Immiscible Displacement in the Interacting Capillary Bundle Model Part II. Applications of Model and Comparison of Interacting and Non-Interacting Capillary Bundle Models

In the first part of this work (Dong et al., Transport Porous Media, 59, 1–18, 2005), an interacting capillary bundle model was developed for analysing immiscible displacement processes in porous media. In this paper, the second part of the work, the model is applied to analyse the fluid dynamics of immiscible displacements. The analysis includes: (1) free spontaneous imbibition, (2) the effects of injection rate and oil–water viscosity ratio on the displacement interface profile, and (3) the effect of oil–water viscosity ratio on the relative permeability curves. Analysis of a non-interacting tube bundle model is also presented for comparison. Because pressure equilibration between the capillaries is stipulated in the interacting capillary model, it is able to reproduce the behaviour of immiscible displacement observed in porous media which cannot be modelled by using non-interacting tube bundle models.     

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

Immiscible Displacement in the Interacting Capillary Bundle Model Part I. Development of Interacting Capillary Bundle Model

An interacting capillary bundle model is developed for analysing immiscible displacement processes in porous media. In this model, pressure equilibration among the capillaries is stipulated and capillary forces are included. This feature makes the model entirely different from the traditional tube bundle models in which fluids in different capillaries are independent of each other. In this work, displacements of a non-wetting phase by a wetting phase at different injection rates were analysed using the interacting capillary bundle model. The predicted evolutions of saturation profiles were consistent with both numerical simulation and experimental results for porous media reported in literature which cannot be re-produced with the non-interacting tube bundle models.     

A procedure to determine the viscosity function from experimental data of capillary flow

The accurate calculation of the viscosity η as function of the shear rate &γdot; from capillary viscometry is still a matter of debate in the literature. In fact, this problem involves the inversion of an integral equation, which leads to multiple solutions due to the unavoidable noise present in the experimental data. The purpose of this work is to develop an efficient procedure to determine the viscosity function from experimental data of capillary flow without presenting the difficulties inherent in other methods discussed previously in the literature. The system identification procedure is used here to estimate the parameters of a viscosity model, which is appropriately selected for the fluid under study through preliminary calculations involving the apparent shear rate – shear stress data. Once the model is chosen by satisfying criteria for the fit goodness and its parameters are evaluated, a smooth and continuous function η(γdot;) is obtained in the range of experimental shear rates. The procedure proposed is also applicable to fluids in shear flow that present two Newtonian plateaus, as it is typically found in macromolecular dilute solutions. The mean value theorem of continuous functions is used to reduce significantly the computational time. Received: 15 November 1999 Accepted: 7 November 2000     

Flow development of xanthan solutions in capillary rheometers

Flow experiments through capillaries with 0.2% xanthan in aqueous solution and 0.1 N NaCl brine were carried out to study the influence of the molecular conformation on the flow development at relatively low shear rates, from 20s^–1 to 400s^–1. Capillaries with a wide range of length-to-diameter ratios, L/D = 4.5 to 1015 were used.The apparent viscosity as a function of L/D at a constant shear rate shows a continuous decrement of the viscosity as L/D increases, until an asymptotic value is reached. The decrement in the apparent viscosity is partially explained in terms of slip. It was found that slip is a function of L/D as well as shear stress, i.e., slip develops during flow, thus inducing spatial anisotropy in the fluid until a stable state is reached. However, the substantial difference in apparent viscosity between short capillaries and capillaries longer than 300 D may be attributed to dominant elongational flow due to the contraction in the small capillaries and slip in long capillaries.The flow in a sufficiently long capillary can be divided in four regions rather than three, as is usually assumed. In the first region, which corresponds to the entry, elongational and shear flow coexist and elongational flow dominant. In the second region, end effects and slip development are coupled. In the third region the flow is fully developed and end effects are negligible. However, the fluid shows physical characteristics different from those of the fluid at rest, as a consequence of prior slip development. The fourth zone is the exit region in which the velocity rearranges due to the change of boundary conditions. The length of each region depends on the conformation of the macromolecules and shear rate. In addition, it was found that the stiffness of xanthan increases with the increase of the ionic strength.Finally, a performance of Bagley's analysis in the whole range of L/D studied showed that the use of the Bagley correction is not a reliable way to correct for end effects when the flow is not fully developed and/or in the presence of slip.Dedicated to Arthur S. Lodge at the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Poromechanical Modelling and Inverse Approach of Drying Tests on Weakly Permeable Porous Rocks

The present paper deals with the determination of permeability in partially saturated conditions for weakly permeable porous rocks such as argillites or deep clayey formations. The level of permeability can be obtained via the measurements of transient weight loss of a sample submitted to a decrease in relative humidity imposed by saline solution in a hermetic chamber. An identification method based on simplified uncoupled 1D-linear and 1D-non-linear modelling was presented in a previous paper (Giraud et al. Trans Porous Media 69(2):259–280, 2006). The present paper takes into account generalized mass transfer phenomena such as Darcean advective transport of liquid and gas mixtures and Fickean diffusive transport of the vapour specie inside a gas mixture. Poromechanical coupling as well as 3D effects due to the geometry and finite dimensions of the tested samples are also covered by this approach. The coupled THM finite element computer code Code_Aster is then used to model the forward problem. The parameter identification procedure is based upon the solution of an inverse problem. The Levenberg–Marquardt algorithm was used for the problem of minimization. Comparisons between previous simplified 1D modelling and 2D-axisymmetrical coupled modelling show that the former method efficiently provides the correct order of magnitude of the level of permeability or the equivalent storage coefficients. Due to the boundary condition, the real 2D-axisymmetrical geometry of the sample must not be neglected if we are to obtain accurate results.     

Insights into the Relationships Among Capillary Pressure,Saturation, Interfacial Area and Relative Permeability Using Pore-Network Modeling

To gain insight in relationships among capillary pressure, interfacial area, saturation, and relative permeability in two-phase flow in porous media, we have developed two types of pore-network models. The first one, called tube model, has only one element type, namely pore throats. The second one is a sphere-and-tube model with both pore bodies and pore throats. We have shown that the two models produce distinctly different curves for capillary pressure and relative permeability. In particular, we find that the tube model cannot reproduce hysteresis. We have investigated some basic issues such as effect of network size, network dimension, and different trapping assumptions in the two networks. We have also obtained curves of fluid–fluid interfacial area versus saturation. We show that the trend of relationship between interfacial area and saturation is largely influenced by trapping assumptions. Through simulating primary and scanning drainage and imbibition cycles, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (P _c –S _w –a _nw ) points as well as to relative permeability, saturation, and interfacial area (k _r –S _w –a _nw ) points. The two fitted three-dimensional surfaces show very good correlation with the data points. We have fitted two different surfaces to P _c –S _w –a _nw points for drainage and imbibition separately. The two surfaces do not completely coincide. But, their mean absolute difference decreases with increasing overlap in the statistical distributions of pore bodies and pore throats. We have shown that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure–saturation (P _c –S _w ) and the relative permeability–saturation (k _r –S _w ) curves.     

Simultaneous determination of shear and extensional viscosities and wall slip by on-line rheometry with parameter fitting: an application to EPDM rubber

Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence, are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C. Mean flow velocity in the capillaries was between 5 × 10⁻³ and 5 × 10⁻¹ m s⁻¹. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about 100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high extension rates (up to 800 s⁻¹) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion and optimization of die design.     

Topological Invariants in a Model of a Time-Delayed Chua's Circuit

In the last 30 years, some authors have been studying several classes of boundary value problems (BVP) for partial differential equations (PDE) using the method of reduction to obtain a difference equation with continuous argument which behavior is determined by the iteration of a one-dimensional (1D) map (see, for example, Romanenko, E. Yu. and Sharkovsky, A. N., International Journal of Bifurcation and Chaos 9(7), 1999, 1285–1306; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 5(5), 1995, 1419–1425; Sharkovsky, A. N., Analysis Mathematica Sil 13, 1999, 243–255; Sharkovsky, A. N., in “New Progress in Difference Equations”, Proceedings of the ICDEA'2001, Taylor and Francis, 2003, pp. 3–22; Sharkovsky, A. N., Deregel, Ph., and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Sharkovsky, A. N., Maistrenko, Yu. L., and Romanenko, E. Yu., Difference Equations and Their Applications, Kluwer, Dordrecht, 1993.). In this paper we consider the time-delayed Chua's circuit introduced in (Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668.) which behavior is determined by properties of one-dimensional map, see Sharkovsky, A. N., Deregel, Ph., and Chua, L. O., International Journal of Bifurcation and Chaos 5(5), 1995, 1283–1302; Maistrenko, Yu. L., Maistrenko, V. L., Vikul, S. I., and Chua, L. O., International Journal of Bifurcation and Chaos 5(3), 1995, 653–671; Sharkovsky, A. N., International Journal of Bifurcation and Chaos 4(5), 1994, 303–309; Sharkovsky, A. N., Maistrenko, Yu. L., Deregel, Ph., and Chua, L. O., Journal of Circuits, Systems and Computers 3(2), 1993, 645–668. To characterize the time-evolution of these circuits we can compute the topological entropy and to distinguish systems with equal topological entropy we introduce a second topological invariant.     

Nonequilibrium Effects During Spontaneous Imbibition

Accurate models of multiphase flow in porous media and predictions of oil recovery require a thorough understanding of the physics of fluid flow. Current simulators assume, generally, that local capillary equilibrium is reached instantaneously during any flow mode. Consequently, capillary pressure and relative permeability curves are functions solely of water saturation. In the case of imbibition, the assumption of instantaneous local capillary equilibrium allows the balance equations to be cast in the form of a self-similar, diffusion-like problem. Li et al. [J. Petrol. Sci. Eng. 39(3) (2003), 309–326] analyzed oil production data from spontaneous countercurrent imbibition experiments and inferred that they observed the self-similar behavior expected from the mathematical equations. Others (Barenblatt et al. [Soc. Petrol. Eng. J. 8(4) (2002), 409–416]; Silin and Patzek [Transport in Porous Media 54 (2004), 297–322]) assert that local equilibirum is not reached in porous media during spontaneous imbibition and nonequilibirium effects should be taken into account. Simulations and definitive experiments are conducted at core scale in this work to reveal unequivocally nonequilbirium effects. Experimental in-situ saturation data obtained with a computerized tomography scanner illustrate significant deviation from the numerical local-equilibrium based results. The data indicates: (i) capillary imbibition is an inherently nonequilibrium process and (ii) the traditional, multi-phase, reservoir simulation equations may not well represent the true physics of the process.     

Multibody Formulation with Large Bending Finite Elements (LBFE)

The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg. 49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg. 58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg. 13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering 32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech. 53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech. 53, 1986, 855–863].     

Elongational and shear rheology of carbon nanotube suspensions

Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.     

Analysis of capillary interaction and oil recovery under ultrasonic waves

Although, the effects of ultrasonic irradiation on multiphase flow through porous media have been studied in the past few decades, the physics of the acoustic interaction between fluid and rock is not yet well understood. Various mechanisms may be responsible for enhancing the flow of oil through porous media in the presence of an acoustic field. Capillary related mechanisms are peristaltic transport due to mechanical deformation of the pore walls, reduction of capillary forces due to the destruction of surface films generated across pore boundaries, coalescence of oil drops due to Bjerknes forces, oscillation and excitation of capillary trapped oil drops, forces generated by cavitating bubbles, and sonocapillary effects. Insight into the physical principles governing the mobilization of oil by ultrasonic waves is vital for developing and implementing novel techniques of oil extraction. This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation on capillary imbibition. Laboratory experiments were performed using cylindrical Berea sandstone and Indiana limestone samples with all sides (quasi-co-current imbibition), and only one side (counter-current imbibition) contacting with the aqueous phase. The oil saturated cores were placed in an ultrasonic bath, and brought into contact with the aqueous phase. The recovery rate due to capillary imbibition was monitored against time. Air–water, mineral oil–brine, mineral oil–surfactant solution and mineral oil-polymer solution experiments were run each exploring a separate physical process governing acoustic stimulation. Water–air imbibition tests isolate the effect of ultrasound on wettability, capillarity and density, while oil–brine imbibition experiments help outline the ultrasonic effect on viscosity and interfacial interaction between oil, rock and aqueous phase. We find that ultrasonic irradiation enhances capillary imbibition recovery of oil for various fluid pairs, and that such process is dependent on the interfacial tension and density of the fluids. Although more evidence is needed, some runs hint that wettability was not altered substantially under ultrasound. Preliminary analysis of the imbibition recoveries also suggests that ultrasound enhances surfactant solubility and reduce surfactant adsorption onto the rock matrix. Additionally, counter-current experiments involving kerosene and brine in epoxy coated Berea sandstone showed a dramatic decline in recovery. Therefore, the effectiveness of any ultrasonic application may strongly depend on the nature of interaction type, i.e., co- or counter-current flow. A modified form of an exponential model was employed to fit the recovery curves in an attempt to quantify the factors causing the incremental recovery by ultrasonic waves for different fluid pairs and rock types.     

基于水平集方法的毛管上升特征研究

毛管上升现象与许多行业密切相关，系统地对此现象进行研究具有重大意义。与传统理论研究方法不同，本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比，验证了模拟方法的可靠性。此外，详细地研究了毛管振荡现象，并分析了影响毛管振荡行为的主要因素。结果表明，水平集方法能够精确地表征毛管振荡现象，与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡，主要归结于非湿相气体的粘滞力作用；湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大，惯性力越大，促进了毛管振荡；而湿相粘度变大，会增大粘滞力作用，因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的，流体的惯性力是造成毛管振荡的主要原因，而粘滞力是减弱毛管振荡行为的主要因素，使液柱振荡逐渐衰减，并稳定至平衡高度。     

Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities

An idealized model of a porous rock consisting of a bundle of capillary tubes whose cross-sections are regular polygons is used to assess the importance of viscous coupling or lubrication during simultaneous oil-water flow. Fluids are nonuniformly distributed over tubes of different characteristic dimension because of the requirements of capillary equilibrium and the effect of interfacial viscosity at oil-water interfaces is considered. With these assumptions, we find that the importance of viscous coupling depends on the rheology of the oil-water interface. Where the interfacial shear viscosity is zero, viscous coupling leading to a dependence of oil relative permeability on oil-water viscosity ratio for viscosity ratios greater than one is important for a range of pore cross-section shapes and pore size distributions. For nonzero interfacial shear viscosity, viscous coupling is reduced. Using values reported in the literature for crude oil-brine systems, we find no viscous coupling.     

Notes on Groundwater Age in Forward and Inverse Modeling

Several example applications of the groundwater age equation are used to derive some basic results about age in aquifers and to draw linkages among published results involving temporal moments and aquifer–aquitard diffusive mass transfer. We then describe a brief numerical study of an inverse problem in which hydraulic conductivities are identified using both piezometric head and groundwater age data where inclusion of age data helps to reduce evidential nonuniqueness. This reflects the global representation of flow process contained in age data, and that the value of age data in inverse identification of flow properties depends on the paths taken by the sampled groundwater. Paper presented at PORO2007, the 7th North American Workshop on Applications of the Physics of Porous Media, Puerto Vallarta, Mexico, 2–6 November, 2007.     

The instron rheometer

The rheometer is based on an original design by the Monsanto Chemical Co., for the study of flow properties of polymer melts. Shear rates over the range 10¹ to 10⁶ reciprocal seconds are obtained by driving a plunger at constant rates through a barrel with interchangeable capillary tubes at the exit. The resulting shear stress is measured by the accurate load measuring system of the basic instrument.Errors due to the length to diameter ratio of the capillaries, plunger friction, polymer compressibility, temperature rise due to friction and pressure drop in the barrel, are discussed and correction methods suggested.Standard and special applications of the rheometer are discussed indicating that it can be used to determine factors other than apparent viscosity.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in Instron Application Series SA-3     

Effect of network topology on two-phase imbibition relative permeability

In a previous study Arns et al. (2004, Transport Porous Media 55, 21–46) we considered the role of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition displacements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore–throat and longer range spatial correlations.