Static Porosity Research Articles

Hydrodynamic Porosity: A New Perspective on Flow through Porous Media, Part I

Pore-scale flow velocity is an essential parameter in determining transport through porous media, but it is often miscalculated. Researchers use a static porosity value to relate volumetric or superficial velocities to pore-scale flow velocities. We know this modeling assumption to be an oversimplification. The variable fraction of porosity conducive to flow, what we define as hydrodynamic porosity, θmobile, exhibits a quantifiable dependence on the Reynolds number (i.e., pore-scale flow velocity) in the Laminar flow regime. This fact remains largely unacknowledged in the literature. In this work, we quantify the dependence of θmobile on the Reynolds number via numerical flow simulation at the pore scale for rectangular pores of various aspect ratios, i.e., for highly idealized dead-end pore spaces. We demonstrate that, for the chosen cavity geometries, θmobile decreases by as much as 42% over the Laminar flow regime. Moreover, θmobile exhibits an exponential dependence on the Reynolds number, Re = R. The fit quality is effectively perfect, with a coefficient of determination (R2) of approximately 1 for each set of simulation data. Finally, we show that this exponential dependence can be easily fitted for pore-scale flow velocity through use of only a few Picard iterations, even with an initial guess that is 10 orders of magnitude off. Not only is this relationship a more accurate definition of pore-scale flow velocity, but it is also a necessary modeling improvement that can be easily implemented. In the companion paper (Part 2), we build upon the findings reported here and demonstrate their applicability to media with other pore geometries: rectangular and non-rectangular cavities (circular and triangular).

Fracturing and Porosity Channeling in Fluid Overpressure Zones in the Shallow Earth’s Crust

At the time of energy transition, it is important to be able to predict the effects of fluid overpressures in different geological scenarios as these can lead to the development of hydrofractures and dilating high-porosity zones. In order to develop an understanding of the complexity of the resulting effective stress fields, fracture and failure patterns, and potential fluid drainage, we study the process with a dynamic hydromechanical numerical model. The model simulates the evolution of fluid pressure buildup, fracturing, and the dynamic interaction between solid and fluid. Three different scenarios are explored: fluid pressure buildup in a sedimentary basin, in a vertical zone, and in a horizontal layer that may be partly offset by a fault. Our results show that the geometry of the area where fluid pressure is successively increased has a first-order control on the developing pattern of porosity changes, on fracturing, and on the absolute fluid pressures that sustained without failure. If the fluid overpressure develops in the whole model, the effective differential and mean stress approach zero and the vertical and horizontal effective principal stresses flip in orientation. The resulting fractures develop under high lithostatic fluid overpressure and are aligned semihorizontally, and consequently, a hydraulic breccia forms. If the area of high fluid pressure buildup is confined in a vertical zone, the effective mean stress decreases while the differential stress remains almost constant and failure takes place in extensional and shear modes at a much lower fluid overpressure. A horizontal fluid pressurized layer that is offset shows a complex system of effective stress evolution with the layer fracturing initially at the location of the offset followed by hydraulic breccia development within the layer. All simulations show a phase transition in the porosity where an initially random porosity reduces its symmetry and forms a static porosity wave with an internal dilating zone and the presence of dynamic porosity channels within this zone. Our results show that patterns of fractures, hence fluid release, that form due to high fluid overpressures can only be successfully predicted if the geometry of the geological system is known, including the fluid overpressure source and the position of seals and faults that offset source layers and seals.

Effect of polyHIPE porosity on its hydrodynamic properties

Several polymerized high internal phase emulsions (polyHIPE) of various porosity but the same pore diameter were prepared. It was demonstrated that the pore size distribution of void pores and interconnecting pores is similar and it can be described by a log-normal distribution. Flow-through porosity matches closely static porosity and the non-polymerizable fraction of initial emulsion, demonstrating an open structure of polyHIPE that allows flow through the entire porous polymer. Pulse response experiments demonstrated flow uniformity. Pressure drop analysis allowed estimation of porosity effect on permeability. Fitting of experimental data with different pressure drop models revealed that interconnecting pore diameter should be used as a characteristic dimension to describe pressure drop on polyHIPE accurately. Linear correlation between permeability and flow-through porosity demonstrated that the effect of the porous polymer structure on the flow properties is independent of porosity. This finding suggests that polyHIPE hydrodynamics does not change with porosity, facilitating prediction of their performance for various applications where flow-through mode is important.

Finite-difference simulation of coreflooding based on a reconstructed CT scan; modeling transient oscillating and pulse decay permeability experiment

Numerical simulation and experimental research of fluid flow in porous media enhance the practices of petroleum reservoirs' management. Experiments on acquired reservoir-rock samples are conducted for accurate characterization and realization of the insitu hydrocarbon reserves. Implementing precise numerical simulation of those experiments is crucial to acquire accurate conclusions from the obtained experimental results. Coreflooding experiments quantify reservoir rock's storage capacity, measure its transport connectivity, and evaluate recovery methods' effectiveness for that rock. In this paper, a reconstruction image-processing workflow of cores' CT scan is developed to build a finite difference numerical model for simulating coreflooding experiments. In a transient coreflooding experiment, a controlled pressure pulse with a known frequency and amplitude is transmitted to the rock sample. Rock permeability can be quantified by analytically solving the diffusivity flow equation for that experiment. Simulating the transient permeability experiment is very sensitive to the level of details of the pores' structure described in the numerical model. A transient permeability experiment with two different transient modes, sinusoidal oscillation, and pulse decay, was conducted on a standard Berea core sample. The Berea CT scan was image-processed to reconstruct the static porosity and permeability model in Petrel software using a 3D variogram geostatistical population. Injection and production sources were assigned to the finite gridblock, which correspond to flow nozzles of injection and production coreflooding setup's heads. Scheduled flow and controlled-pressure boundary-conditions were imposed on the dynamic model. Eclipse simulator was used to solve the dynamic model and calculate the pressure in each gridblock. The outlet pressure was calculated at each time step by three different realization approaches for porosity and permeability, i.e., from experiments, from statistical analysis for the CT scan, and by the proposed image processing workflow. The simulated outlet pressure from the prosed workflow matched ideally, with a Pearson correlation coefficient of 0.98 and 0.99, the recorded one in the two experiments compared to underestimated or overestimated outlet pressure from the other two traditional realization approaches, i.e., statistical or experimental.

Effect of static porosity fluctuations on reactive transport in a porous medium

Reaction-diffusive transport phenomena in porous media are ubiquitous in engineering applications, biological and geochemical systems. The porosity field is usually random in space, but most models consider the porosity field as a well-defined deterministic function of space and time and ignore the porosity fluctuations. They use a reaction–diffusion equation written in terms of an average porosity and average concentration fields. In this contribution, we treat explicitly the effect of spatial porosity fluctuations on the dynamics of a concentration field for the case of a one-dimensional reaction-transport system with nonlinear kinetics. Three basic assumptions are considered. (i) The porosity fluctuations are assumed to have Gaussian properties and an arbitrary variance; (ii) we assume that the noise correlation length is small compared to the relevant macroscopic length scale; (iii) and we assume that the kinetics of the reactive term in the equations for the fluctuations is a self-consistently determined constant. Elimination of the fluctuating part of the concentration field from the dynamics leads to a renormalized equation involving the average concentration field. It is shown that the noise leads to a renormalized (generally smaller) diffusion coefficient and renormalized kinetics. Within the framework of the approximations used, numerical simulations are in agreement with our theory. We show that the porosity fluctuations may have a significant effect on the transport of a reactive species, even in the case of a homogeneous average porosity.

Influence of Air on the Bouncing Dynamics of Shallow Vibrated Granular Beds: Kroll’s Model Predictions

In the present work, we explore the modification of the periodicity of the motion of shallow granular columns in the framework of Kroll’s one-dimensional model for the motion of a vibrated bed. Within the model, bed dynamics depend on two parameters, the dimensionless maximum acceleration, Γ, and a dissipative parameter, α, depending on air viscosity, grain density, bed static porosity, oscillation frequency and grain diameter. We show how the bifurcation diagram for the flight time of the bed as a function of Γ changes with α. For α = 0, Kroll’s prediction equals that of the inelastic bouncing ball model. When α is increased, bifurcations shift to higher Γ up to a point where not even a single bifurcation is predicted in a range of Γ where an inelastic bouncing ball displays several bifurcations. We also illustrate how the flight time reduces nonlinearly with increasing α in a monotonic way. We introduce isoperiodic maps to illustrate regions of single, double, or more periodicities in the phase space. W...

X-ray and neutron scattering: from ideal zeolites to real guest-host systems

Tetrahedral MOFs, microporous metallophosphates and zeolites share common framework topologies despite very different chemical nature of their crystalline skeleton. In the case of zeolites or metallophosphates, the polymeric [TO2]_ framework is based on single tetrahedral atoms T (T= Si4+/Al3+ or Ga3+/B3+/P5+ respectively) connected by corner oxygen atoms O. In the case of MOFs, the skeleton is built from supertetraedra formed by a central metal atom complexed by 4 organic linkers (terephtalate,...); hence homologous structures expanded by a "scale factor". In "molecular sieves", the static porosity but also the "breathing effect" control, in first approximation, the adsorption and the self-diffusion of guest molecules. These latter are finely tuned by the interaction of these molecules with the framework itself (though H-bonds or electrostatic interactions), with charge compensating cations in basic zeolites (through coulombic interaction), or with other adsorbed molecules. However, the interplay between guest molecule adsorption, framework relaxation, cation redistribution and atomic charge transfer leads to an inextricable problem for the modeling and prediction of adsorption properties in these systems in absence of any polarizable and adaptive force field. We will present experimental charge density studies on activated industrial zeolites FAU, MFI and MOR. The electrostatic properties derived on these systems (electric field, atomics charges) are validated by a comparison with those derived, experimentally and theoretically, on a comprehensive set of simpler quartz-type materials (SiO2, AlPO4, GaPO4,...) representative of typical microporous compositions. Finally, we will combine the informations brought by diffraction, diffuse scattering and Monte-Carlo modelling to analyse the adsorption process or the role of the template in the stabilisation of the framework in these systems and in the famous MIL-53 MOF

Mechanical characterization of pharmaceutical solids: A comparison between rheological tests performed under static and dynamic porosity conditions

The aim of this work was to verify how and to what extent rheological tests, carried out under dynamic (Heckel) and static (creep, stress/strain) porosity conditions, may serve as a valuable complement to the classic Heckel tests in the characterization of viscoelastic and densification properties of solid materials for pharmaceutical use. Six different modified (pregelatinized) starches were compressed in a rotary tablet machine equipped to measure force and punch displacement. Tablets were obtained using flat-faced 6 mm diameter punches at different compression pressures. Compression cycles performed at the maximal pressure of 200 MPa were used to build the Heckel plots. Ejected tablets at the 10%, 20%, 30%, and 40% porosity levels were used for the stress/strain and creep tests. Parameters obtained with both types of tests were consistent with each other. In particular, among the six starches, lower viscosity values corresponded to lower P Y values, and lower elastic modulus values corresponded to lower elastic recovery of the tablet. Mechanical properties of materials can be better characterized if viscoelastic tests performed under dynamic porosity conditions (Heckel analysis) are supported by classical viscoelastic tests carried out under conditions of static porosity.

A Model for Dynamics of Expansion of Gas-Solid Fluidized Beds

A semiempirical model of the dynamics of the expansion of a gas-solid fluidized bed can portray the experimentally observed nonuniform static porosity as well as the transient distribution. The model contains only a single adjustable parameter, the coefficient of the bed expansion rate, which varies along the bed height. Its value increases as the gas velocity increases; however, it is only slightly dependent on the bed mass except for a very shallow bed. The predicted value of the time to complete the bed expansion appears to agree with the results of approximate measurements by visual observations. Propagation of the initial disturbance near the jet zone could be described by the model.