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1.
We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r1−n, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t(1−n)/(3−n), where t is the time. 相似文献
2.
Degassing and in situ development of a mobile gas phase takes place when an aqueous phase equilibrated with a gas at a pressure higher than the subsurface pressure is injected in water-saturated porous media. This process, which has been termed supersaturated water injection (SWI), is a novel and hitherto unexplored means of introducing a gas phase in the subsurface. We give herein a first macroscopic account of the SWI process on the basis of continuum scale simulations and column experiments with CO2 as the dissolved gas. A published empirical mass transfer correlation [Nambi IM, Powers SE. Mass transfer correlations for nonaqueous phase liquid dissolution from regions with high initial saturations. Water Resour Res 2003;39(2):1030. doi:10.1029/2001WR000667] is found to adequately describe non-equilibrium transfer of CO2 between the aqueous and gas phases. Remarkably, the dynamics of gas-water two-phase flow, observed in a series of SWI experiments in homogeneous columns packed with silica sand or glass beads, are accurately predicted by traditional two-phase flow theory and the corresponding gas relative permeability is determined. A key consequence of this finding, namely that the displacement of the aqueous phase by gas is compact at the macroscopic scale, is consistent with pore scale simulations of repeated mobilization, fragmentation and coalescence of large gas clusters (i.e., large ganglion dynamics) driven entirely by mass transfer. The significance of this finding for the efficient delivery of a gas phase below the water table is discussed in connection to the alternative process of in situ air sparging, and potential advantages of SWI are highlighted. 相似文献
3.
CO2 injection and storage in deep saline aquifers involves many coupled processes, including multiphase flow, heat and mass transport, rock deformation and mineral precipitation and dissolution. Coupling is especially critical in carbonate aquifers, where minerals will tend to dissolve in response to the dissolution of CO2 into the brine. The resulting neutralization will drive further dissolution of both CO2 and calcite. This suggests that large cavities may be formed and that proper simulation may require full coupling of reactive transport and multiphase flow. We show that solving the latter may suffice whenever two requirements are met: (1) all reactions can be assumed to occur in equilibrium and (2) the chemical system can be calculated as a function of the state variables of the multiphase flow model (i.e., liquid and gas pressure, and temperature). We redefine the components of multiphase flow codes (traditionally, water and CO2), so that they are conservative for all reactions of the chemical system. This requires modifying the traditional constitutive relationships of the multiphase flow codes, but yields the concentrations of all species and all reaction rates by simply performing speciation and mass balance calculations at the end of each time step. We applied this method to the H2O–CO2–Na–Cl–CaCO3 system, so as to model CO2 injection into a carbonate aquifer containing brine. Results were very similar to those obtained with traditional formulations, which implies that full coupling of reactive transport and multi-phase flow is not really needed for this kind of systems, but the resulting simplifications may make it advisable even for cases where the above requirements are not met. Regarding the behavior of carbonate rocks, we find that porosity development near the injection well is small because of the low solubility of calcite. Moreover, dissolution concentrates at the front of the advancing CO2 plume because the brine below the plume tends to reach high CO2 concentrations quite rapidly. We conclude that carbonate dissolution needs not to be feared. 相似文献
4.
5.
The standard approach for geologic storage of CO2 consists of injecting it as a supercritical CO2 phase. This approach places stringent requirements on the caprock, which must display: (1) high entry pressure to prevent the buoyancy driven upwards escape of CO2; (2) low permeability to minimize the upwards flux of brine displaced by the CO2; and (3) high strength to ensure that pressure build up does not cause caprock failure. We propose an alternative approach for cases when the above requirements are not met. The approach consists of extracting brine from the storage formation and then re-injecting it so that it mixes with CO2 at depth in the injection well. Mixing at depth reduces the pressure required for brine and CO2 at the surface. This CO2-saturated brine will sink to the aquifer bottom because it is denser than resident brine, which eliminates the risk of buoyant escape of CO2. The method is particularly favorable when the aquifer dips, because CO2-saturated brine will tend to flow downslope. We perform two- and three-dimensional numerical simulations to study how far upslope the extraction well needs to be located to ensure a very long operation without CO2 ever breaking through. Several sets of simulations were carried out to evaluate the effect of slope, temperature, pressure and CO2 concentration, which is significantly reduced if flue gas (i.e., without capture) is mixed with the brine. We analyze energy requirements to find that the system requires high permeability to be viable, but its performance is improved by taking advantage of the thermal energy of the extracted brine. 相似文献
6.
Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required. 相似文献
7.
This study presents a new unsteady-state method for measuring two-phase relative permeability by obtaining local values of the three key parameters (saturation, pressure drop, and phase flux) versus time during a displacement. These three parameters can be substituted to two-phase Darcy Buckingham equation to directly determine relative permeability. To obtain the first two, we use a medical X-ray Computed Tomography (CT) scanner to monitor saturation in time and space, and six differential pressure transducers to measure the overall pressure drop and the pressure drops of five individual sections (divided by four pressure taps on the core) continuously. At each scanning time, the local phase flux is obtained by spatially integrating the saturation profile and converting this to the flux using a fractional flow framework. One advantage of this local method over most previous methods is that the capillary end effect is experimentally avoided; this improvement is crucial for experiments using low viscosity fluids such as supercritical and gas phases. To illustrate the new method, we conduct five CO2-brine primary drainage experiments in a 60.8 cm long and 116 mD Berea sandstone core at 20 °C and 1500 psi. In return, we obtain hundreds of unsteady-state CO2 and brine relative permeability data points that are consistent with steady-state relative permeability data from the same experiments. Due to the large amount of relative permeability data obtained by the new unsteady-state method, the uncertainties of the exponents in the Corey-type fits decrease by up to 90% compared with the steady-state method. 相似文献
8.
Prediction of CO2 injection performance in deep subsurface porous media relies on the ability of the well to maintain high flow rates of carbon dioxide during several decades typically without fracturing the host formation or damaging the well. Dynamics of solid particulate suspensions in permeable media are recognized as one major factor leading to injection well plugging in sandstones. The invading supercritical liquid-like fluid can contain exogenous fine suspensions or endogenous particles generated in situ by physical and chemical interactions or hydrodynamic release mechanisms. Suspended solids can plug the pores possibly leading to formation damage and permeability reduction in the vicinity of the injector. In this study we developed a finite volume simulator to predict the injectivity decline near CO2 injection wells and also for production wells in the context of enhanced oil recovery. The numerical model solves a system of two coupled sets of finite volume equations corresponding to the pressure-saturation two-phase flow, and a second subsystem of solute and particle convection-diffusion equations. Particle transport equations are subject to mechanistic rate laws of colloidal, hydrodynamic release from pore surfaces, blocking in pore bodies and pore throats, and interphase particle transfer. The model was validated against available laboratory experiments at the core scale. Example results reveal that lower CO2 residual saturation and formation porosity enhance CO2-wet particle mobility and clogging around sinks and production wells. We conclude from more realistic simulations with heterogeneous permeability spanning several orders of magnitude that the control mode of mobilization, capture of particles, and permeability reduction processes strongly depends on the type of permeability distribution and connectivity between injection and production wells. 相似文献
9.
Brine migration and saltwater intrusion into freshwater aquifers are among the hazards which may result from injecting CO2 into deep saline formations. Comprehensive risk assessment should include estimates of the salinization of freshwater aquifers, preferably based on numerical simulation results. A crucial task is to choose an appropriate conceptual model and relevant scenarios. Overly conservative assumptions may lead to estimation of unacceptably high risks, and thus prevent the implementation of a CO2 storage project unnecessarily. On the other hand, risk assessment should not lead to an underestimation of hazards. This study compares two conceptual model approaches for the numerical simulation of brine-migration scenarios through a vertical fault and salt intrusion into a fresh water aquifer. The first approach calculates salt discharge into freshwater using an immiscible two-phase model with constant salinity in the brine phase. The second approach takes compositional effects into account and considers salinity as a variable parameter in the water phase. A spatial model coupling is introduced to adapt the increased model complexity to the required complexity of the physics. The immiscible two-phase model is applied in the CO2 storage reservoir and spatially coupled to a single-phase (water) two-component (water, salt) model, where salt mass fraction is a variable. A Dirichlet–Neumann technique is used for the coupling conditions at the interface of the two models. The results show that the predicted salt discharges can vary by orders of magnitude depending on the choice of the model. The implications of the results for risk assessment are discussed. 相似文献
10.
《水文科学杂志》2013,58(4):626-641
Abstract An analytical solution of planar flow in a sloping soil layer described by the linearized extended Boussinesq equation is presented. The solution consists of the sum of steady-state and transient-series solutions, the latter in a separation-of-variables form, and can satisfy an arbitrary initial condition via collocation; this feature reduces the number of series terms, making the solution efficient. Key parameter is the dimensionless linearization depth η o (R), R being the dimensionless recharge. The variable η o (R), not the slope, characterizes the flow as kinematic or diffusive, and R ≈ 0.2 demarcates the two regimes. The transient series converges rapidly for large η o (large R, near-diffusive flow) and slowly as η o → 0 (kinematic flow). The quasi-steady (QS) state method of Verhoest & Troch is also analysed and it is shown that the QS depth profiles approximate the transient ones well, only if Δt exceeds a system-dependent transition time between flow states (possibly >>1 day). In an application example for a 30-day recharge series, the QS solution differs from the transient one by as much as 20% (RMSE = 15%), does not track recharge changes as well and fails to conserve mass. 相似文献
11.
Geological storage of carbon dioxide (CO2) is a promising technology for reducing atmospheric emissions. The large discrepancy in the time- and length-scales between up-dip migration of buoyant supercritical CO2 and the sinking fingers of dissolved CO2 poses a challenge for numerical simulations aimed at describing the fate of the plume. Hence, several investigators have suggested methods to simplify the problem, but to date there has been no reference solution with which these simplified models can be compared. We investigate the full problem of Darcy-based two-phase flow with gravity-current propagation and miscible convective mixing, using high-resolution numerical simulations. We build on recent developments of the Automatic Differentiation - General Purpose Research Simulator (AD-GPRS) at Stanford. The results show a CO2 plume that travels for 5000 years reaching a final distance of 14 km up-dip from the injection site. It takes another 2000 years before the CO2 is completely trapped as residual (40%) and dissolved (60%) CO2. Dissolution causes a significant reduction of the plume speed. While fingers of dissolved CO2 appear under the propagating gravity current, the resident brine does not become fully saturated with CO2 anywhere under the plume. The overall mass transfer of CO2 into the brine under the plume remains practically constant for several thousands of years. These results can be used as a benchmark for verification, or improvements, of simplified (reduced-dimensionality, upscaled) models. Our results indicate that simplified models need to account for: (i) reduced dissolution due to interaction with the plume, and (ii) gradual reduction of the local dissolution rate after the fingers begin to interact with the bottom of the aquifer. 相似文献
12.
The multi-phase flow of liquid/supercritical CO2 and water (non-wetting and wetting phases, respectively) in a two-dimensional silicon micromodel was investigated at reservoir conditions (80 bar, 24 °C and 40 °C). The fluorescent microscopy and microscopic particle image velocimetry (micro-PIV) techniques were combined to quantify the flow dynamics associated with displacement of water by CO2 (drainage) in the porous matrix. To this end, water was seeded with fluorescent tracer particles, CO2 was tagged with a fluorescent dye and each phase was imaged independently using spectral separation in conjunction with microscopic imaging. This approach allowed simultaneous measurement of the spatially-resolved instantaneous velocity field in the water and quantification of the spatial configuration of the two fluid phases. The results, acquired with sufficient time resolution to follow the dynamic progression of both phases, provide a comprehensive picture of the flow physics during the migration of the CO2 front, the temporal evolution of individual menisci, and the growth of fingers within the porous microstructure. During that growth process, velocity jumps 20–25 times larger in magnitude than the bulk velocity were measured in the water phase and these bursts of water flow occurred both in-line with and against the bulk flow direction. These unsteady velocity events support the notion of pressure bursts and Haines jumps during pore drainage events as previously reported in the literature [1–3]. After passage of the CO2 front, shear-induced flow was detected in the trapped water ganglia in the form of circulation zones near the CO2–water interfaces as well as in the thin water films wetting the surfaces of the silicon micromodel. To our knowledge, the results presented herein represent the first quantitative spatially and temporally resolved velocity-field measurements at high pressure for water displacement by liquid/supercritical CO2 injection in a porous micromodel. 相似文献
13.
The present work describes the results of a modeling study addressing the geological sequestration of carbon dioxide (CO2) in an offshore multi-compartment reservoir located in Italy. The study is part of a large scale project aimed at implementing carbon capture and storage (CCS) technology in a power plant in Italy within the framework of the European Energy Programme for Recovery (EEPR). The processes modeled include multiphase flow and geomechanical effects occurring in the storage formation and the sealing layers, along with near wellbore effects, fault/thrust reactivation and land surface stability, for a CO2 injection rate of 1 × 106 ton/a. Based on an accurate reproduction of the three-dimensional geological setting of the selected structure, two scenarios are discussed depending on a different distribution of the petrophysical properties of the formation used for injection, namely porosity and permeability. The numerical results help clarify the importance of: (i) facies models at the reservoir scale, properly conditioned on wellbore logs, in assessing the CO2 storage capacity; (ii) coupled wellbore-reservoir flow in allocating injection fluxes among permeable levels; and (iii) geomechanical processes, especially shear failure, in constraining the sustainable pressure buildup of a faulted reservoir. 相似文献
14.
Markus Giese Thomas Reimann Rudolf Liedl Benoit Dewandel Jean-Christophe Maréchal Martin Sauter 《Ground water》2020,58(4):611-621
Inner boundary conditions describe the interaction of groundwater wells with the surrounding aquifer during pumping and are associated with well-skin damage that limits water production and water derived from wellbore storage. Pumping test evaluations of wells during immediate and early time flow require assignment of inner boundary conditions. Originally, these concepts were developed for vertical well screens, and later transferred to wellbores intersecting highly conductive structures, such as preferential flow zones in fractured and karstic systems. Conceptual models for pumping test analysis in complex bedrock geology are often simplified. Classic analytical solutions generally lump or ignore conditions that limit or enhance well productivity along the well screen at the onset of pumping. Numerical solutions can represent well drawdowns in complex geological settings, such as karst systems, more precisely than many analytical solutions by accounting for additional physical processes and avoiding assumptions and simplifications. Suitable numerical tools for flow simulations in karst are discrete pipe-continuum models that account for various physical processes such as the transient hydraulics of wellbores intersecting highly conductive structures during pumping. 相似文献
15.
In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity kD results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter BD results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered. 相似文献
16.
Determining consistent sets of vent conditions for next expected eruptions at Vesuvius is crucial for the simulation of the sub-aerial processes originating the volcanic hazard and the eruption impact. Here we refer to the expected eruptive scales and conditions defined in the frame of the EC Exploris project, and simulate the dynamics of magma ascent along the volcanic conduit for sub-steady phases of next eruptions characterized by intensities of the Violent Strombolian (VS), Sub-Plinian 2 (SP2), and Sub-Plinian 1 (SP1) scale. Sets of conditions for the simulations are determined on the basis of the bulk of knowledge on the past history of Vesuvius [Cioni, R., Bertagnini, A., Santacroce, R., Andronico, D., Explosive activity and eruption scenarios at Somma–Vesuvius (Italy): towards a new classification scheme. Journal of Volcanology and Geothermal Research, this issue.]. Volatile contents (H2O and CO2) are parameterized in order to account for the uncertainty in their expected amounts for a next eruption. In all cases the flow in the conduit is found to be choked, with velocities at the conduit exit or vent corresponding to the sonic velocity in the two-phase non-equilibrium magmatic mixture. Conduit diameters and vent mixture densities are found to display minimum overlapping between the different eruptive scales, while exit gas and particle velocities, as well as vent pressures, largely overlap. Vent diameters vary from as low as about 5 m for VS eruptions, to 35–55 m for the most violent SP1 eruption scale. Vent pressures can be as low as less than 1 MPa for the lowest volatile content employed of 2 wt.% H2O and no CO2, to 7–8 MPa for highest volatile contents of 5 wt.% H2O and 2 wt.% CO2 and large eruptive scales. Gas and particle velocities at the vent range from 100–250 m/s, with a tendency to decrease, and to increase the mechanical decoupling between the phases, with increasing eruptive scale. Except for velocities, all relevant vent quantities are more sensitive to the volatile content of the discharged magma for the highest eruptive scales considered. 相似文献
17.
We present advances in compositional modeling of two-phase multi-component flow through highly complex porous media. Higher-order methods are used to approximate both mass transport and the velocity and pressure fields. We employ the Mixed Hybrid Finite Element (MHFE) method to simultaneously solve, to the same order, the pressure equation and Darcy's law for the velocity. The species balance equation is approximated by the discontinuous Galerkin (DG) approach, combined with a slope limiter. In this work we present an improved DG scheme where phase splitting is analyzed at all element vertices in the two-phase regions, rather than only as element averages. This approximation is higher-order than the commonly employed finite volume method and earlier DG approximations. The method reduces numerical dispersion, allowing for an accurate capture of shock fronts and lower dependence on mesh quality and orientation. Further new features are the extension to unstructured grids and support for arbitrary permeability tensors (allowing for both scalar heterogeneity, and shear anisotropy). The most important advancement in this work is the self-consistent modeling of two-phase multi-component Fickian diffusion. We present several numerical examples to illustrate the powerful features of our combined MHFE–dg method with respect to lower-order calculations, ranging from simple two component fluids to more challenging real problems regarding CO2 injection into a vertical domain saturated with a multi-component petroleum fluid. 相似文献
18.
The vertical stratification of carbon dioxide (CO2) injected into a deep layered aquifer made up of high-permeability and low-permeability layers, such as Utsira aquifer at Sleipner site in Norway, is investigated with a Buckley–Leverett equation including gravity effects. In a first step, we study both by theory and simulation the application of this equation to the vertical migration of a light phase (CO2), in a denser phase (water), in 1D vertical columns filled with different types of porous media: homogeneous, piecewise homogeneous, layered periodic and finally heterogeneous. For each case, we solve the associated Riemann problems and propose semi-analytical solutions describing the spatial and temporal evolution of the light phase saturation. These solutions agree well with simulation results. We show that the flux continuity condition at interfaces between high-permeability and low-permeability layers leads to CO2 saturation discontinuities at these interfaces and, in particular, to a saturation increase beneath low-permeability layers. In a second step, we analyze the vertical migration of a CO2 plume injected into a 2D layered aquifer. We show that the CO2 vertical stratification under each low-permeability layer is induced, as in 1D columns, by the flux continuity condition at interfaces. As the injection takes place at the bottom of the aquifer the velocity and the flux function decrease with elevation and this phenomenon is proposed to explain the stratification under each mudstone layer as observed at Sleipner site. 相似文献
19.
Predicting the behavior of overland flow with analytical solutions to the kinematic wave equation is appealing due to its relative ease of implementation. Such simple solutions, however, have largely been constrained to applications on simple planar hillslopes. This study presents analytical solutions to the kinematic wave equation for hillslopes with modest topographic curvature that causes divergence or convergence of runoff flowpaths. The solution averages flow depths along changing hillslope contours whose lengths vary according hillslope width function, and results in a one-dimensional approximation to the two-dimensional flow field. The solutions are tested against both two-dimensional numerical solutions to the kinematic wave equation (in ParFlow) and against experiments that use rainfall simulation on machined hillslopes with defined curvature properties. Excellent agreement between numerical, experimental and analytical solutions is found for hillslopes with mild to moderate curvature. The solutions show that curvature drives large changes in maximum flow rate qpeak and time of concentration tc , predictions frequently used in engineering hydrologic design and analysis. 相似文献
20.
The water krw and oil kro relative permeability curves of a glass-etched planar pore network are estimated with history matching from transient displacement experiments performed at varying values of the capillary number, Ca , for two fluid systems: one of intermediate and one of strong wettability. The transient krw,kro are compared to corresponding ones measured with the steady-state method on the same porous medium [Avraam DG, Payatakes AC. Flow regimes and relative permeabilities during steady-state two-phase flow in porous media. J Fluid Mech 1995;293:207–36; Avraam DG, Payatakes AC. Generalized relative permeability coefficients during steady-state two-phase flow in porous media and correlation with the flow mechanisms. Transport Porous Med 1995;20:135–68; Avraam DG, Payatakes AC. Flow mechanisms, relative permeabilities, and coupling effects in steady-state two-phase flow through porous media. The case of strong wettability. Ind Eng Chem Res 1999;38:778–86.], and potential differences from them are interpreted in the light of the differences between the transient growth pattern, and the steady-state two-phase flow regime. For intermediate wettability, the transient kro and krw exceed the corresponding steady-state functions at low Ca values and have the tendency to become smaller than the steady-state ones at high Ca values. For strong wettability, the transient kro and krw are increasing functions of Ca, the transient kro is higher than the steady-state one, whereas the transient krw decreases substantially and becomes lower than the steady-state one at low Ca values. The dynamic capillary pressure estimated from transient experiments is a decreasing function of Ca in agreement with previous theoretical and experimental studies. 相似文献