Journal articles: 'Equivalent Capillary Radius' – Grafiati (2025)

Abstract:

Abstract The apparent viscosity of foam flowing through smooth capillaries was measured experimentally, and a mathematical model was developed. Foam texture (a measure of bubble volume) is a key parameter in determining the following properties of foam flowing through a capillary:whether the foam exists as bulk foam or as a chain of bubbles where each pair of bubbles is separated by an individual lamella,the number of lamellae per unit length of the capillary, andthe radius of curvature of the gas-liquid interface. The apparent viscosity is the sum of three contributions:that from slugs of liquid between bubbles,the resistance to deformation of the interface of a bubble passing through a capillary, andthe surface tension gradient that results when surface active material is swept from the front of a bubble and accumulates at the back of it. The sensitivity of both measured and calculated apparent viscosity is presented as a function of bubble size, capillary radius, ratio of bubble radius to capillary radius, velocity, quality, and surface tension gradient. Introduction An early conceptual model for the relative permeability of two-phase flow was the bundle of capillary tubes model. In this model, the wetting phase flowed in the smaller capillaries and the nonwetting phase flowed in the larger capillaries. The relationship between the flow rate and pressure drop in a capillary was described by the pressure drop in a capillary was described by the Hagen-Poiseuille law. The flow of a discontinuous nonwetting phase, such as a foam, cannot be described by the Hagen-Poiseuille law. The purpose of this investigation was to determine the relationship between flow rate and pressure drop for the flow of foam through a capillary. This relationship is described by an apparent viscosity that is required to modify the Hagen-Poiseuille law for the flow of foam. Our previous observations of flow of foam lamellae in transparent porous models showed that lamellae move from pore to pore by translation. Breaking and re-forming of lamellae were rare; so was bubble coalescence. These observations suggest that the apparent viscosity of foam or lamellae in uniform, smooth capillaries is related to and, indeed, is one component of the mobility of foam in porous media. A reasonable conceptual model of a natural porous medium is a bundle of interconnected capillaries of different sizes and containing constrictions. All capillary sections, or pores, near to one another have the same capillary pressure. Thus, phase saturations may differ from pore to pore, but the radii of curvature of the gas/ liquid interfaces are equal. When flow in such an array of capillaries is modeled, resistance to flow in parallel channels of both the same and different sizes is conceived to be in parallel. Flow in smooth, uniform pore sections is in series with flow through constrictions. The component of resistance owing to smooth, uniform pore sections is approximated by resistance to flow in smooth, uniform capillaries. Measurements and theory presented here show that the most important variable affecting foam viscosity in uniform, smooth capillaries is foam texture (bubble size). Foam of finer texture has more lamellae per unit length and, as a result, greater resistance to flow. This is true both for flow of bulk foam and series of lamellae. The principal factors affecting apparent viscosity of foam in uniform capillaries are dynamic changes at gas/liquid interfaces. These are illustrated in Fig. 1.Slugs of liquid between gas bubbles resist flow.Viscous and capillary forces result in interfaces that are deformed against the restoring force of surface tension. The extent of this deformation and the resulting bubble shape partially determine apparent viscosity as a function of flow rate.Another factor determining apparent viscosity as a function of velocity is expansion of the interface at the leading end of a bubble, accompanied by compression at the trailing end. This sweeping action causes surface active material to be depleted at the front and to accumulate at the back of the bubble. The result is a surface tension gradient that resists flow. Scaling of Foam Texture and Capillary Radius Since foam texture is a measure of the average volume or equivalent radius of its bubbles, one would expect that an important scale factor is the ratio of this equivalent radius to the equivalent radius of a porous medium or the radius of a capillary. This ratio can be expressed either as the wetted perimeter per unit area of the solid or as the number of lamellae per unit length of capillary. These quantities are denoted as nL and are referred to as the number of equivalent lamellae per unit length. This concept is illustrated in Fig. 2. SPEJ P. 176

Abstract:

Transport characteristics of capillary endothelia have been studied in numerous preparations. Little is known, however, regarding transport across the ultrastructurally similar arterial endothelium. The present studies describe a method for determining endothelial electrical resistance in the isolated, Ringer-perfused rabbit aorta. By use of silver-silver chloride electrodes, total resistance (RT) of the vessel wall was found to be 18.4 +/- 6.5 omega . cm2 (mean +/- SD; n = 10) in response to transmural passage of constant current pulses. After detergent removal of the endothelium, outer layer resistance (Rol) was 8.7 +/- 5.1 omega . cm2. Endothelial resistance (Re) was calculated to be 9.7 +/- 4.1 omega . cm2, since RT = Rol + Re. Combination of Re with previously measured hydraulic conductivity of this endothelium yielded an equivalent endothelial pore radius of 85 A, whereas a fractional pore area of 6.5 X 10(-4) was estimated from conductivity data. An alternative analysis demonstrated an endothelial slit width of 102 A. Re is similar to electrical resistances of leaky epithelia, frog mesenteric capillary, and frog muscle capillary, suggesting similar permeability characteristics in both arterial and capillary endothelia.

Abstract:

Albuminuria in nephrotic states is thought to arise from the formation of large pores in the glomerular capillary wall as large hydrodynamic probes, like Ficoll, have increased fractional clearance. In the present study, we tested for large pore formation in a novel manner. We accounted for the rates of plasma elimination as determined for tritium-labeled tracers of uncharged polydisperse Ficoll (radii range: 35–85 Å) and two globular 14C-labeled proteins, albumin (radius: 36 Å) and IgG (radius: 55 Å), in control and puromycin aminonucleoside nephrotic (PAN) Sprague-Dawley rats. The plasma elimination rates were then matched to the urinary excretion of these labeled materials ( n = 7). Albumin and IgG plasma retention rates were identical and far enhanced compared with the retention rates of inert transport markers of equivalent hydrodynamic radius; their elimination rate corresponded to the elimination of a 75-Å radius Ficoll ( n = 5) and >105-Å radius dextran ( n = 5). In PAN, they were eliminated as ∼36- and ∼55-Å radii Ficoll, respectively, equivalent to their hydrodynamic radii. In contrast, there was no comparable increase in the elimination rate of Ficoll in PAN. The total plasma clearance of Ficoll in control and PAN rats and the urinary clearance in PAN rats were essentially the same for all radii. On the other hand, the urinary clearance of >45-Å radii Ficoll in controls was considerably lower with increasing radii, demonstrating a postfiltration cellular uptake in controls, which, when inhibited in nephrotic states, would account for apparent large pore formation.

Abstract:

The permeability characteristics of the peritubular capillary membrane in the rat kidney were investigated on the basis of the transport of hippuran, inulin, myoglobin, horseradish peroxidase, albumin, and gamma-globulin from peritubular capillary blood to renal hilar lymph. Data obtained in a previous investigation on single-nephron plasma flow, filtration fraction, net driving force, and fluid reabsorption along the peritubular capillary were also used. The data were analyzed in a computer-based model taking into account the transport both by diffusion and by convection. The results show that the membrane contains a few large pores through which the plasma proteins leak out into the renal interstitium and a system of several smaller pores responsible for the fluid reabsorption. The mean equivalent radius of the large pores was estimated from the larger molecular probes to be approximately 180 A (range 150-225 A), and the corresponding total pore area over pore length was estimated at 3 X 10(-4) cm (range 6 X 10(-4) to 1 X 10(-4) cm). The small-pore system was analyzed from the transport of hippuran, inulin, and myoglobin and from fluid reabsorption and showed a pore radius of somewhat below 20 A and pore areas over pore length of 50 cm. Here, the fluid reabsorption and the transport of hippuran turned out to be a sensitive marker of the pore area and the transport of inulin and myoglobin of the pore radius.

Abstract:

The multiple-indicator dilution technique was used to investigate the permeability characteristics of capillaries in the cat small intestine during hypoxia. Reducing the arterial oxygen tension from 108 to 35 mmHg for 10 min increased the calculated equivalent pore radius of intestinal capillaries from 59 to 67 A. This effect was sustained for at least 15 min after the hypoxic episode. Hypoxia did not alter intestinal lymphatic protein clearance. Thus, the dimensions of the large pores did not change. This study demonstrates that 10 min of severe hypoxia increases vascular permeability in the small intestine and that this change occurs only in the small pores and is sustained, at least briefly, after restoration of normoxia. Hypoxia does not significantly change the permeability to macromolecules.

Abstract:

The steady axisymmetric flow of viscous liquid relative to a gas bubble due to its buoyancy-driven motion in a round tube is computed by solving the nonlinear Navier–Stokes equations using a Galerkin finite-element method with a boundary-fitted mesh. When the bubble is relatively small compared with the tube size (e.g. the volume-equivalent radius of the bubble is less than a quarter of the tube radius R), the bubble exhibits similar behaviour to one moving in an extended liquid, developing a spherical-cap shape with increasing Reynolds number (Re) if the capillary number is not too small. The long-bubble (also known as a Taylor bubble) characteristics can be observed with bubbles of volume-equivalent radius greater than the tube radius, especially when the surface tension effect is relatively weak (e.g. for Weber number We greater than unity). The computed values of Froude number Fr for most cases agree well with the correlation formulae derived from experimental data for long bubbles, and even with (short) bubbles of volume-equivalent radius three-quarters of the tube radius. All of the computed surface profiles of long bubbles exhibit a prolate-like nose shape, yet various tail shapes can be obtained by adjusting the parameter values of Re and We. At large Weber number (e.g. We=10), the bubble tail forms a concave profile with a gas ‘cup’ developed at small Re and a ‘skirt’ at large Re with sharply curved rims. For We≤1, the bubble tail profile appears rounded without large local curvatures, although a slightly concave tail may develop at large Re. non-uniform annular film adjacent to the tube wall is commonly observed when Weber number is small, especially for bubbles of volume <3πR3, suggesting that the surface tension effect can play a complicated role. Nonetheless the computed value of Fr is found to be generally independent of the bubble length for bubbles of volume-equivalent radius greater than the tube radius. If the bubble length reaches about 2.5 tube radii, the value of its frontal radius becomes basically the same as that for long bubbles of much larger volume. An examination of the distribution of the z-component of traction along the bubble surface reveals the basic mechanism for long bubbles rising at a terminal velocity that is independent of bubble volume.

Abstract:

Hydrocarbon reservoirs with a large column height as well as tight gas rocks require a large range of capillary pressures to describe the saturation of fluids present in these formations. While mercury injection capillary pressure (MICP) can achieve high equivalent capillary pressures, the tests are destructive to the core plugs. Centrifuge techniques have gained in popularity since they are faster than the porous plate technique, but they are limited in the achievable pressure range. Here, we propose the use of fluorinated oils to extend the achievable capillary pressure of the air-brine centrifuge technique by a factor of two. We use Fluorinert FC-70 in an inverted bucket configuration which doubles the radius of rotation and keeps the density contrast comparable to an air-brine system. Furthermore, we show the application to NMR T2 cut-off determination as a function of capillary pressure. Since Fluorinert does not contain any hydrogen, there is no signal overlapping with the brine in the core plugs. Furthermore, in the inverted bucket configuration, the outlet face of the plug is not in contact with a drainage surface so that the Hassler-Brunner boundary condition of Pc = 0 is satisfied. Additionally, the method allows the storage under a liquid Fluorinert phase, which prevents evaporation and significantly extends the available time for NMR measurements at low water saturations.

Abstract:

The steady axisymmetric behaviour of a relatively small bubble moving with a flowing liquid in a straight round tube is studied by computationally solving the nonlinear Navier–Stokes equations, using a Galerkin finite-element method with boundary-fitted mesh, for wide ranges of capillary number C a and Reynolds number R e . Here a bubble is considered relatively small when its volume-equivalent radius is less than that of the tube. At small values of R e , the velocity of a bubble increases with bubble size for large values of C a but decreases with bubble size for small values of C a . At large values of R e , however, a bubble of large size appears to move at a slower velocity for any given value of C a . When R e is large (e.g. R e = 100) and C a > 0.1, a bubble of radius greater than half of the tube radius moves at a velocity that seems to be independent of bubble size. The strong inertial effect at large R e makes a small bubble of radius greater than a quarter of the tube radius to deform into a noticeable oblate shape as C a increases from very small value, and then to be elongated into a bullet shape with further increasing C a after C a reaches an intermediate value. Even very small bubbles (e.g. of radius equal to one-tenth of the tube radius) can still be significantly deformed provided that the value of C a is adequately large. Despite significant shape deformations that may still occur, bubbles of radius less than a quarter of that of the tube almost always move at the same velocity as that of the local liquid flow at the tube centreline (i.e. twice that of the average liquid velocity), regardless the values of R e and C a . This fact suggests that very small bubbles are basically carried by the local liquid flow.

Abstract:

Polydisperse mixtures of dextran or Ficoll have been frequently used as molecular probes for studies of glomerular permselectivity because they are largely inert and not processed (reabsorbed) by the proximal tubules. However, dextrans are linear, flexible molecules, which apparently are hyperpermeable across the glomerular barrier. By contrast, the Ficoll molecule is almost spherical. Still, there is ample evidence that Ficoll fractional clearances (sieving coefficients) across the glomerular capillary wall (GCW) are markedly higher than those for neutral globular proteins of an equivalent in vitro Stokes-Einstein (SE) radius. Physical data, obtained by “crowding” experiments or measurements of intrinsic viscosity, suggest that the Ficoll molecule exhibits a rather open, deformable structure and thus deviates from an ideally hard sphere. This is also indicated from the relationship between (log) in vitro SE radius and (log) molecular weight (MW). Whereas globular proteins seem to behave in a way similar to hydrated hard spheres, polydisperse dextran and Ficoll exhibit in vitro SE radii that are much larger than those for compact spherical molecules of equivalent MW. For dextran, this can be partially explained by a high-molecular-size asymmetry. However, for Ficoll the explanation may be that the Ficoll molecule is more flexible (deformable) than are globular proteins. An increased compressibility of Ficoll and an increased deformability and size asymmetry for dextran may be the explanation for the fact that the permeability of the GCW is significantly higher when assessed using polysaccharides such as Ficoll or dextran compared with that obtained using globular proteins as molecular size probes. We suggest that molecular deformability, besides molecular size, shape, and charge, plays a crucial role in determining the glomerular permeability to molecules of different species.

Abstract:

This paper specifically addresses the effect of the sintering temperature curve in manufacturing nickel powder capillary structure (wick) for a loop heat pipe (LHP) with flat evaporator. The sintering temperature curve is composed of three regions: a region of increasing temperature, a region of constant temperature, and a region of decreasing temperature. The most important region is the increasing temperature region, as the rate of temperature increase directly affects the performance of the wick.When the slope of the region of increasing temperature is 0.8 (equivalent to 8 OC/min), the structure of the manufactured wick is complete, with the best heat transfer performance result. Experimental resultsshowed that the optimal heat transfer performance is 160W, the minimal total thermal resistance is approximately 0.43OC/W, and the heat flux is 17W/cm2; the optimal wick manufactured has an effective pore radius of 5.2 μm, a permeability of 5.9×10-13m2, and a porosity of 64%.

Abstract:

In this paper, firstly, the X-ray micro computed tomography (micro-CT) is used for the analysis of internal structure of sand-packed beds. Binary data which are able to describe the pore structures of these beds were obtained from a series of imaging processing of rescaling, media filtering, and thresholding. Then a Maximal Ball (MB) algorithm is applied to these binary data to extract the equivalent pore networks. The parameters of the pore networks, such as radius, coordination number and shape factors of pore and throat are computed. The results demonstrate that the MB method can extract reasonable and faithful pore network of the different sand packed samples. Finally, the relative permeability and capillary pressure of drainage and imbibition cycle of water and oil are predicated. The numerical simulation results demonstrated good accordance with that of the experiments. Pore network simulation shows good results for two phase flow in porous media.

Abstract:

In this study, our goal is to identify the interaction between airway lining fluid viscous and surface forces and parenchymal tethering forces during pulmonary airway reopening. The type of closure we modeled occurs when the airway walls and surrounding parenchyma collapse and are held in apposition by the lining fluid. We mimicked this system with a polyethylene tube coated with a Newtonian lining fluid supported by open-cell foam. Reopening occurs when a finger of air travels through the collapsed region. We measured the airway pressure (Paw) required to open the airway at a constant velocity (U). Increasing the foam stiffness (K), lining fluid viscosity (mu), and surface tension (gamma) results in an increase in Paw. Furthermore, increasing the downstream suction pressure (Pds), through tethering, causes an equivalent reduction in Paw. The upstream radius is the primary length scale, and fluid forces are represented by the capillary number: Ca = microU/gamma. On the basis of these results, we predicted the likelihood that tethering would begin to reopen collapsed airways in various disease states. This analysis showed that the ratio of tethering to fluid forces determines airway patency, which is defined as follows: lambda = PTrans/(gamma/R), where PTrans = Paw-Pds and R is airway radius. Finally, lung volume-dependent surface tension appears to be necessary to stabilize the lung.

Abstract:

A closed-form analytic solution for the motion of axisymmetric rigid pellets suspended in a Newtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. The analysis is motivated by its possible relevance to the rheology of blood in the microcirculation wherein the endothelial-cell glycocalyx – a carbohydrate-rich coat of macromolecules consisting of proteoglycans and glycoproteins expressed on the luminal surface of the capillary wall – might exhibit similar behaviour to the wall layer modelled here. Estimates of the permeability of the glycocalyx are taken from experimental data for fibrinogen gels formed in vitro. In a tube without pellets lined with a porous wall layer having a thickness which is 15% of the tube radius and having a permeability in the range of fibrinogen gels, approximately a 70% greater pressure drop is required to achieve the same volume flow as would occur in an equivalent smooth-walled tube without a wall layer. If, in the presence of this same wall layer, a rigid spherical pellet is introduced which is 99.5% of the free-lumen radius, the apparent viscosity increases by as much as a factor of four with a concomitant reduction in tube hematocrit of about 10% relative to the corresponding values in an equivalent smooth-walled tube having the same sphere-to-tube diameter ratio without a wall layer.

Abstract:

Osmotic transient responses in organ weight after changes in perfusate osmolarity have implied steric hindrance to small-molecule transcapillary exchange, but tracer methods do not. We obtained osmotic weight transient data in isolated, Ringer-perfused rabbit hearts with NaCl, urea, glucose, sucrose, raffinose, inulin, and albumin and analyzed the data with a new anatomically and physicochemically based model accounting for 1) transendothelial water flux, 2) two sizes of porous passages across the capillary wall, 3) axial intracapillary concentration gradients, and 4) water fluxes between myocytes and interstitium. During steady-state conditions ∼28% of the transcapillary water flux going to form lymph was through the endothelial cell membranes [capillary hydraulic conductivity ( Lp) = 1.8 ± 0.6 × 10–8 cm · s–1 · mmHg–1], presumably mainly through aquaporin channels. The interendothelial clefts (with Lp = 4.4 ± 1.3 × 10–8 cm · s–1 · mmHg–1) account for 67% of the water flux; clefts are so wide (equivalent pore radius was 7 ± 0.2 nm, covering ∼0.02% of the capillary surface area) that there is no apparent hindrance for molecules as large as raffinose. Infrequent large pores account for the remaining 5% of the flux. During osmotic transients due to 30 mM increases in concentrations of small solutes, the transendothelial water flux was in the opposite direction and almost 800 times as large and was entirely transendothelial because no solute gradient forms across the pores. During albumin transients, gradients persisted for long times because albumin does not permeate small pores; the water fluxes per milliosmolar osmolarity change were 200 times larger than steady-state water flux. The analysis completely reconciles data from osmotic transient, tracer dilution, and lymph sampling techniques.

Abstract:

The classic analysis by Anderson and Malone ( Biophys J 14: 957–982, 1974) of the osmotic flow across membranes with long circular cylindrical pores is extended to a fiber matrix layer wherein the confining boundaries are the fibers themselves. The equivalent of the well-known result for the reflection coefficient σ0 = (1 − φ)2, where φ is the partition coefficient, is derived for a periodic fiber array of hexagonally ordered core proteins. The boundary value problem for the potential energy function describing the solute distribution surrounding each fiber is solved by defining an equivalent fluid annulus in which the pressures and osmotic forces are determined. This model is of special interest in the osmotic flow of water across a capillary wall, where recent experimental studies suggest that the endothelial glycocalyx is a quasiperiodic fiber array that serves as the primary molecular sieve for plasma proteins. Results for the reflection coefficient are presented in terms of two dimensionless numbers, α = a/ R and β = b/ R, where a and b are the solute and fiber radii, respectively, and R is the outer radius of the fluid annulus. In general, the results differ substantially from the classic expression for a circular pore because of the large difference in the shape of the boundary along which the osmotic force is generated. However, as in circular pore theory, one finds that the reflection coefficients for osmosis and filtration are the same.

Abstract:

Equivalent Radius (EQR) is a relatively new normalized capillary pressure method for modeling of the saturation height function. In this method petrophysical data such as well logs, special and routine core analysis have been used in an integrated manner. The main purpose of this study is to investigate dynamic behavior of the fluid flow through porous media with a new integrated technique for saturation height function modeling. Amongst different methods, EQR method that originally developed by Engstrom in 1996 has been selected for further study. Although this method can model the initial water saturation with high accuracy but it only can be applicable for low permeability formations. However, there is still an incomplete understanding its application for other rock units with higher degree of porosity and permeability. For this purpose, we present a Modified EQR (MEQR) based on iterative curve fitting procedure. To demonstrate the capabilities of MEQR method, one of the Iranian oil field data located in southwest of Iran with quite high degree of permeability in its porous sandstone layers has been used. It is shown that this technique can accurately predict the initial water saturation in all rock types and in each cell of the reservoir with very good correlation coefficient achieved in comparison with interpreted saturation well logs.

Abstract:

Quantitative ultrastructural analyses were performed on red (oxidative) and white (glycolytic) skeletal muscles from two species of antarctic fish to identify features of subcellular structure that may be related to muscle metabolism at cold body temperature. Trematomus newnesi (Boulenger) is an active pelagic species and Notothenia gibberifrons (Lönnberg) is a sluggish bottom-dweller. White fibres of both species are poorly vascularized [capillary density, NA(c,f), for T. newnesi 73.9±11.3mm−2; for N. gibberifrons is 76.0±14.1mm−2], and have low percentages of cell volume occupied by mitochondria [volume density, Vv(mit,f), for T. newnesi is 0.014±0.005; for N. gibberifrons is 0.006±0.003]. Ultrastructure of oxidative fibres in both species resembles that of cold-acclimated temperate-zone fishes. Mitochondrial volume densities of red fibres reflect differences in ecotype between species [Vv(mit,f) for T. newnesi is 0.348±0.012; for N. gibberifrons is 0.249±0.007]. The less clustered array of mitochondria in oxidative fibres of T. newnesi compared with N. gibberifrons may support an equivalent flux of aqueous metabolites between mitochondrial and cytoplasmic compartments, despite a greater mean intracellular diffusion distance (τh) between these compartments in T. newnesi than in N. gibberifrons (τh=1.05±0.07μm and 0.77±0.06μm, respectively). Although Vv(mit.)) is higher in red fibres of the active species, capillary supply is less extensive [capillary length density, Jv(c,f), for T. newnesi is 481.3±49.0mm mm−3; N. gibberifrons is 696.3±33.7mm mm−3] and the maximal diffusion-distance for oxygen is greater in T. newnesi than in N. gibberifrons (Krogh's radius, R=26.3±1.64μm and 21.5±0.51μm, respectively). A mismatch appears to exist between oxygen supply [Jv(c,f)] and oxygen demand [Vv(mit,f)] in T. newnesi red fibres in view of published data for other fishes. The twofold higher volume density of lipid [Vv(lip,f)] in T. newnesi compared with N. gibberifrons may resolve this paradox [Vv(lip,f) is 0.026±0.002 and 0.012±0.004, respectively]. Because oxygen is at least four times more soluble in lipid than in aqueous cytoplasm, lipid may enhance oxygen flux through oxidative muscle and play a role similar to myoglobin in these myoglobin-poor fishes.

Abstract:

Summary The main purpose of the present work is to predict the permeability of a porous medium from its three-dimensional (3D) porous structure network. In this work, 3D porous structure is reconstructed by the truncated Gaussian method using Fourier transform and starting from a 2D binary image obtained from a thin section of a porous sample. The skeleton of the 3D porous structure provides a way of visualizing the graph of the pore network. It is determined using a thinning algorithm, which is conceived to preserve topology. It gives both visual and quantitative information about the connectivity of the pore space, the coordination number for every node and local hydraulic radius. Once the network of the pore structure is obtained, the macroscopic transport properties, such as the permeability, can be predicted. The method is applied to a 500 mD Berea sandstone and the predicted permeability is in good agreement with the experimental value and empirical correlations. Introduction The prediction of equilibrium and transport properties of porous media is a long-standing problem of great theoretical and practical interest, particularly in petroleum reservoir engineering.1 Past theoretical attempts to derive macroscopic transport coefficients from the microstructure of porous media entailed a simplified representation of the pore space, often as a bundle of capillary tubes.1–3 These models have been widely applied because of their convenience and familiarity to the engineers. But they do have some limitations. For example, they are not well suited for describing the effect of the pore space interconnectivity and long range correlation in the system. Network models have been advanced to describe phenomena at the microscopic level and have been extended in the last few years to describe various phenomena at the macroscopic level. These models are mostly based on a network representation of the porous media in which larger pores (pore bodies) are connected by narrower pores (pore throats). Network models represent the most important and widely used class of geometric models for porous media.2 A network is a graph consisting of a set of nodes or sites connected by a set of links or bonds. The nodes can be chosen deterministically or randomly as in the realization of a Poisson or other stochastic point process. Similarly the links connecting different nodes may be chosen according to some deterministic or random procedure. Finally, the nodes are dressed with convex sets such as spheres representing pore bodies, and the bonds are dressed with tubes providing a connecting path between the pore bodies. The original idea of representing a porous structure by a network is rather old, but it was only in the early 1980s that systematic and rigorous procedures were developed to map, in principle, any disordered rock onto an equivalent random network of bonds and sites. Once this mapping is complete one can study a given phenomenon in porous media in great detail.3 Dullien1 reviewed the details of various pore-scale processes, including detailed descriptions of many aspects of network models. The most important features of pore network geometry and topology that affect fluid distribution and flow in reservoir rocks are the pore throat and pore body size distributions, the pore body-to-pore throat size aspect ratio and the pore body coordination number.4 These data have been tentatively assumed in the previous works. The extension of these techniques to real porous media has been complicated by the difficulty in describing the complex three-dimensional (3D) pore structure of real porous rocks. Information about the pore structure of reservoir rocks is often obtained from mercury intrusion and sorption isotherm. Mercury intrusion and sorption isotherm data provide statistical information about the pore throat size distribution, or, more correctly, the distribution of the volumes that may be invaded within specified pore throat sizes. Advanced techniques such as microcomputed tomography5 and serial sectioning6,7 do provide a detailed description of the 3D pore structures of rocks. Recently, image analysis methods used over pictures of highly polished surfaces of porous materials (e.g., Refs. 8-10), taken with an electron scanning microscope have been used to describe the porous structure. Image analysis techniques such as opening (2D and 3D)11,13 and median line graphs (2D)13 were developed. Information on porous structure is obtained from the analysis of 2D binary images. For isotropic media, a 3D microstructure may be reconstructed from any statistically homogeneous 2D section. The general objective of a reconstructed porous structure is to mimic more closely the geometry of real media. This method has been previously applied to the prediction of important petrophysical and reservoir engineering properties, such as permeability8 and formation factor14 with reasonable success. Thovert et al.15 used the reconstructed porous structure and developed thinning algorithms to obtain the graph of the 3D pore structure. Some topological characteristics such as the number of loops were derived. Bakke and O/ren16 generated 3D pore networks based on numerical modeling of the main sandstone forming geological processes. Absolute and relative permeability were computed for a Bentheimer sandstone. However, although their algorithms worked well on their models, the problem of connectivity preservation for a 3D thinning algorithm appears to be only correctly taken into account by Ma,17 who proposed sufficient conditions for providing a 3D thinning algorithm to preserve connectivity.

Abstract:

In capillary flow, integral momentum approach is used to derive the governing equation, which requires an expression for the pressure field at the inlet of the capillary. Generally, the pressure field for circular capillary is deduced with hemispherical control volume. This expression has been extended for other noncircular capillaries with an equivalent radius approximation. In case of high aspect ratio channels, the semicylindrical control volume needs to be considered. In the present study, the correct expression for the entrance pressure field for high aspect ratio capillaries is derived with such appropriate control volume.

Abstract:

AbstractPore network modeling (PNM) has been widely investigated in the study of multiphase transport in porous media due to its high computational efficiency. The advantage of PNM is achieved in part at the cost of using simplified geometrical elements. Therefore, the validation of pore network modeling needs further verification. A Shan-Chen (SC) multiphase lattice Boltzmann model (LBM) was used to simulate the multiphase flow and provided as the benchmark. PNM using different definitions of throat radius was performed and compared. The results showed that the capillary pressure and saturation curves agreed well when throat radius was calculated using the area-equivalent radius. The discrepancy of predicted phase occupations from different methods was compared in slice images and the reason can be attributed to the capillary pressure gradients demonstrated in LBM. Finally, the relative permeability was also predicted using PNM and provided acceptable predictions when compared with the results using single-phase LBM.

Abstract:

This study focus on saturation evaluation of Chang 8 tight sandstone reservoir in Longdong West area of Ordos Basin, China. An improved saturation calculation method was proposed based on the equivalent rock capillary bundle theory. Firstly, according to characteristics of reservoir pore structure and rock conductivity, the conductive space of reservoir rock is equivalent to the parallel conductive of micro capillary bundle representing the micro pores and the coarse capillary bundle representing the macro pores. Then, the variable cementation index(m) saturation model was deduced by using Poiseuille flow equation and Darcy's law. During the calculation of model parameters, the T2 spectrum data of nuclear magnetic resonance (NMR) was used to calculate the equivalent radius of reservoir micro pores and macro pores, which ensured the ability of model popularization and application. Finally, the proposed saturation calculation method is applied to reservoir evaluation of the study area, and compared with the classical Archie saturation model. The application effect shows that the calculated saturation from the proposed variable m model is much closer to the sealed coring data than that from classical Archie model, and the average relative error of saturation calculated by the variable m model is within 7%, which proves that the proposed saturation calculation method is applicable and effective.

Abstract:

A lattice model of liquid crystalline microstructure has been developed. It provides the basis for the three-dimensional solution of the Frank elasticity equations for given boundary conditions while, in addition, providing a mechanistic representation of the development of texture as the microstructure relaxes with time. It is also able to represent disclination motion and the processes associated with their interaction. In particular, it has been used to study (s = ± 1/2) disclination loops, both those described by a single rotation vector, 17, and those in which 17 has a constant angular relationship with the loop line and are equivalent to a point singularity at a distance much larger than the loop radius. The application of the model to disclinations of unit strength, which are unstable both energetically and topologically, has shown that the decomposition into two 1/2 strength lines of lower total energy occurs much more readily than topological escape in the third dimension. The implication for structures observed in capillary tubes is discussed. The influence on microstructure of a splay constant much higher than that of twist or bend is explored in the context of main-chain liquid crystalline polymers, in particular, the stabilization of tangential +1 lines under such conditions is predicted in accord with observed microstructural features.