Simple models of the hydrofracture process

Marder, Michael; Chen, C. H.; Patzek, Tadeusz W

doi:10.1103/physreve.92.062408

Cited by 20 publications

(16 citation statements)

References 19 publications

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“…Surface area of same order was reported by Johri and Zoback [63] based on field fracture data and mechanical modeling. Marder et al [56] presented an analytical solution of fracture generation and simulated 2000 wells to show that the typical spacing between the large fracture planes should be 1-4 m to maintain production in mudrock. They argued that physically such a small fracture spacing may be impossible, but this distance can be considered as characteristic distance for the branching, complex fracture network.…”

Section: Constraints On Srv Parametersmentioning

confidence: 99%

“…The hydrofracture permeability is infinite relative to the stimulated matrix. Adapted from [56]. (b) Planar view of half-SRV after hydrofracturing.…”

Section: Introductionmentioning

confidence: 99%

“…(b) Hydrofracture frequencies inferred from the information contained in the paper on the Eagle Ford Connoco Phillips pilot by Raterman et al[64]. The dotted horizontal lines represent the range of effective fracture spacing postulated by the authors of[1,2,56].…”

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confidence: 99%

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The Key Factors That Determine the Economically Viable, Horizontal Hydrofractured Gas Wells in Mudrocks

2020

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We assemble a multiscale physical model of gas production in a mudrock (shale). We then tested our model on 45 horizontal gas wells in the Barnett with 12–15 years on production. When properly used, our model may enable shale companies to gain operational insights into how to complete a particular well in a particular shale. Macrofractures, microfractures, and nanopores form a multiscale system that controls gas flow in mudrocks. Near a horizontal well, hydraulic fracturing creates fractures at many scales and increases permeability of the source rock. We model the physical properties of the fracture network embedded in the Stimulated Reservoir Volume (SRV) with a fractal of dimension D < 2 . This fracture network interacts with the poorly connected nanopores in the organic matrix that are the source of almost all produced gas. In the practically impermeable mudrock, the known volumes of fracturing water and proppant must create an equal volume of fractures at all scales. Therefore, the surface area and the number of macrofractures created after hydrofracturing are constrained by the volume of injected water and proppant. The coupling between the fracture network and the organic matrix controls gas production from a horizontal well. The fracture permeability, k f , and the microscale source term, s, affect this coupling, thus controlling the reservoir pressure decline and mass transfer from the nanopore network to the fractures. Particular values of k f and s are determined by numerically fitting well production data with an optimization algorithm. The relationship between k f and s is somewhat hyperbolic and defines the type of fracture system created after hydrofracturing. The extremes of this relationship create two end-members of the fracture systems. A small value of the ratio k f / s causes faster production decline because of the high microscale source term, s. The effective fracture permeability is lower, but gas flow through the matrix to fractures is efficient, thus nullifying the negative effect of the smaller k f . For the high values of k f / s , production decline is slower. In summary, the fracture network permeability at the macroscale and the microscale source term control production rate of shale wells. The best quality wells have good, but not too good, macroscale connectivity.

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Section: Constraints On Srv Parametersmentioning

confidence: 99%

“…The hydrofracture permeability is infinite relative to the stimulated matrix. Adapted from [56]. (b) Planar view of half-SRV after hydrofracturing.…”

Section: Introductionmentioning

confidence: 99%

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The Key Factors That Determine the Economically Viable, Horizontal Hydrofractured Gas Wells in Mudrocks

2020

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“…This low permeability results from the small cross-sections of pore throats and the scaledependent connectivity that ranges from strong at nanoscale to increasingly sparser at micro and higher scales. Patzek et al (2013) and Marder et al (2015) showed that methane in shales is produced through the highways of loosely connected micropores and multiscale cracks, man-made and natural, into which a background continuum of the tiny nanopores feeds gas. This background continuum with the ordered, densely packed methane molecules can masquerade at times as the BET-like, multi-layer methane adsorption, Yu et al (2016).…”

Section: Introductionmentioning

confidence: 99%

“…3. The fractured gas-bearing mudrock formations (shales) are the essentially multiscale, Nelson (2009), and multiphysics systems, Marder et al (2015), and their behavior is complex. Yet, we try to replace shale complexity with a set of slim cylindrical capillaries that flow methane with slip at the capillary walls.…”

Section: Introductionmentioning

confidence: 99%

Knudsen-Like Scaling May Be Inappropriate for Gas Shales

Patzek

2017

SPE Annual Technical Conference and Exhibition

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SummaryWe assert that a classification of gas flow regimes in shales that is widely accepted in the petroleum industry, may be inconsistent with the physics of high-pressure gas flow in capillaries. This classification follows from the 1946 work by Brown et al. (1946) that deals with the flow of gases in large industrial metal pipes, elbows and orifices under vacuum, with gas pressures of the order of 1 mm Hg or less. In another pioneering paper that year, Tsien (1946) analyzed the hypersonic flight of rockets in the thermosphere (above 50 miles of altitude), and established the widely accepted Knudsen flow regimes for the high-Reynolds, high-Mach flow of rarified gases. We show why both these papers are not quite applicable to flow of compressed gas in the hot, high-pressure shale pores with rough surfaces. In addition, it may be inappropriate to use the capillary tube metaphor to describe shale micropores or microcracks, simply because each is fed with gas by dozens or hundreds of intricately connected nanopores, which themselves may be slits rather than circular cylinders, and are charged with the dense, liquid-like gas.In the small-scale, low-velocity flows of gases, failure of the standard Navier-Stokes description (the standard Darcy law in petroleum engineering) can be quantified by the Knudsen number, ratio of the mean free path, λ, of gas molecules at the reservoir pressure and temperature to the characteristic pore radius, R. We carefully enumerate the multiple restrictive conditions that must hold for the slip-flow boundary condition to emerge. We also describe the dependence of the slip correction factor on the gas pressure and temperature, as well as the median pore size and rock roughness. In the derivation, we revisit the original approaches of Helmholtz and von Piotrowski (1860) and Maxwell, Niven (1890), which were somehow lost in the multiple translations from physics to petroleum engineering.For example, in Barnett mudrocks, naturally occurring pores are predominantly associated with organic matter and pyrite framboids. In organic matter, the median pore length is 100 nm, Loucks et al. (2009), and the pore radii are likely to be between 1 and 10 nm, Clarkson et al. (2013). Other thermally mature mudrocks may be similar, Bustin (2009), or not, Clarkson et al. (2013). With R = 50 nm, the ratio of λ/R is less than 0.1 for pressures exceeding 60 bars. When we compare the actual slip-flow correction with the accepted classification of gas flow regimes, there is an order of magnitude discrepancy. It appears that our new classification is conservative for pores larger than 5 nm in radius. Therefore, unless the fraction of gas molecules that are bounced off diffusively from the rough pore walls is very low, slip flow is unlikely to dominate in shales. SPE 187068-MSThe generally accepted "Knudsen-diffusion" in shales is based on a mistranslation of the flow physics and may give theoretically unsound predictions of the increased permeability of shales to gas flow. This increase of permeability is real...

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Fracture sealing and its impact on the percolation of subsurface fracture networks

Zhu

Khirevich

et al. 2021

Preprint

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Current uderstanding of the impact of fracture sealing on macro-scale fluid flow is insufficient. Here, we generate well-connected orthogonal fracture networks in two-and three-dimensions using a discrete fracture network method. The fracture sealing is simulated by dividing fractures into segments (2D) and blocks (3D). Impacts of fracture sealing on the percolation status of orthogonal fracture networks are systematically studied. Different aperture shapes, segment lengths, and spacing distributions are broadly considered. We find that a small amount of sealing can prevent the formation of spanning clusters, suggesting that global connectivity is rarely realized. Local clusters can trigger hydraulic responses if their sizes are large enough. The connectivity reduction caused by fracture sealing can be reversed by significant stress perturbations, such as hydraulic fracturing. The well-connected and critically oriented fractures become critically stressed and slide because of the increased pore pressure. Partially sealed and mechanically stable fractures can also contribute to fluid flow by enlarging the stimulated reservoir volume (SRV). A new procedure to estimate the SRV size is proposed, and the estimated results are qualitatively consistent with microseismicity maps and field observations.

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Simple models of the hydrofracture process

Cited by 20 publications

References 19 publications

The Key Factors That Determine the Economically Viable, Horizontal Hydrofractured Gas Wells in Mudrocks

The Key Factors That Determine the Economically Viable, Horizontal Hydrofractured Gas Wells in Mudrocks

Knudsen-Like Scaling May Be Inappropriate for Gas Shales

Fracture sealing and its impact on the percolation of subsurface fracture networks

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