Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H2, CH4) or permanent (CO2, radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

Linking direct and continuum fluid flow models for fractured media: The intersection problem

<p>Finding an adequate bridge between direct and continuum modeling approaches has been the fundamental issue of upscaling fluid flow in rock masses. Typically, numerical simulations of direct fluid flow (e.g. Stokes or Lattice-Boltzmann) in fractured or porous media serve as small-scale building blocks for larger-scale continuum flow simulations (e.g. Darcy). For fractured rock masses, the discrete-fracture-network (DFN) modeling approach is often used as an initial step to upscale flow properties by parameterizing the permeability of each fracture with its hydraulic aperture and solving steady-state flow equations within the fracture system. However, numerical simulations of Stokes flow in small fracture networks (FN) indicate that, depending on the orientation of the applied pressure gradient, fluid flow tends to localize at places where fractures intersect. This effect causes discrepancies between direct and equivalent continuum flow modeling approaches, which ought to be taken into account when modeling flow at the network scale.</p><p>In this study, we compare direct flow simulations of small fracture networks to their continuum representation obtained with several techniques in order to find an upscaling approach that takes these intersection effects into account. Direct flow simulations are conducted by solving the Stokes equations in 3D using our open-source finite-difference software LaMEM. Continuum flow simulations are realized with a newly developed parallel finite-element code, which solves fully anisotropic 3D Darcy flow with specific permeability tensors for each voxel. The direct flow simulations serve as benchmarks to optimize the continuum flow models by comparing resulting permeabilities. We tested two different schemes to generate the equivalent continuum representation: </p><p>(1) Fully resolved isotropic permeability discretizations (fracture permeability is obtained from a refined cubic law) where voxel sizes are a fraction of the minimal hydraulic aperture of the FN or</p><p>(2) coarse anisotropic permeability discretizations (permeability tensors are rotated according to fracture orientation) with voxel sizes larger than the minimal hydraulic aperture of the FN.</p><p>We then assess different scenarios to incorporate the intersection effects by adding, averaging and/or multiplying the permeabilities of the intersecting fractures within intersection voxels. Preliminary results for scheme 1 suggest that a simple addition of both intersecting fracture permeabilities delivers the best fit to the results of the direct flow simulations, if the voxel size is about 68% of the minimal hydraulic aperture. Scheme 2 systematically underestimates the direct flow permeabilities by about 26%.</p>

Evaluation of a counter-flow microchannel heat exchanger performance with air-water vapor mixture to liquid water

Given its configuration and operation conditions, the performance of a counter-flow microchannel heat exchanger (MCHX) is evaluated through detailed calculations. The fluids, both liquid water and air, are considered as continuum flow flowing in microchannels. The MCHX has 59 sheets, and each sheet has 48 microchannels. The microchannels for both fluids have the same cross section of 0.8mm×1mm and same length of 200mm. Log mean temperature difference method is adopted for this evaluation. Using appropriate equations, the properties of air-water vapor mixture are calculated based on that of the two components. Given the inlet temperature for liquid water(35℃) and air (170℃),the calculated outlet temperature for both fluids are 55.5℃ and 43.3℃, respectively. The results also show that the air at the outlet is saturated. The overall heat transfer coefficient reaches 100W/m2ꞏK, which is much higher than that of conventional heat exchanger with similar fluid combinations.

Analysis of Flow Characteristics and Pressure Drop for an Impinging Plate Fin Heat Sink with Elliptic Bottom Profiles

The performance of impingement air cooled plate fin heat sinks differs significantly from that of parallel flow plate fin heat sinks. The impinging flow situations at the entrance and the right-angled bends of the plate fin heat sink are quite involved. Flow characteristics of a plate fin heat sink with elliptic bottom profiles cooled by a rectangular impinging jet with different inlet widths are studied by numerical simulations. The results of pressure drop of numerical simulations and experimental results match quite well. The numerical results show that at the same flow rate, the pressure drop decreases with the increase of the impingement inlet width, and the pressure drop increases significantly with the increase of the fin height. The larger the impingement inlet width of air-cooled plate fin heat sink, the milder the pressure drop changes with velocity. Pressure drop for an impinging plate fin heat sink without elliptic bottom profiles is larger than that with elliptic bottom profiles at the same inlet width and velocity. Based on the fundamental developing laminar continuum flow theory, an improved model which is very concise and nice for quick real world approximations is proposed. Furthermore, this paper verifies the effectiveness of this simple impinging pressure drop model.

Controlling Parameters During Continuum Flow in Shale-Gas Production: A Fracture/Matrix-Modeling Approach

Summary The purpose of this paper is to investigate the main controlling factors during a continuum-flow regime in shale-gas production in the context where well-induced fractures, extending from the well perforations, improve reservoir conductivity and performance. A mathematical 1D+1D model is presented that involves a high-permeability fracture extending from a well perforation through symmetrically surrounding shale matrix with low permeability. Gas in the matrix occurs in the form of adsorbed material attached to kerogen (modeled by a Langmuir isotherm) and as free gas in the nanopores. The pressure gradient toward the fracture and well perforation causes the free gas to flow. With pressure depletion, gas desorbs out of the kerogen into the pore space and then flows to the fracture. When the pressure has stabilized, desorption and production stop. The production of shale gas and mass distributions indicate the efficiency of species transfer between fracture and matrix. We show that the behavior can be scaled and described according to the magnitude of two characteristic dimensionless numbers: the ratio of diffusion time scales in shale and fracture, α, and the pore-volume (PV) ratio between the shale and fracture domains, β. Fracture/matrix properties are varied systematically to understand the role of fracture/matrix interaction during production. Further, the role of fracture geometry (varying width) is investigated. Input parameters from experimental and field data in the literature are applied. The product αβ expresses how much time it takes to diffuse the gas in place through the fracture to the well compared with the time it takes to diffuse that gas from the matrix to the fracture. For αβ≪1, the residence time in the fracture is of negligible importance, and fracture properties such as shape, width, and permeability can be ignored. However, if αβ≈1, the residence time in the fracture becomes important, and variations in all those properties have significant effects on the solution. The model allows for intuitive interpretation of the complex shale-gas-production system. Furthermore, the current model creates a base that can easily incorporate nonlinear-flow mechanisms and geomechanical effects that are not readily found in standard commercial software, and further be extended to field-scale application.