finite conductivity hydraulic fractures

A single-phase two-dimensional mathematical model was used for analyzing the behavior of a gas well intersecting a finite conductivity vertical fracture at the center of a closed square gas reservoir. Turbulent flow in both the fracture and the formation was included in the model. The analysis of the simulated well tests at constant mass rate at the sand face showed that the early portions of log m( p) vs. log t f plots do not display the characteristic one-half slope line when the dimensionless fracture conductivity ( F CD ) is less than 416. Instead, the plots display much smaller slopes, regardless of fracture length, flow rate, formation permeability, and initial reservoir pressure. The time required to reach the radial behavior constant slope line on m( p wf) vs. log t f plot was found to increase with: (1) increasing fracture conductivity ( F CD); (2) increasing fracture length; (3) decreasing formation permeability; and (4) increasing flow rate. Turbulent flow is found to be most significant inside the fracture. The square-root time method [ m(p) vs. t μc g ] during the linear flow period yields a good estimate of the quantity kx 2 when fracture conductivity ( F CD)⩾416. In addition, this method could be used to estimate kx 2 when F CD>5 if the linear flow period inside the fracture can be defined. Finally, this paper shows that high-conductivity fractures are more important as a design criterion than the length of the fracture.