Fluid Flow In Porous Rocks Research Articles

Application of Artificial Neural Networks for Predicting Relative Permeability in Talang Akar Formation

Relative permeability is a substantial parameter for estimating multi-phase fluid flow in porous rocks. It is a complex physical property that is influenced by the behavior and interactions between the fluid and rock phases. Relative permeability measurement of rock samples in laboratory can be carried out using steady-state or non-steady-state techniques. Permeability measurement is relatively difficult and time consuming. Because of the difficulty in measurement, empirical models are often used to estimate relative permeability or extrapolate to limited laboratory data. Artificial neural network (ANN) is a method that can be applied to obtain complex correlations of parameters that influence each other. In this study, ANN is used to predict the relative permeability of oil and water. The proposed model evaluates the relative permeability of a phase as a function of rock absolute permeability, porosity, depth, permeability of other phases and water saturation. A total of 159 relative permeability data from Talang Akar Formation were used for the training and testing processes. Based on the comparison between measured and calculated data, the correlation coefficients for relative permeability to water and oil using ANN method are 0.77 and 0.94 respectively. While those using regression analysis are 0.88 and 0.73 respectively.

High accuracy capillary network representation in digital rock reveals permeability scaling functions

Permeability is the key parameter for quantifying fluid flow in porous rocks. Knowledge of the spatial distribution of the connected pore space allows, in principle, to predict the permeability of a rock sample. However, limitations in feature resolution and approximations at microscopic scales have so far precluded systematic upscaling of permeability predictions. Here, we report fluid flow simulations in pore-scale network representations designed to overcome such limitations. We present a novel capillary network representation with an enhanced level of spatial detail at microscale. We find that the network-based flow simulations predict experimental permeabilities measured at lab scale in the same rock sample without the need for calibration or correction. By applying the method to a broader class of representative geological samples, with permeability values covering two orders of magnitude, we obtain scaling relationships that reveal how mesoscale permeability emerges from microscopic capillary diameter and fluid velocity distributions.

Non-invasive quantification of throat-size distribution and corresponding capillary pressure

Pore-throat-size distribution (PSD) controls fundamental petrophysical properties regulating the fluid flow in porous rocks and impacts characterization of water and hydrocarbon reserves. However, the methods available for estimating PSD (e.g. mercury injection porosimetry, gas adsorption/condensation, and electron microscopy) require rock samples and, thus, are not adequate for field applications using borehole geophysical measurements. Therefore, the aims of this paper include (1) appraising pore geometry features (e.g., tortuosity, PSD) using multi-physics formation data, (2) introducing a new non-invasive process to estimate PSD through the combined interpretation of permittivity, resistivity, as well as nuclear magnetic resonance (NMR) measurements, and (3) demonstrating that the new process can be applied to reliably estimate capillary pressure curves and displacement pressure.We introduce a process based on a new equation for non-invasive estimation of PSD in porous media. This novel throat-size equation requires information obtained through the analysis of NMR and electric measurements. We calculate the distribution of pore sizes from the T2 distribution by assuming the pores can be approximated by spheres. The pore-to-throat size ratio and the tortuosity are estimated from the combined analysis of permittivity, resistivity, and NMR measurements. Then, we can use the pore-size distribution and the pore-to-throat ratio to calculate the PSD. The new non-intrusive process relies on fundamental petrophysics and entirely removes the necessity of calibration efforts. Results demonstrate that the relative differences between the calculated mean pore-throat sizes against the corresponding values obtained from mercury injection capillary pressure (in core samples) and the generalized network modeling results (in pore-scale images) are approximately 10% and 40%, respectively. These differences are not expressive since the effective pore-throat sizes can vary by orders of magnitude in different rock types.

Functionalisation of Polydimethylsiloxane (PDMS)- Microfluidic Devices coated\xa0with Rock Minerals

Fluid flow in porous rocks is commonly capillary driven and thus, dependent on the surface characteristics of rock grains and in particular the connectivity of corners and crevices in which fluids reside. Traditional microfluidic fabrication techniques do not provide a connected pathway of crevices that are essential to mimic multiphase flow in rocks. Here, geo-material microfluidic devices with connected pathways of corners and crevices were created by functionalising Polydimethylsiloxane (PDMS) with rock minerals. A novel fabrication process that provides attachment of rock minerals onto PDMS was demonstrated. The geo-material microfluidic devices were compared to carbonate and sandstone rocks by using energy dispersive X-ray spectroscopy, scanning electron microscopy (SEM), contact angle measurements, and a surface profilometer. Based on SEM coupled with energy-dispersive X-ray spectrometry (SEM-EDS) analyses, roughness measurements, contact angle, wettability, and roughness were comparable to real rocks. In addition, semivariograms showed that mineral deposition across the different geo-material devices was nearly isotropic. Lastly, important multiphase flow phenomena, such as snap-off and corner flow mechanisms, equivalent to those occurring in reservoir rocks have been visualised. The presented approach can be used to visualise rock-fluid interactions that are relevant to subsurface engineering applications, such as hydrocarbon recovery and CO2 sequestration.

Diffusion Equations for Fluid Flow in Porous Rocks

The multiphase flow in porous media is a subject of great complexities with a long rich history in the field of fluid mechanics. This is a subject with important technical applications, most notably in oil recovery from petroleum reservoirs and so on. The single-phase fluid flow through a porous medium is well characterized by Darcy’s law. In the petroleum industry and in other technical applications, transport is modeled by postulating a multiphase generalization of the Darcy’s law. In this connection, distinct pressures are defined for each constituent phase with the difference known as capillary pressure, determined by the interfacial tension, micro pore geometry and surface chemistry of the solid medium. For flow rates, relative permeability is defined that relates the volume flow rate of each fluid to its pressure gradient. In the present paper, there is a derivation and analysis about the diffusion equation for the fluid flow in porous rocks and some important results have been founded. The permeability is a function of rock type that varies with stress, temperature etc., and does not depend on the fluid. The effect of the fluid on the flow rate is accounted for by the term of viscosity. The numerical value of permeability for a given rock depends on the size of the pores in the rock as well as on the degree of interconnectivity of the void space. The pressure pulses obey the diffusion equation not the wave equation. Then they travel at a speed which continually decreases with time rather than travelling at a constant speed. The results shown in this paper are much useful in earth sciences and petroleum industry.

Characterizing flow in oil reservoir rock using SPH: absolute permeability

In this paper, a three-dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous rock is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including flows related to permeable rock for both groundwater and petroleum reservoir research. While previous approaches to such problems using SPH have involved the use of idealized pore geometries (cylinder/sphere packs etc), in this paper we detail the characterization of flow in models with geometries taken from 3D X-ray microtomographic imaging of actual porous rock; specifically 25.12 % porosity dolomite. This particular rock type has been well characterized experimentally and described in the literature, thus providing a practical ‘real world’ means of verification of SPH that will be key to its acceptance by industry as a viable alternative to traditional reservoir modeling tools. The true advantages of SPH are realized when adding the complexity of multiple fluid phases, however, the accuracy of SPH for single phase flow is, as yet, under developed in the literature and will be the primary focus of this paper. Flow in reservoir rock will typically occur in the range of low Reynolds numbers, making the enforcement of no-slip boundary conditions an important factor in simulation. To this end, we detail the development of a new, robust, and numerically efficient method for implementing no-slip boundary conditions in SPH that can handle the degree of complexity of boundary surfaces, characteristic of an actual permeable rock sample. A study of the effect of particle density is carried out and simulation results for absolute permeability are presented and compared to those from experimentation showing good agreement and validating the method for such applications.

Conforming Finite-Element Methods for Modeling Convection in an Incompressible Rock Matrix

Coupled heat transport and fluid flow in porous rocks play a role in many geological phenomena, including the formation of hydrothermal mineral deposits, the productivity of geothermal reservoirs and the reliability of geo-sequestration. Due to the low compressibility of the fluid and rock matrix and the long-time scales the fluid can be treated as incompressible. The solution of the incompressible Darcy flux problem and the advection-dominated heat transport both provide numerically challenging problems typically addressed using methods specialized for the individual equations. In order to avoid the usage of two different meshes and solution approximations for pressure, flux, and temperature we propose to use standard conforming finite-element methods on the same mesh for both problems. The heat transport equation is solved using a linearized finite-element flux corrected transport scheme which introduces minimum artificial diffusion based on the discretized transport problem. The Darcy flux calculation from pressure uses a global post-processing strategy which at the cost of an extra partial differential equation leads to highly accurate flux approximation. In the limit of zero element size the flux is in fact incompressible. We investigate the numerical performance of our proposed method on a test problem using the parallelized modeling environment escript. We also test the approach to simulate convection in geologically relevant scenarios.

Characterization of fluid flow in a shear band in porous rock using neutron radiography

The challenge of understanding how localized deformation modifies fluid flow in porous rock is addressed. New approaches are presented, based on neutron radiography and digital image analyses, to track fluid flow in rock specimens and to calculate flow velocity fields providing local flow measurements. The results show that neutron radiography, backed up by appropriate image analysis, is a very powerful tool in this context, being far more sensitive to the fluids in the rock than X‐ray radiography. Analysis of neutron radiography images of water imbibition into a laboratory‐deformed sandstone specimen has provided new measurements of local fluid flow velocities within a shear band, indicating that flow is faster and water storage is higher in the band (attributed to higher capillary forces associated with damage).

Rigorous bounds for seismic dispersion and attenuation due to wave-induced fluid flow in porous rocks

The Hashin-Shtrikman (HS) bounds define the range of bulk and shear moduli of an elastic composite, given the moduli of the constituents and their volume fractions. Recently, the HS bounds have been extended to the quasi-static moduli of composite viscoelastic media. Because viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on the complex plane. We analyze these general viscoelastic bounds for a particular case of a porous solid saturated with a Newtonian fluid. In our analysis, for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semicircle and a segment of the real axis, connecting formal HS bounds that are computed for an inviscid fluid. Importantly, viscoelastic bounds for poroelastic media turn out to be independent of frequency. However, because the bounds are quasi-static, the frequency must be much lower than Biot’s characteristic frequency. Furthermore, we find that the bounds for the bulk modulus are attainable (realizable). We also find that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot’s global flow dispersion, because the latter strongly depends on inertial forces.

Core-flood experiment for transport of reactive fluids in rocks

Investigation of the transport of reactive fluids in porous rocks is an intriguing but challenging task and relevant in several areas of science and engineering such as geology, hydrogeology, and petroleum engineering. We designed and constructed an experimental setup to investigate physical and chemical processes caused by the flow of reactive and volatile fluids such as supercritical CO(2) and/or H(2)S in geological formations. Potential applications are geological sequestration of CO(2) in the frame of carbon capture and storage and acid-gas injection for sulfur disposal and/or enhanced oil recovery. The present paper outlines the design criteria and the realization of reactive transport experiments on the laboratory scale. We focus on the spatial and time evolution of rock and fluid composition as a result of chemical rock fluid interaction and the coupling of chemistry and fluid flow in porous rocks.

X-ray imaging of water motion during capillary imbibition: Geometry and kinetics of water front in intact and damaged porous rocks

[1] Imaging fluid flow in porous rocks is a constant challenge in Earth sciences. We present the results of an experimental study to image capillary imbibition processes using an industrial X-ray scanner to investigate fluid motion processes in relation with microstructural properties for various porous rocks. Two-dimensional density maps obtained at a constant time step of about 3 s in standard capillary rise experiments on intact and damaged rock samples are analyzed. Both sandstones and carbonate rocks have been studied. The geometry of the water front depends on the sample geometry but also on the rock microstructure and the dynamics of capillary processes as its curvature changes during water rising. We discuss the effect of anisotropy, heterogeneity, microstructures, and driving forces on the kinetics and geometry of the water front. Once a good knowledge of the intact rock behavior was achieved, mechanical damage was induced in creep experiments at increasing stress levels with a continuous recording of acoustic emissions. The density maps obtained during imbibition under the scanner were analyzed to show how the mechanical deformation alters the fluid displacement patterns. We found that the velocity and the geometry of the waterfront are strongly disturbed in comparison to the intact rock. However, our study was not really conclusive on the effect of fractures on fluid flow patterns. Conducting capillary imbibition experiments coupled with imaging techniques using an X-ray scanner is a powerful technique to image fluid flow patterns in reservoir rocks and how they are affected by deformation.

Faulting and fluid flow in porous rocks and sediments: implications for mineralisation and other processes

Faults in sedimentary rocks can act as fluid pathways or barriers to flow and display a range of deformation styles. These features can be explained by behaviours observed in deformation experiments on sedimentary rocks that reveal a transition from dilatant brittle faulting and permeability enhancement to cataclasis and permeability reduction, with increasing porosity, grain size and confining pressure. This transition implies that faults in sedimentary rocks are unlikely to act as fluid pathways shallower than ~3 km, unless the sediments have undergone early cementation, or have been exposed following burial and uplift. This has important implications for many geological processes, including fluid circulation in geothermal systems, formation of sediment-hosted mineral deposits and earthquakes in subduction zones. Stratiform Zn–Pb deposits that have been interpreted as syngenetic, seafloor deposits could instead be interpreted as early epigenetic deposits representing the depth at which faults change from fluid pathways to barriers.

An Inside View of Foam

MATERIALS SCIENCE From lending texture to a perfect pint, to mediating fluid flow in porous rock, and even capturing space dust in the wake of a comet, foams have a diverse set of mechanical properties, geometrical structures, and applications. Their remarkable strength-to-weight ratio makes them sought after as physical supports, with their large surface area making them ideal scaffolds for catalytic applications. They tend to be rather delicate, however, and the mechanisms whereby the various structures form and then limit the resulting physical properties have not been clear. Barty et al. use coherent x-ray diffraction to provide a detailed three-dimensional image of the internal structure of the highly porous form of tantalum oxide known as aerogel, often described as “frozen smoke.” Combining the exquisite structural information with detailed simulations, they show that the observed blob-and-beam network structure explains why the materials are weaker than expected. Such insight offers a route toward improving the properties through better control of the preparation process. — ISO Phys. Rev. Lett. 101 , 55501 (2008).

Numerical modelling of faulting and fluid flow in porous rocks: An approach based on critical state soil mechanics

The mechanical behaviour of porous rocks changes from localised, dilatant shear failure to distributed shear-enhanced compaction with increasing porosity, grain size and effective pressure. Shear-enhanced compaction results in permeability reduction, whereas dilatant shear failure results in permeability enhancement if the host rock porosity is low, but reduces permeability if porosity is high. Hence, focused fluid flow requires dilatant shear failure of low porosity rocks. Changes in porosity and effective pressure with depth in sedimentary basins lead to corresponding variations in failure mode and permeability evolution. This study uses results of deformation experiments to parameterise a constitutive behaviour for sandstones, following the principles of critical state soil mechanics. The constitutive behaviour is implemented in a numerical model that couples deformation with permeability evolution and fluid flow. The model is used to investigate effects of grain size, geothermal gradient and deposition rate, verifying previous predictions regarding the relationship between these parameters and the minimum depth at which focused fluid flow may take place. Fluid diverges out of faults or shear zones at the point where they change from fluid pathways to seals. Dilatant faults formed in extension may undergo compaction and strain hardening during basin inversion.

Observation and analysis of frequency-dependent anisotropy from a multicomponent VSP at Bluebell-Altamont field, Utah

In this paper, we present results from the analysis of a multicomponent VSP from a fractured gas reservoir in the Bluebell-Altamont Field, Utah. Our analysis is focused on frequency-dependent anisotropy. The four-component shear-wave data are first band-pass filtered into different frequency bands and then rotated to the natural coordinates so that the fast and slow shear-waves are effectively separated. We find that the polarisations of the fast shear-waves are almost constant over the whole depth interval, and show no apparent variation with frequency. In contrast, the time delays between the split shear-waves decrease as the frequency increases. A linear regression is then applied to fit the time-delay variations in the target and we find that the gradients of linear fits to time delays show a decrease as frequency increases. Finally, we apply a time-frequency analysis method based on the wavelet transform with a Morlet wavelet to the data. The variation of shear-wave time delays with frequency is highlighted in the time-delay and frequency spectra. We also discuss two mechanisms giving rise to dispersion and frequency-dependent anisotropy, which are likely to explain the observation. These are scattering of seismic waves by preferentially aligned inhomogeneneities, such as fractures or fine layers, and fluid flow in porous rocks with micro-cracks and macro-fractures.

Wave Propagation in the Effective Model of Alternating Porous and Impermeable Solid Layers

Elastic properties of finely layered media are of great interest for seismic exploration. Theoretical models give a dependence of overall properties on constituent parameters. On the one hand they help geophysicists to estimate possible ranges of anisotropy and on the other hand they provide a basis for interpretation of measured anisotropic parameters in terms of microstructure. Last forty years such models with elastic constituents have been extensively used. Recently they have been updated for describing fractured rocks (Hsu and Schoenberg, 1993). In this case thin, and soft elastic layer models fracture. However reservoir rocks are porous and permeable. Porosity and permeability are taken into account by well-known Biot model. Finely layered porous sequences have some distinctive properties which are the topic of modern research (Schoenberg, 1996). Therefore it is important to update developed concepts to porous medium. Bakulin and Molotkov (1998, 1997) who generalized Backus averaging on poroelastic medium have done first step. Here we pay attention to one special case when there is only one preferential direction of fluid flow in porous rock. This may be caused by presence of impermeable barriers or lenses, which are modeled as set of solid layers intersecting porous medium. Such model corresponds to highly hydraulically anisotropic rock, which has very strong anisotropy of pore space structure and permeability.

Fluid transport in glass beads phantoms: spatial velocity measurements and confirmation of the stochastic model

A stochastic model of fluid flow in porous rocks has been previously developed to explain the measured distribution of local velocity. The theoretical predictions of this model agree well with experimental results obtained from the magnetic resonance imaging-based measurements of the spatial variation of velocity of water permeating through Bentheimer and Clashach sandstones. To further verify previous results, we have performed new velocity measurement experiments using an efficient velocity encoded π-echo planar imaging sequence on glass bead phantoms that exhibit more regular pore size distribution than rocks. The results show that velocity distributions in glass bead phantoms also exhibit Gaussian profiles and the linear relationship between the velocity variance and the mean velocity (the Mansfield-Issa equation).

Fluid Transport in Porous Rocks. II. Hydrodynamic Model of Flow and Intervoxel Coupling

In a preceding paper [P. Mansfield and B. Issa,J. Magn. Reson. A122, 137–148 (1996)], a stochastic model of fluid flow in porous rocks based upon the experimental observation of water flow through a Bentheimer sandstone core was proposed. The flow maps were measured by NMR-imaging techniques. The stochastic theory led to a Gaussian velocity distribution with a mean value in accord with Darcy's law. Also predicted was a linear relationship between flow variance and mean fluid flow through rock, the Mansfield–Issa equation, originally proposed as an empirical relationship. In the present work a flow coupling mechanism between voxels is proposed. Examination of the flow coupling between isolated voxel pairs leads to a complementary explanation of the Gaussian velocity distribution, and also gives further details of the Mansfield–Issa equation. These details lead to a new expression for the connectivity, 〈C〉, between voxels with an experimental value of 〈C〉 = 5.64 × 10−9for Bentheimer sandstone.

Invasion percolation and Eden growth: Geometry and universality.

The mapping of optimal paths in the strong disorder limit to the strands of invasion percolation clusters is shown to lead to a new universal property of these clusters. We suggest that the corresponding strands arising in the annealed Eden growth process are in the same universality class as directed polymers in weak quenched disorder with an upper critical dimension #6. (S0031-9007(96)00188-3) PACS numbers: 64.60.Ak We address several issues in this Letter. What are the geometries of the optimal polymer in a strongly disordered medium in higher dimensions? What is the upper critical dimensionality for this problem? Is the geometry of the polymer in a strongly disordered medium universal? Our study is carried out in the context of a growing invasion percolation cluster. In this procedure, the bonds of the lattice are assigned strengths in a quenched random manner, and a cluster grows by invading the weakest interfacial bond. We will show that both bond and site variants of percolation lead to the same universality class. We then go on to study an analogous model with annealed instead of quenched disorder. In this case all interfacial bonds have an equal probability of being invaded. We present arguments and numerical evidence that even though the randomness is annealed, the effects of quenched disorder are self-generated within the model leading to geometries that are self-affine and characterized by the roughness exponent aDP . Thus, within the same process, the interface of the Eden cluster is characterized by a dynamical exponent zKPZ, whereas the static wandering exponent of the strands of the cluster is given by 1yzKPZ (a strand is defined as the unique path that excludes dead ends from an arbitrary site to a central seed site). Our results have a wide range of applicability— the strong disorder limit is relevant up to a correlation length in a variety of situations (7) including transport in amorphous semiconductors at low temperatures, electrical conduction and fluid flow in porous rocks, and the magnetic properties of doped semiconductors. Further, there are novel forms of percolation that are equivalent to the problem of the optimal polymer in a strongly disordered environment (6). Our prediction of the self- generated quenched randomness ought to be observable in Eden growth and other random invasion processes. We begin with an alternative way to view the geometry of the polymer in a strongly disordered environment. We

A Quantitative Analysis of Chalk Pore Geometry Using Resin Casts

Abstract As a part of a wider study of the hydraulic properties of Upper Cretaceous chalk from East Yorkshire and the North Sea, a method of pore space casting is being employed. Thus, with the aid of the Scanning Electron Microscope it is possible to obtain by direct visual observation information about the shape and size of pores and grains, the connectiveness and roughness of pore channels, the presence of clay and silicate minerals, and other factors that together control fluid flow in porous rocks. A more detailed understanding of the nature of hydrocarbon or water-bearing rock is becoming increasingly important in pursuance of studies of oil exploration, oil exploitation, and geotechnics. In this paper a method of impregnation and casting the pore space in chalk is described, together with some preliminary observations of chalk pore geometry.