Complex analytical solutions for flow in hydraulically fractured hydrocarbon reservoirs with and without natural fractures

Harmelen, Arnaud van; Weijermars, Ruud

doi:10.1016/j.apm.2017.11.027

Cited by 35 publications

(71 citation statements)

References 31 publications

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“…The method is suitable for modeling the drainage pattern near multiple hydraulic fractures and natural fractures. Figures 1a,b show an example of how natural fractures can completely redistribute the flow in a reservoir, dependent on the fracture characteristics [9]. Our present study highlights two new insights.…”

Section: Introductionmentioning

confidence: 60%

“…Investigations of how hydraulic fractures drain the matrix in shale reservoirs are also possible using our method for streamline simulation and fluid time-of-flight tracing based on complex analysis methods. Applications include the visualization of hydrocarbon migration toward hydraulically fractured wells [9], and fluid drainage near multi-fractured horizontal wells with fracture hits [8,74,81]. The key algorithms and key workflow steps used in our model method are explained below.…”

Section: Methodsmentioning

confidence: 99%

“…Our present approach applies calculus from complex analysis to provide closed-form solutions for single phase flow involving an unlimited number of interacting fractures [9]. …”

Section: Drained Rock Volumementioning

confidence: 99%

“…The point dipole, also known as point doublet, singularity doublet and singularity dipole, is a common occurrence in amongst other electromagnetism [88], aerodynamics [89], and fluid mechanics [90]. Deriving the point dipole After Van Harmelen and Weijermars [9].…”

Section: Single Point Dipolementioning

confidence: 99%

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Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA)

Weijermars¹,

Harmelen²

2018

Energies

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Closed-form solution-methods were applied to visualize the flow near hydraulic fractures at high resolution. The results reveal that most fluid moves into the tips of the fractures. Stranded oil may occur between the fractures in stagnant flow zones (dead zones), which remain outside the drainage reach of the hydraulic main fractures, over the economic life of the typical well (30-40 years). Highly conductive micro-cracks would further improve recovery factors. The visualization of flow near hypothetical micro-cracks normal to the main fractures in a Wolfcamp well shows such micro-cracks support the recovery of hydrocarbons from deeper in the matrix, but still leave matrix portions un-drained with the concurrent fracture spacing of 60 ft (~18 m). Our study also suggests that the traditional way of studying reservoir depletion by mainly looking at pressure plots should, for hydraulically fractured shale reservoirs, be complemented with high resolution plots of the drainage pattern based on time integration of the velocity field.

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Section: Introductionmentioning

confidence: 60%

Section: Methodsmentioning

confidence: 99%

“…Our present approach applies calculus from complex analysis to provide closed-form solutions for single phase flow involving an unlimited number of interacting fractures [9]. …”

Section: Drained Rock Volumementioning

confidence: 99%

Section: Single Point Dipolementioning

confidence: 99%

See 2 more Smart Citations

Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA)

Weijermars¹,

Harmelen²

2018

Energies

Self Cite

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“…The present study uses closed-form analytical solutions based on complex analysis methods (CAM) to model flow in a 2D model of both the natural and hydraulic fractures. In this method, the hydraulic fractures are represented as line sinks and the natural fractures are modeled as an infinite number of line doublets using a new algorithm [22,23]. The interaction of the natural fractures and the hydraulic fractures is modeled in CAM to determine the flow response and pressure changes in the reservoir.…”

Section: Introductionmentioning

confidence: 99%

Impact on Drained Rock Volume (DRV) of Storativity and Enhanced Permeability in Naturally Fractured Reservoirs: Upscaled Field Case from Hydraulic Fracturing Test Site (HFTS), Wolfcamp Formation, Midland Basin, West Texas

Nandlal

Weijermars

2019

Energies

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Hydraulic fracturing for economic production from unconventional reservoirs is subject to many subsurface uncertainties. One such uncertainty is the impact of natural fractures in the vicinity of hydraulic fractures in the reservoir on flow and thus the actual drained rock volume (DRV). We delineate three fundamental processes by which natural fractures can impact flow. Two of these mechanisms are due to the possibility of natural fracture networks to possess (i) enhanced permeability and (ii) enhanced storativity. A systematic approach was used to model the effects of these two mechanisms on flow patterns and drained regions in the reservoir. A third mechanism by which natural fractures may impact reservoir flow is by the reactivation of natural fractures that become extensions of the hydraulic fracture network. The DRV for all three mechanisms can be modeled in flow simulations based on Complex Analysis Methods (CAM), which offer infinite resolution down to a micro-fracture scale, and is thus complementary to numerical simulation methods. In addition to synthetic models, reservoir and natural fracture data from the Hydraulic Fracturing Test Site (Wolfcamp Formation, Midland Basin) were used to determine the real-world impact of natural fractures on drainage patterns in the reservoir. The spatial location and variability in the DRV was more influenced by the natural fracture enhanced permeability than enhanced storativity (related to enhanced porosity). A Carman–Kozeny correlation was used to relate porosity and permeability in the natural fractures. Our study introduces a groundbreaking upscaling procedure for flows with a high number of natural fractures, by combining object-based and flow-based upscaling methods. A key insight is that channeling of flow through natural fractures left undrained areas in the matrix between the fractures. The flow models presented in this study can be implemented to make quick and informed decisions regarding where any undrained volume occurs, which can then be targeted for refracturing. With the method outlined in our study, one can determine the impact and influence of natural fracture sets on the actual drained volume and where the drainage is focused. The DRV analysis of naturally fractured reservoirs will help to better determine the optimum hydraulic fracture design and well spacing to achieve the most efficient recovery rates.

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Fracturing Parameters in Petroleum Reservoirs and Simulation

Majeed

Alshara

Al-Mukhtar

et al. 2019

Advances in Material Sciences and Engineering

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Complex analytical solutions for flow in hydraulically fractured hydrocarbon reservoirs with and without natural fractures

Cited by 35 publications

References 31 publications

Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA)

Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA)

Impact on Drained Rock Volume (DRV) of Storativity and Enhanced Permeability in Naturally Fractured Reservoirs: Upscaled Field Case from Hydraulic Fracturing Test Site (HFTS), Wolfcamp Formation, Midland Basin, West Texas

Fracturing Parameters in Petroleum Reservoirs and Simulation

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