The Transition From Continuum to Molecular Flow

Sherman, Frederick S.

doi:10.1146/annurev.fl.01.010169.001533

Cited by 25 publications

(12 citation statements)

References 35 publications

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“…The explicit expressions for the relevant collision integrals are presented in Sect. 4. As representative examples, we evaluate these collision integrals for the drag coefficient of a disc in Sect.…”

Section: Knmentioning

confidence: 99%

“…The limit 0 Kn → corresponds to the continuum regime in which one needs to solve the full nonlinear Boltzmann equation subject to the appropriate boundary conditions. A proper theory for the drag force at arbitrary Knudsen numbers is an interesting and important challenge [3][4][5][6][7][8][9]. In the absence of reliable theoretical predictions, one often resorts to empirical correlations [10].…”

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of drag on objects in nearly free molecular flow

Sengers

Wang

Kamgar‐Parsi

et al. 2014

Physica A: Statistical Mechanics and its Applications

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Using an analogy between the density expansion of the transport coefficients of moderately dense gases and the inverse-Knudsen-number expansion of the drag on objects in nearly free molecular flows, we formulate the collision integrals that determine the first correction term to the free-molecular drag limit. We then show how the procedure can be applied to calculate the drag coefficients of an oriented disc and a sphere as a function of the speed ratio.

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Section: Knmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinetic theory of drag on objects in nearly free molecular flow

Sengers

Wang

Kamgar‐Parsi

et al. 2014

Physica A: Statistical Mechanics and its Applications

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show abstract

“…However, in shale reservoirs, which have pore throat radii in the range of 1 to 200 nanometers, fluid continuum theory breaks down and gas molecules follow a somewhat random path while still maintaining a general flow direction governed by pressure gradient. Molecules strike against the pore walls and tend to slip at pore walls instead of having zero velocity (Sherman, 1969). Although these phenomena can be modeled accurately using molecular physics, this is not practical for modeling flow of natural gas through shale reservoirs, which requires intensive computation that falls beyond current computational capabilities.…”

Section: Introductionmentioning

confidence: 99%

Impact of Shale-Gas Apparent Permeability on Production: Combined Effects of Non-Darcy Flow/Gas Slippage, Desorption, and Geomechanics

Wang

Marongiu-Porcu

2015

SPE Reservoir Evaluation &Amp; Engineering

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SummaryMany shale gas and ultralow permeability tight gas reservoirs can have matrix permeability values in the range of tens to hundreds of nanodarcies. The ultrafine pore structure of these rocks can cause violation of the basic assumptions behind Darcy's law. Depending on a combination of pressure-temperature (P-T) conditions, pore structure and gas properties, NonDarcy flow mechanisms such as Knudsen diffusion and/or Gas-Slippage effects will impact the matrix apparent permeability. Even though numerous theoretical and empirical models have been proposed to describe the increasing apparent permeability due to Non-Darcy flow/Gas-Slippage behavior in nano-pore space, few literature have investigated the impact of formation compaction and the release of adsorption layer on shale matrix apparent permeability, which can be coupled together with the Non-Darcy flow/Gas-Slippage mechanism, during reservoir depletion.In this article, we first presented a thoroughly review on gas flow in shale nano-pore space and discussed what factors can impact shale matrix apparent permeability, besides the well-studied Non-Darcy flow/Gas-Slippage behavior. Then, a unified shale matrix apparent permeability model is proposed to bridge the effects of Non-Darcy flow/Gas-Slippage, geomechanics (formation compaction) and the release of adsorption layer into a single, coherent equation. In addition, a mathematical framework for an unconventional reservoir simulator that developed in this study is also presented.Different matrix apparent permeability models are implemented in the numerical simulator to examine what factors impact the matrix apparent permeability most. Furthermore, how these factors influence the average apparent permeability in the Simulated Reservoir Volume (SRV) and long-term production are also discussed. Finally, the impact of natural fracture networks on matrix apparent permeability evolution is investigated. The results indicate that even though the conductive fracture networks play a vital role in shale gas production, the matrix apparent permeability evolution during pressure depletion can still make a difference.

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“…Maxwell (1887) first pointed out from kinetic point of view that the "non-slip boundary condition" in continuum theory is not always the truth, the temperature jump and velocity slip at the wall will become significant under certain situation [3]. Sherman further illustrated that the continuum theory starts to fail near the wall as the flow became rarefied [4]. Early studies on rarefied gas are mostly focused on the boundary condition and wall properties in the slip flow regime.…”

Section: Introductionmentioning

confidence: 99%