scholarly journals A Novel Radial-Composite Model of Pressure Transient Analysis for Multistage Fracturing Horizontal Wells with Stimulated Reservoir Volume

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yunpeng Hu ◽  
Xiaoling Zhang ◽  
Ziyun Cheng ◽  
Wei Ding ◽  
Liangchao Qu ◽  
...  
Keyword(s):  
Horizontal Well ◽  
Storage Capacity ◽  
Radial Flow ◽  
Horizontal Wells ◽  
Outer Zone ◽  
Middle Zone ◽  
Linear Flow ◽  
Type Curves ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume

In the process of stimulated reservoir volume of tight reservoir, horizontal well can form three zones, the inner zone is multistage fracturing zone, the middle zone is skin damage zone, and the outer zone is undamaged zone. In this paper, a transient well test analysis model of multistage fracturing horizontal well in three area composite reservoir is proposed. Based on Laplace transformation, point source integration, and superposition principle, the infinite conductivity multifracture model of three area composite reservoir is obtained. The linear equations of finite conductivity multifracture in Laplace space are established by using the equal conditions of flow and pressure at the fracture wall. Gauss-Newton iteration method and Stehfest number are used to obtain the solution of wellbore pressure. The accuracy of the results is verified by numerical simulation. Then, the flow characteristics of multistage fracturing horizontal wells in three area composite reservoirs are analyzed by type curves. The flow is divided into ten stages, which are the bilinear flow, the linear flow, the first radial flow stage, the inner zone linear flow, the inner zone radial flow, the middle zone linear flow, the middle zone radial flow, the outer zone linear flow, the outer zone radial flow, and the boundary dominated flow. The pressure derivative curves show different characteristics in different flow stages. The influences of fracture conductivity, fracture spacing, radius ratio of the middle zone to inner zone, radius ratio of the outer zone to the middle zone, permeability ratio of inner zone to the middle zone, permeability ratio of inner zone to outer zone, storage capacity ratio of inner zone to the middle zone, and storage capacity ratio of inner zone to outer zone on type curves are analyzed. Finally, the application and reliability of the proposed model are verified by a case example.

scholarly journals Productivity Model for Shale Gas Reservoir with Comprehensive Consideration of Multi-mechanisms

2015 ◽  
Vol 8 (1) ◽  
pp. 235-247 ◽  
Author(s):  
Ya Deng ◽  
Rui Guo ◽  
Zhongyuan Tian ◽  
Cong Xiao ◽  
Haiying Han ◽  
...  
Keyword(s):  
Shale Gas ◽  
Horizontal Well ◽  
Flow Behavior ◽  
Stress Sensitivity ◽  
Transitional Flow ◽  
Gas Reservoirs ◽  
Type Curves ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume ◽  
Shale Gas Reservoirs

Multi-stage fracturing horizontal well currently has been proved to be the most effective method to produce shale gas. This method can activate the natural fractures system defined as stimulated reservoir volume (SRV), the remaining region similarly is defined as un-stimulated reservoir volume (USRV). At present, no type curves have been developed for hydraulic fractured shale gas reservoirs in which the SRV zone has triple-porosity dual-depletion flow behavior and the USRV zone has double porosity flow behavior. In this paper, the SRV zone and USRV zone respectively are simplified as cubic triple-porosity and slab dual porosity media. We have established a new productivity model for multifractured horizontal well shale gas with Comprehensive consideration of desorption, diffusion, viscous flow, stress sensitivity and dual-depletion mechanism in matrix. The rate transient responses are inverted into real time space with stehfest numerical inversion algorithm. Type curves are plotted, and different flow regimes in shale gas reservoirs are identified. Effects of relevant parameters are analyzed as well. The whole flow period can be divided into 8 regimes: bilinear flow in SRV; pseudo elliptic flow; dual inter-porosity flow; transitional flow; linear flow in USRV; inter-porosity flow and boundary-dominated flow. The stress sensitivity basically has negative influence on the whole productivity period .The less the value of Langmuir volume and the lager the value of Langmuir pressure, the more lately the inter-porosity flow and boundary-dominated flow occurs. It in concluded that the USRV zone has positive influence on production and could not be ignored.

scholarly journals A Semianalytical Solution for Multifractured Horizontal Wells in Box-Shaped Reservoirs

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Lei Wang ◽  
Xiaodong Wang ◽  
He Zhang ◽  
Yunpeng Hu ◽  
Chen Li
Keyword(s):  
Radial Flow ◽  
Flow Characteristics ◽  
Horizontal Wells ◽  
Flow Region ◽  
Linear Flow ◽  
Type Curves ◽  
Production Ratio ◽  
Dirac Function ◽  
Sensitive Parameters ◽  
First Time

This paper presented a 3D point sink model through using Dirac function. Then, 3D point sink solution in boxed reservoirs was obtained through using Laplace transform and Fourier transform methods. Based on the flux and pressure equivalent conditions in Laplace space, a semianalytical solution for multifractured horizontal wells was also proposed for the first time. The production rate distribution was discussed in detail for multifractured horizontal wells. The calculative results show the outermost fractures had higher production ratio due to larger drainage area and the inner fractures were lower due to the strong interface between fractures. Type curves were established to analyze the flow characteristics, which would be divided into six stages, for example, bilinear flow region, the first linear flow region, the first radial flow region, the second linear flow region, the second radial flow region, and the boundary dominated flow region, respectively. Finally, effects of some sensitive parameters on type curves were also analyzed in detail.

scholarly journals Two-dimensional numerical investigations on the termination of bilinear flow in fractures

2013 ◽  
Vol 5 (1) ◽  
pp. 391-425
Author(s):  
◽  
R. Jung ◽  
J. Renner
Keyword(s):  
Flow Field ◽  
Master Curve ◽  
Radial Flow ◽  
Dimensionless Time ◽  
Linear Flow ◽  
Type Curves ◽  
Straight Line ◽  
The Matrix ◽  
Line Characteristic ◽  
Fourth Root

Abstract. Bilinear flow occurs when fluid is drained from a permeable matrix by producing it through an enclosed fracture of finite conductivity intersecting a well along its axis. The terminology reflects the combination of two approximately linear flow regimes, one in the matrix with flow essentially perpendicular to the fracture and one along the fracture itself associated with the non-negligible pressure drop in it. We investigated the characteristics, in particular the termination, of bilinear flow by numerical modeling allowing an examination of the entire flow field without prescribing the flow geometry in the matrix. Fracture storage capacity was neglected relying on previous findings that bilinear flow is associated with a quasi-steady flow in the fracture. Numerical results were generalized by dimensionless presentation. Definition of a dimensionless time that other than in previous approaches does not use geometrical parameters of the fracture permitted identifying the dimensionless well pressure for the infinitely long fracture as the master curve for type curves of all fractures with finite length from the beginning of bilinear flow up to fully developed radial flow. In log-log-scale the master curve's logarithmic derivative initially follows a 1/4-slope-straight line (characteristic for bilinear flow) and gradually bends into a horizontal line (characteristic for radial flow) for long times. During the bilinear flow period, isobars normalized to well pressure propagate with fourth and second root of time in fracture and matrix, respectively. The width-to-length ratio of the pressure field increases proportional to the fourth root of time during the bilinear period and starts to deviate from this relation close to the deviation of well pressure and its derivative from their fourth-root-of-time relations. At this time, isobars are already significantly inclined with respect to the fracture. The type curves of finite fractures all deviate counterclockwise from the master curve instead of clockwise or counterclockwise from the 1/4-slope-straight line as previously proposed. The counterclockwise deviation from the master curve was identified as the arrival of a normalized isobar reflected at the fracture tip sixteen times earlier. Nevertheless, two distinct regimes were found regarding pressure at the fracture tip when bilinear flow ends. For dimensionless fracture conductivities TD < 1, a significant pressure increase is not observed at the fracture tip until bilinear flow is succeeded by radial flow at a fixed dimensionless time. For TD > 10, the pressure at the fracture tip has reached substantial fractions of the associated change in well pressure when the flow field transforms towards intermittent formation linear flow at times that scale inversely with the fourth power of dimensionless fracture conductivity. Our results suggest that semi-log plots of normalized well pressure provide a means for the determination of hydraulic parameters of fracture and matrix after shorter test duration than for conventional analysis.

A Semianalytical Model for Horizontal-Well Productivity With Pressure Drop Along the Wellbore

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1603-1614 ◽  
Author(s):  
Wanjing Luo ◽  
Changfu Tang ◽  
Yin Feng
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Horizontal Well ◽  
Horizontal Wells ◽  
Productivity Index ◽  
Type Curves ◽  
Penetration Ratio ◽  
New Type ◽  
The One

Summary This study aims to develop a semianalytical model to calculate the productivity index (PI) of a horizontal well with pressure drop along the wellbore. It has been indicated that by introducing novel definitions of horizontal-well permeability and conductivity, the equation of fluid flow along a horizontal well with pressure drop has the same form as the one for fluid flow in a varying-conductivity fracture. Thus, the varying-conductivity-fracture model and PI model can be used to obtain the PI of a horizontal well. Results indicate that the PI of a horizontal well depends on the interaction between horizontal-well conductivity, penetration ratio, and Reynolds number. New type curves of the penetration ratios with various combinations of parameters have been presented. A complete-penetration zone and a partial-penetration zone can be identified on the type curves. Based on the type curves, two examples have also been presented to illustrate the advantages of this work in optimizing parameters of horizontal wells.

Optimizing the Number of Fractures in a Horizontal Well

SPE Journal ◽  
2019 ◽  
Vol 24 (03) ◽  
pp. 1364-1377 ◽  
Author(s):  
Vyacheslav Guk ◽  
Mikhail Tuzovskiy ◽  
Don Wolcott ◽  
Joe Mach
Keyword(s):  
Horizontal Well ◽  
Horizontal Wells ◽  
Optimal Number ◽  
Hydraulic Fractures ◽  
Single Fracture ◽  
Multiple Fracture ◽  
Multiple Fractures ◽  
Type Curves ◽  
Fracture Width ◽  
Technical Potential

Summary Horizontal wells with multiple hydraulic fractures have become a standard completion for the development of tight oil and gas reservoirs. Successful optimization of multiple-fracture design on horizontal wells began empirically in the Barnett Shale in the late 1990s (Steward 2013; Gertner 2013). More recently, research has focused on further improving fracturing performance by developing a model-derived optimum. Some researchers have focused on an economic optimum on the basis of multiple runs of an analytical or numerical model (Zhang et al. 2012; Saputelli et al. 2014). With such an approach, a new set of model runs is necessary to optimize the design each time the input parameters change significantly. Running multiple simulations for every optimization case might not always be practical. An alternative approach is to develop well-performance curves with dimensionless variables on the basis of the performance model. Such an approach was the basis for unified fracture design (UFD) for a single fracture in a vertical well (Economides et al. 2002). However, a similar systemized method to calculate the optimum for a horizontal well with multiple hydraulic fractures was missing. The objective of this study was to develop a rigorous and unified dimensionless optimization technique with type curves for the case of multiple transverse fractures in a horizontal well—an extension of UFD. The mathematical problem was solved in dimensionless variables. Multiple fractures include the proppant number (NP), penetration ratio (Ix), dimensionless conductivity (CfD), and aspect ratio (yeD) for each fracture, which is inversely proportional to the number of fractures. The direct boundary element (DBE) method was used to generate the dimensionless productivity index (JD) for a given range of these parameters (28,000 runs) for the pseudosteady-state case. Finally, total well JD was plotted as a function of the number of fractures for various NP. The effect of minimum fracture width was studied, and the optimization curves were adjusted for three cases of minimum fracture width. The provided dimensionless type curves can be used to identify the optimized number of fractures and their geometry for a given set of parameters, without running a more complicated numerical model multiple times. First, the proppant mass (and hence, NP) used for the fracture design can be selected on the basis of economic or other considerations. For this purpose, a relationship between total JD and NP, which accounts for the minimum fracture width requirement, was provided. Then, the optimal number of fractures can be calculated for a given NP using the generated type curves with minimum width constraints. The following observations were made during the study on the basis of the performed runs: For a given volume or proppant, NP, total JD for multiple fractures increases to an asymptote as the number of fractures increases. This asymptote represents a technical potential for multiple fractures and for high proppant numbers (NP≥100), with a technical potential of 3πNP. Below this asymptote, the more fractures that are created for a fixed NP, the larger the JD. In practice, minimum fracture width constrains the fracture geometry, and therefore maximum JD. For the case when 20/40 sand is used for multiple hydraulic fracturing of a 0.01-md formation with square total area, the optimal number of factures is approximately NP25. Application of horizontal drilling technology with multiple fractures assumes the availability of high proppant numbers. It was shown mathematically that the alternative low proppant numbers (NP≤20 for the previous case) are impractical for multiple fractures, because total JD cannot be significantly higher than JD for an optimized single fracture in the same area. This means that low formation permeability and/or high proppant volumes are needed for multiple fracture treatments.

Performance Evaluation of a Horizontal Well With Multiple Fractures by Use of a Slab-Source Function

SPE Journal ◽  
2015 ◽  
Vol 20 (03) ◽  
pp. 652-662 ◽  
Author(s):  
Daoyong Yang ◽  
Feng Zhang ◽  
John A. Styles ◽  
Junmin Gao
Keyword(s):  
Horizontal Well ◽  
Source Function ◽  
Early Stage ◽  
Pressure Response ◽  
Multiple Fractures ◽  
Fracture Conductivity ◽  
Linear Flow ◽  
Type Curves ◽  
Semianalytical Method ◽  
Reservoir Simulator

Summary A novel slab-source function was formulated and successfully applied to accurately evaluate performance of a horizontal well with multiple fractures in a tight formation. More specifically, such a slab-source function in the Laplace domain has assigned a geometrical dimension to the source, whereas pressure response of a rectangular reservoir with closed outer boundaries can be determined. A semianalytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments, each of which is treated as a slab source, assuming that there exists unsteady flow between the adjacent segments. The newly developed function was validated with numerical solution obtained from a reservoir simulator and then its application was extended to a field case. The pressure response together with its corresponding derivative type curves was reproduced to examine effects of number of stages, fracture conductivity, and fracture dimension under various penetration conditions. The fracture conductivity is found to mainly influence early-stage bilinear-/linear-flow regime, whereas a smaller conductivity will force more fluid to enter the toe of the fracture than its heel. The penetrating ratio will impose a significant impact on the pressure response at the early stage, forcing the bilinear/linear flow to become radial flow.

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