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Realistic immiscible viscous fingering, showing all of the complex finger structure observed in experiments, has proven to be very difficult to model using direct numerical simulation based on the two-phase flow equations in porous media. Recently, a method was proposed by the authors to solve the viscous-dominated immiscible fingering problem numerically. This method gave realistic complex immiscible fingering patterns and showed very good agreement with a set of viscous unstable 2D water → oil displacement experiments. In addition, the method also gave a very good prediction of the response of the system to tertiary polymer injection. In this paper, we extend our previous work by considering the effect of wettability/capillarity on immiscible viscous fingering, e.g. in a water → oil displacements where viscosity ratio μ o / μ w ≫ 1 . We identify particular wetting states with the form of the corresponding capillary pressure used to simulate that system. It has long been known that the broad effect of capillarity is to act like a nonlinear diffusion term in the two-phase flow equations, denoted here as D (S w) . Therefore, the addition of capillary pressure, P c (S w) , into the equations acts as a damping or stabilisation term on viscous fingering, where it is the derivative of this quantity that is important, i.e. D (S w) ∼ d P c (S w) / d S w . If this capillary effect is sufficiently large, then we expect that the viscous fingering to be completely damped, and linear stability theory has supported this view. However, no convincing numerical simulations have been presented showing this effect clearly for systems of different wettability, due to the problem of simulating realistic immiscible fingering in the first place (i.e. for the viscous-dominated case where P c = 0 ). Since we already have a good method for numerically generating complex realistic immiscible fingering for the P c = 0 case, we are able for the first time to present a study examining both the viscous-dominated limit and the gradual change in the viscous/capillary force balance. This force balance also depends on the physical size of the system as well as on the length scale of the capillary damping. To address these issues, scaling theory is applied, using the classical approach of Rapport (1955), to study this scaling in a systematic manner. In this paper, we show that the effect of wettability/capillarity on immiscible viscous fingering is somewhat more complex and interesting than the (broadly correct) qualitative description above. From a "lab-scale" base case 2D water → oil displacement showing clear immiscible viscous fingering which we have already matched very well using our numerical method, we examine the effects of introducing either a water wet (WW) or an oil wet (OW) capillary pressure, of different "magnitudes". The characteristics of these two cases (WW and OW) are important in how the value of corresponding D (S w) functions, relate to the (Buckley–Leverett) shock front saturation, S wf , of the viscous-dominated ( P c = 0 ) case. By analysing this, and carrying out some confirming calculations, we show clearly why we expect to see much clearer immiscible fingering at the lab scale in oil wet rather than in water wet systems. Indeed, we demonstrate why it is very difficult to see immiscible fingering in WW lab systems. From this finding, one might conclude that since no fingering is observed for the WW lab-scale case, then none would be expected at the larger "field" scale. However, by invoking scaling theory—specifically the viscous/capillary scaling group, C VC1 , (and a corresponding "shape group", C S 1 ), we demonstrate very clearly that, although the WW viscous fingers do not usually appear at the lab scale, they emerge very distinctly as we "inflate" the system in size in a systematic manner. In contrast, we demonstrate exactly why it is much more likely to observe viscous fingering for the OW (or weakly wetting) case at the lab scale. Finally, to confirm our analysis of the WW and OW immiscible fingering conclusions at the lab scale, we present two experiments in a lab-scale bead pack where μ o / μ w = 100 ; no fingering is seen in the WW case, whereas clear developed immiscible fingering is observed in the OW case. [ABSTRACT FROM AUTHOR]

Capillary trapping is considered as one of the safest geologic CO2 storage mechanisms due to its hydrodynamic stability. However, the thermodynamic stability of capillary trapping was questioned by our recent work (Xu in Geophys Res Lett 46(23):13804–13813, 2019). Gravity induces the top bubbles to grow at expense of bottom bubbles through the diffusion of dissolved gas components, that finally may form a gas cap and posing a risk of leakage, even in absence of convection. Here, we improve the gravity-induced ripening model introduced earlier and conduct theoretical and numerical analysis. Four regimes of bubble ripening are identified according to the modified Bond number and initial gas saturation, resulting in different scaling between the equilibrium time and the length scale. Vertical heterogeneity is also shown to have a great impact on the ripening process. When the permeability gradient is downward, the capillary pressure gradient competes with the gravitational gradient and results in a complex gas redistribution behavior. Capillarity dominates in a short time, while gravitational potential determines the global saturation profile in long term. This work provides a new physical perspective in evaluating CO2 sequestration security and has a potential application in other porous systems that gas generated and evolve under strong external fields. [ABSTRACT FROM AUTHOR]

The typical characteristic of a thin porous layer is that its thickness is much smaller than its in-plane dimensions. This often leads to physical behaviors that are different from three-dimensional porous media. The classical Richards equation is insufficient to simulate many flow conditions in thin porous media. Here, we have provided an alternative approach by accounting for the dynamic capillarity effect. In this study, we have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The X-ray transmission method was used to measure saturation distributions along the fibrous sample. We simulated the experimental results using Richards equation either with classical capillary equation or with a so-called dynamic capillarity term. We have found that the standard Richards equation was not able to simulate the experimental results, and the dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. The experimental data presented here may also be used by other researchers to validate their models. Article Highlights: We have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The experimental data were simulated using the Richards equation either with classical capillary equation or with a so-call dynamic capillarity term. The dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. [ABSTRACT FROM AUTHOR]

Countercurrent spontaneous imbibition (SI) is an important flow mechanism for oil recovery in fractured reservoirs during waterflooding. SI plays a key role in the mobilization of oil in the matrix because it facilitates water infiltration by capillarity even when the matrix permeability is low, which limits fluid transport by advection. However, the modeling of SI in fractured media under dynamic conditions has been insufficiently studied. Most imbibition models assume conventional exponential functions and empirical constants based on experimental results of oil recovery under static conditions. Thus, the modeling of water distribution in the fracture and the matrix has been ignored which may lead to incorrect estimates of the efficiency of countercurrent SI to recover oil. Using the classic fractional flow equation, we present a semi-analytical solution to model countercurrent SI in a water-wet fractured medium by including a transfer function to account for continuous fluid exchange between the fracture and the matrix. The model is numerically solved using finite differences by including an effective imbibition time as a function of water advance in the fracture, which overcomes the difficulty of solving iterative numerical summations as shown in other imbibition models. The novelty of the presented solution is that it enables the modeling of water infiltration in the matrix under dynamic conditions. We verified the semi-analytical model against 2D numerical simulations and validated against experimental data to demonstrate that the model accurately predicts oil recovery and water infiltration in the matrix. [ABSTRACT FROM AUTHOR]

Rates of spontaneous imbibition of water and nonaqueous liquids into dry limestones have been measured at 25 °C. Thirteen English and French limestones were used, with eight liquids (water, decane, dodecane, sec-butanol, iso-propanol, tetrahydrofuran, perfluorodimethylcyclohexane, ethanediol). For the nonaqueous liquids, the measured sorptivity generally scales as (surface-tension/viscosity) 1 / 2 (here called F-scaling). Water sorptivities deviate from F-scaling, indicating partial wetting. A wetting coefficient (wetting index) is derived. Data show that there is little difference in the Hirschwald saturation coefficient measured with the different liquids, although there is a large variation between stones. Results suggest that physicochemical alteration of exposed pore surfaces strongly (and unpredictably) influences the capillary absorption of water by limestones. [ABSTRACT FROM AUTHOR]

We present gravimetrical and optical imaging experiments on the capillarity-driven imbibition of silicone oils in monolithic silica glasses traversed by 3D networks of pores (mesoporous Vycor glass with 6.5 nm or 10 nm pore diameters). As evidenced by a robust square root of time Lucas-Washburn (L-W) filling kinetics, the capillary rise is governed by a balance of capillarity and viscous drag forces in the absence of inertia and gravitational effects over the entire experimental times studied, ranging from a few seconds up to 10 days. A video on the infiltration process corroborates a collective pore filling as well as pronounced imbibition front broadening resulting from the capillarity and permeability disorder, typical of Vycor glasses. The transport process is analyzed within a Darcy scale description, considering a generalized prefactor of the L-W law, termed Lucas-Washburn-Darcy imbibition ability. It assumes a Hagen-Poiseuille velocity profile in the pores and depends on the porosity, the mean pore diameter, the tortuosity and the velocity slip length and thus on the effective hydraulic pore diameter. For both matrices a reduced imbibition speed and thus reduced imbibition ability, compared to the one assuming the nominal pore diameter, bulk fluidity and bulk capillarity, can be quantitatively traced to an immobile, pore wall adsorbed boundary layer of 1.4 nm thickness. Presumably, it consists of a monolayer of water molecules adsorbed on the hydrophilic pore walls covered by a monolayer of flat-laying silicone oil molecules. Our study highlights the importance of immobile nanoscopic boundary layers on the flow in tight oil reservoirs as well as the validity of the Darcy scale description for transport in mesoporous media. [ABSTRACT FROM AUTHOR]

The development of the capillary fringe during gravity drainage has a significant influence on saturation and pressure distributions in porous formations (Sarkarfarshi et al. in Int J Greenh Gas Control 23:61-71, 2014). This paper introduces an analytical solution for gravity drainage in an axisymmetric geometry with significant capillary pressure. The drainage process results from the injection of a lighter and less viscous injectant into a porous medium saturated with a heavier and more viscous pore fluid. If the viscous force dominates the capillary and the buoyancy forces, then the flow regime is approximated by differential equations and the admissible solution comprises a front shock wave and a trailing simple wave. In contrast to existing analytical solutions for capillary gravity drainage problems (e.g., Nordbotten and Dahle in 47(2) 2011; Golding et al. in J Fluid Mech 678:248-270 2011), this solution targets the saturation distribution during injection at an earlier point in time. Another contribution of this analytical solution is the incorporation of a completely drained flow regime close to the injection well. The analytical solution demonstrates the strong dependency of the saturation distribution upon relative permeability functions, gas entry capillary pressure, and residual saturation. The analytical results are compared to results from a commercial reservoir engineering software package ( $$\hbox {CMG } \hbox {STARS}^{\mathrm{TM}}$$ ). [ABSTRACT FROM AUTHOR]

Unfavorable mobility ratio and reservoir heterogeneities contribute to water fingering phenomenon that leads to relatively low oil recovery factors in heavy oil fields. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Capillary-driven mobility alteration of the water phase by emulsion drops leads to not only more uniform macroscopic reservoir sweep, but also a pore scale reduction in the residual oil saturation. Despite recent developments, fundamental aspects of dilute oil-in-water emulsion flow through porous media and its application as an EOR method are still not clear. Experiments were performed in a 1D flow configuration using silica sandpacks and sandstone cores to determine the effect of permeability, emulsion drop size, dispersed phase concentration and size of injected emulsion bank on the volume of displaced oil, a crude heavy oil from Campos Basin ( $$20^{\circ }$$ API). X-ray computerized tomography images obtained during experiments in a Castlegate sandstone block in a 1/4 5-spot configuration revealed that emulsion acts both in the macroscale and pore scale, improving the macroscopic sweep and lowering the residual oil saturation. [ABSTRACT FROM AUTHOR]

In this study, a grain-scale modelling technique has been developed to generate the capillary pressure-saturation curves for swelling granular materials. This model employs only basic granular properties such as particles size distribution, porosity, and the amount of absorbed water for swelling materials. Using this model, both drainage and imbibition curves are directly obtained by pore-scale simulations of fluid invasion. This allows us to produce capillary pressure-saturation curves for a large number of different packings of granular materials with varying porosity and/or amount of absorbed water. The algorithm is based on combining the Discrete Element Method for generating different particle packings with a pore-unit assembly approach. The pore space is extracted using a regular triangulation, with the centres of four neighbouring particles forming a tetrahedron. The pore space within each tetrahedron is referred to as a pore unit. Thus, the pore space of a particle packing is represented by an assembly of pore units for which we construct drainage and imbibition capillary pressure-saturation curves. A case study on Hostun sand is conducted to test the model against experimental data from literature and to investigate the required minimum number of particles to have a Representative Elementary Volume. Then, the capillary pressure-saturation curves are constructed for Absorbent Gelling Material particles, for different combinations of porosity values and amounts of absorbed water. Each combination yields a different configuration of pore units, and thus distinctly different capillary pressure-saturation curves. All these curves are shown to collapse into one curve for drainage and one curve for imbibition when we normalize capillary pressure and saturation values. We have developed a formula for the Van Genuchten parameter $$\alpha $$ (which is related to the inverse of the entry pressure) as a function of porosity and the amount of absorbed water. [ABSTRACT FROM AUTHOR]

When water drains from a porous medium, a small quantity of residual water typically remains trapped in the medium. The residual water saturation, $$S_{\mathrm{wr}}$$ , is a measure of the ratio of the volume of residual water to the volume of voids in the porous medium. While conventional multiphase flow concepts suggest that $$S_{\mathrm{wr}}$$ has a single value that is a property of the fluids and medium, significant evidence exists that $$S_{\mathrm{wr}}$$ may actually have a dynamic component, exhibiting different observed values when drainage takes place at different rates. Previous work by the authors used experimental measurements to explore this phenomenon. The work described here further explores the phenomenon through the use of a dynamic pore network model specifically designed to study the effects of changing fluid continuity in porous media resulting from dynamic drainage. The model is based on cylindrical pore throats and volumeless pore bodies. The relatively simple structure of the model makes it well suited to the purposes of the work, in that it provides a mechanism to simulate the effect of fluid continuity on drainage from a spatially random porous medium defined by a minimal number of parameters. Results suggest that the phenomenon may occur as a result of pore-scale preferential flow causing desaturation of the porous medium at the water-wet boundary. Significant sensitivity is observed to both porous medium configuration and resistance to water flow across the water-wet boundary. [ABSTRACT FROM AUTHOR]

In this work, we study the dynamics of capillary-driven fluid invasion in three different settings including: (1) a single capillary tube, (2) a homogeneous porous medium, and (3) a fractured porous medium. A Lambert W functional form is proposed to describe the invasion dynamics in a single capillary tube, that predicts both early-time Washburn-type behavior ( $$\sqrt{t}$$ ) and late-time behavior. We extend the formulation to describe homogenous porous media and to include viscosity, pressure, and gravity effects in both advancing and defending fluids. Solutions for closed systems, where the advancing fluid compresses the defending fluid, are then developed. Finally, we extend the theory to describe fractured systems and propose a convolution integral formulation and a new explicit solution for fluid invasion into a fractured porous medium. [ABSTRACT FROM AUTHOR]

Modeling of the processes of elution from porous systems is essential importance for development of the removing oily contaminations from the soils and intensification of the oil recovery processes. In the paper, capillary model of gravitational elution of high viscosity substances from the porous medium by using low viscosity liquids was derived. This model allowed for the prediction of changes in time of such parameters like: level of bed saturation with oil, relative bed permeability, liquid flow rate, flow resistance, volume of eluted liquid during the process. When modeling, phenomena and the physical properties associated with the analyzed process, such as, for example, the effects of surface tension, fluids viscosity, specific size of the granular bed, initial oil saturation of bed, variable process driving force, and the flow of liquid through the preferential flow paths, were taken into account. This allowed for the more complete imaging of elution process. The model has been verified on the basis of the results of experimental studies. In addition, the discussion on the behavior of the model due to changes in values of various parameters was carried out. [ABSTRACT FROM AUTHOR]

One-dimensional traveling wave solutions for imbibition processes into a homogeneous porous medium are found within a recent generalized theory of macroscopic capillarity. The generalized theory is based on the hydrodynamic differences between percolating and nonpercolating fluid parts. The traveling wave solutions are obtained using a dynamical systems approach. An exhaustive study of all smooth traveling wave solutions for primary and secondary imbibition processes is reported here. It is made possible by introducing two novel methods of reduced graphical representation. In the first method the integration constant of the dynamical system is related graphically to the boundary data and the wave velocity. In the second representation the wave velocity is plotted as a function of the boundary data. Each of these two graphical representations provides an exhaustive overview over all one-dimensional and smooth solutions of traveling wave type, that can arise in primary and secondary imbibition. Analogous representations are possible for other systems, solution classes, and processes. [ABSTRACT FROM AUTHOR]

The reduction in permeability of sediments due to blockages caused by the trapping of suspended particles is a common concern for the extraction processes of oil or natural gas. In this study, the effect of trapped fine particles in sand sediments is studied numerically using a three-dimensional lattice Boltzmann method. The geometrical properties of larger, immobile, sand grains are digitally extracted by the spherical harmonics series expansions of CT scans of real sand grains. The migrating fine particles are assumed to be spherical in shape with their volumes following a log-normal distribution. These fine particles, together with larger frame sands, are positioned, without overlapping, within a microscopic, cubic, domain with periodic boundaries. The remaining empty volume is filled with water and imposing a pressure gradient simulates the flow of fluid through the sediment. As a result of fine particles becoming trapped by the frame sand, the initial porosity of which is 0.589, the absolute permeability of the system is reduced by approximately 60-90 %, corresponding to fine particle saturations of 0.15-0.29, respectively. The permeability change due to the trapping of fine particles is also modelled theoretically using not only volume saturations but also specific surface areas of both the frame sands and the fine particles with a coefficient of proportionality. [ABSTRACT FROM AUTHOR]

We introduce a finite-difference method to simulate pore scale steady-state creeping fluid flow in porous media. First, a geometrical approximation is invoked to describe the interstitial space of grid-based images of porous media. Subsequently, a generalized Laplace equation is derived and solved to calculate fluid pressure and velocity distributions in the interstitial space domain. We use a previously validated lattice-Boltzmann method (LBM) as ground truth for modeling comparison purposes. Our method requires on average 17 % of the CPU time used by LBM to calculate permeability in the same pore-scale distributions. After grid refinement, calculations of permeability performed from velocity distributions converge with both methods, and our modeling results differ within 6 % from those yielded by LBM. However, without grid refinement, permeability calculations differ within 20 % from those yielded by LBM for the case of high-porosity rocks and by as much as 100 % in low-porosity and highly tortuous porous media. We confirm that grid refinement is essential to secure reliable results when modeling fluid flow in porous media. Without grid refinement, permeability results obtained with our modeling method are closer to converged results than those yielded by LBM in low-porosity and highly tortuous media. However, the accuracy of the presented model decreases in pores with elongated cross sections. [ABSTRACT FROM AUTHOR]

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability-porosity relationships represented by the Kozeny-Carman equations and Archie's law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability-porosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability-porosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature. [ABSTRACT FROM AUTHOR]

Leakage of CO through fractures in saline formations will increase the CO-brine interface and promote CO dissolution. We use a 2D, finite difference MATLAB model to simulate dissolution rates from a vertical fracture, with CO flowing through it, in a secondary storage formation. The instigation of convection currents increases dissolution rates leading to higher dissolution in higher Rayleigh number systems. Comparison of our results with fracture flow rates shows that for typical fracture apertures dissolution from a fracture is small relative to the amount of CO flowing through the fracture. Temporal and spatial variations in fracture permeability may reduce fracture flow rates and increase the relative amount of CO dissolved from the fracture compared to the CO flowing through the fracture. Further work on CO dissolution in relation to fracture heterogeneity, flow of CO within fractures and the interaction of multiple fractures will improve our ability to predict CO dissolution rates for site characterisation. [ABSTRACT FROM AUTHOR]

The flow properties of complex fluids through porous media give rise to multiphase flow displacement mechanisms that operate at different scales, from pore-level to Darcy scale. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced-oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Pore-scale flow visualization as well as core flooding results available in the literature have demonstrated that the enhanced recovery factor is regulated by the capillary number of the flow. However, the mechanisms by which additional oil is displaced during emulsion injection are still not clear. In this work, we carried out two different experiments to evaluate the effect of emulsion flooding both at pore and macro scales. Visualization of the flow through sand packed between transparent plexiglass parallel plates shows that emulsion flooding improves the pore-level displacement efficiency, leading to lower residual oil saturation. Oil recovery results during emulsion flooding in tertiary mode (after waterflooding) in parallel sandstone cores with very different absolute permeability values prove that emulsion flooding also leads to enhancement of conformance or volumetric sweep efficiency. Combined, the results presented here show that injection of emulsion offers multiscale mechanisms resulting from capillary-driven mobility control. [ABSTRACT FROM AUTHOR]

An ensemble-based technique has been developed and successfully applied to simultaneously estimate the relative permeability and capillary pressure by history matching the observed production profile. Relative permeability and capillary pressure curves are represented by using a power-law model. Then, forward simulation is performed with the initial coefficients of the power-law model, all of which are to be tuned automatically and finally determined once the observed data is assimilated completely and history matched. The newly developed technique has been validated by a synthetic coreflooding experiment with two scenarios. The endpoints are fixed for the first scenario, whereas they are completely free in the second scenario. Simultaneous estimation of relative permeability and capillary pressure has been found to improve gradually as more observation data is assimilated. There exists an excellent agreement between both the updated relative permeability and capillary pressure and their corresponding reference values, once the discrepancy between the simulated and observed production history has been minimized. Compared with coefficients of capillary pressure curve, coefficients of relative permeability curves, irreducible water saturation and residual oil saturation are found to be more sensitive to the observed data. In addition, water relative permeability is more sensitive to the observation data than either oil relative permeability or capillary pressure. It is shown from its application to a laboratory coreflooding experiment that relative permeability and capillary pressure curves can be simultaneously evaluated once all of the experimental measurements are assimilated and history matched. [ABSTRACT FROM AUTHOR]

Most reservoirs in Iran are heterogeneous fractured carbonate reservoirs. Heterogeneity causes an earlier breakthrough and an unstable front which leads to a lower recovery. A series of experiments were conducted whereby the distilled water displaced n-Decane in strongly oil-wet glass micro-models containing a single fracture. Experimental data from image analysis of immiscible displacement processes are used to modify the Buckley-Leverett and fractional flow equations by a heterogeneity factor. It is shown that the heterogeneity factor in the modified equations can be expressed as a function of fracture length and orientation. [ABSTRACT FROM AUTHOR]

Fractures serve as primary conduits having a great impact on the migration of injected fluid into fractured permeable media. Appropriate transport properties such as relative permeability and capillary pressure are essential for successful simulation and prediction of multi-phase flow in such systems. However, the lack of a thorough understanding of the dynamics governing immiscible displacement in fractured media, limits our ability to properly represent their macroscopic transport properties. Previous experimental observations of imbibition front evolution in fractured rocks are examined in the present study using an automated history-matching approach to obtain representative relative permeability and capillary pressure curves. Predicted imbibition front evolution under different flow conditions resulted in an excellent agreement with experimental observations. Sensitivity analyses, in combination with direct experimental observation, allowed exploring the competing effects of relative permeability and capillary pressure on the development of saturation distribution and imbibing front evolution in fractured porous media. Results show that residual saturations are most sensitive to matrix relative permeability to oil, while the ratio of oil and water relative permeability, rock heterogeneity, boundary condition, and matrix-fracture capillary pressure contrast, affect displacement shape, speed, and geometry of the imbibing front. [ABSTRACT FROM AUTHOR]

This article is the first investigation on the dual permeability flow issue for horizontal well-production in a naturally fractured dual-porosity reservoir. Based on the inter-porosity flow from matrix system to fracture system and treating the media directly connected with horizontal wellbore as matrix and fracture systems, we established a model of horizontal well-production and then solved the model using some modern mathematical methods, such as Laplace integral transformation, separation of variables, eigenvalue, and eigenfunction. Later in the article, we obtained the standard log-log type curves using numerical simulation and analyzed the transient flow behavior thoroughly, which showed it is dual porosity and dual permeability flow behavior. The numerical simulation results showed that there are obvious differences between dual permeability and single permeability models. The dual permeability flow behavior accelerates energy supplement during production and reduces the classical matrix-fracture (V-shaped) response. We also showed that type curves characteristics are affected by external boundary conditions, the parameter κ, ω and λ, etc. The research results show that our model would be a good semi-analytical model supplied to users. Because the single permeability modeling ignores the direct fluid supply from matrix to wellbore, we recommend using the dual permeability modeling to make well testing and rate decline interpretation in real case studies. [ABSTRACT FROM AUTHOR]

A numerical method used for solving a two-phase flow problem as found in typical oil recovery is investigated in the setting of physics-based two-level operator splitting. The governing equations involve an elliptic differential equation coupled with a parabolic convection-dominated equation which poses a severe restriction for obtaining fully implicit numerical solutions. Furthermore, strong heterogeneity of the porous medium over many length scales adds to the complications for effectively solving the system. One viable approach is to split the system into three sub-systems: the elliptic, the hyperbolic, and the parabolic equation, respectively. In doing so, we allow for the use of appropriate numerical discretization for each type of equation and the careful exchange of information between them. We propose to use the multiscale finite volume element method (MsFVEM) for the elliptic and parabolic equations, and a nonoscillatory difference scheme for the hyperbolic equation. Performance of this procedure is confirmed through several numerical experiments. [ABSTRACT FROM AUTHOR]

Co-injection of water with CO is an effective scheme to control initial gas saturation in porous media. A fractional flow rate of water of approximately 5-10% is sufficient to reduce initial gas saturations. After water injection following the co-injection, most of the gas injected in the porous media is trapped by capillarity with a low fractional volume of migrating gas. In this study, we first derive an analytical model to predict the gas saturation levels for co-injection with water. The initial gas saturation is controlled by the fractional flow ratio in the co-injection process. Next, we experimentally investigate the effect of initial gas saturation on residual gas saturation at capillary trapping by co-injecting gas and water followed by pure water injection, using a water and nitrogen system at room temperature. Depending on relative permeability, initial gas saturation is reduced by co-injection of water. If the initial saturation in the Berea sandstone core is controlled at 20-40%, most of the gas is trapped by capillarity, and less than 20% of the gas with respect to the injected gas volume is migrated by water injection. In the packed bed of Toyoura standard sand, the initial gas saturation is approximately 20% for a wide range of gas with a fractional flow rate from 0.50 to 0.95. The residual gas saturation for these conditions is approximately 15%. Less than approximately 25% of the gas migrates by water injection. The amount of water required for co-injection systems is estimated on the basis of the analytical model and experimental results. [ABSTRACT FROM AUTHOR]

The effect of vertical heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a non-uniform basic temperature gradient resulting from vertical throughflow, is studied analytically using linear stability theory. It is found that, to first order, a linear variation of the reciprocal of permeability with depth has no effect on the critical value of the Rayleigh number Ra based on the harmonic mean of the permeability, but a quadratic variation increasing in the upwards direction leads to a reduction in Ra. [ABSTRACT FROM AUTHOR]

The ultimate driving force for counter-current spontaneous imbibition of a fluid into a porous material is the capillary pressure developed under dynamic conditions at the imbibition front. This is a difficult variable to measure. We report experiments using restricted counter-current spontaneous imbibition to find the maximum capillary pressure developed during imbibition of a light mineral oil (and brine) into initially air-filled sandstone core samples with one end-face open. The production of air from the core was prevented by covering its open face with a low permeability core segment set against the main test segment. The location of the imbibition front and the pressure resulting from compression of air ahead of the imbibition front were monitored. In some cases, in order to achieve stabilized gas pressures with the front still advancing through the core, the air in the core was compressed at the start of the imbibition test. The subsequently measured stabilized air pressures dropped only slightly as imbibition slowed. The measured pressures are directly related to the effective capillary pressures that drive spontaneous imbibition. After spontaneous imbibition ceased, the pressure was released by flow of air through the sealed end of the core and further spontaneous imbibition occurred in co-current mode. Comparison of the stabilized pressures with previously published oil/brine imbibition results showed close agreement after compensation for the difference in interfacial tension. [ABSTRACT FROM AUTHOR]

Direct insight into the mechanisms of flow and displacements within small-scale (cm) systems having permeability heterogeneities that are not parallel to the flow direction (cross-bedding and fault zones) have been carried out. In our experiments, we have used visual models with unconsolidated glass bead packs having carefully controlled permeability contrasts to observe the processes with coloured fluids and streamlines. The displacements were followed visually and by video recording for later analysis. The experiments show the significance that heterogeneities have on residual saturations and recovery, as well as the displacement patterns themselves. During a waterflood, high permeability regions can be by-passed due to capillary pressure differences, giving rise to high residual oil saturations in these regions. This study demonstrates the importance of incorporating reservoir heterogeneity into core displacement analysis, but of course the nature of the heterogeneity has to be known. In general, the effects created by the heterogeneities and their unknown boundaries hamper interpretation of flood experiments in heterogeneous real sandstone cores. Our experiments, therefore, offer clear visual information to provide a firmer understanding of the displacement processes during immiscible displacement, to present benchmark data for input to numerical simulators, and to validate the simulator through a comparison with our experimental results for these difficult flow problems. [ABSTRACT FROM AUTHOR]

The physical effect of multiphase fluid distribution and flow at permeability boundaries has not been fully investigated, particularly at the pore scale (1-100 μm), although such behaviour can significantly affect the overall scaled-up reservoir trapping capacity and production performance. In this article, microscale physical models have been used to qualitatively study the pore scale flow events at permeability boundaries, both high to low and vice versa, to gain a better understanding of the role of these boundaries and water saturation on multiphase displacement behaviour at the pore scale. We have used etched glass models of stripes of large and small (a factor of two) pores with circular matrix. Capillary pressure, which is the controlling parameter is itself dependant on pore size and its spatial distribution, the magnitude of the interfacial tensions and the wettability between the fluids and the solid surface of the models. Sometimes, the only way the non-wetting fluid can penetrate the boundary is through a fortuitous leakage, whereby the presence of an initial saturation reduces the controlling capillary pressure. Examples are demonstrated including mechanisms of end-effects and how capillary boundary resistance (due to capillary forces) can be broken down and fluid movement across the boundary can develop. These micromodel experiments show vividly that connate water can assist in these processes, particularly oil trapping and leakage of water across a permeability boundary. [ABSTRACT FROM AUTHOR]

The infiltration of a wetting droplet into the porous medium is a two-step process referred to as primary and secondary infiltration. In the primary infiltration there is a free liquid present at the porous medium surface, and when no fluid is left on the surface, the secondary infiltration is initiated. In both situations the driving force is the capillary pressure that is influenced by the local medium heterogeneities. A capillary network model based on the micro-force balance is developed with the same formulation applied to both infiltrations. The only difference between the two is that the net liquid flow into the porous medium in the secondary infiltration is equal to zero. The primary infiltration starts as a single-phase (fully saturated) flow and may proceed as a multiphase flow. The multiphase flow emerges as the interface (flow front) becomes irregular in shape. The immobile clusters of the originally present phase can be locally formed due to entrapment. Throughout the infiltration, it was found that portions of the liquid phase can be detached from the main body of the liquid phase forming some isolated liquid ganglia that increase in number and decrease in size. The termination of the secondary infiltration occurs once the ganglia become immobile due to their reduction in size. From the transient solution, the changes in the liquid saturation and capillary pressure during the droplet infiltration are determined. The solution developed in this study is used to investigate the droplet infiltration dynamics. However, the solution can be used to study the flow in fuel cell, nano-arrays, composites, and printing. [ABSTRACT FROM AUTHOR]

This article presents a numerical investigation of the combined effects of capillary pressure, salinity and in situ thermodynamic conditions on CO-brine-rock interactions in a saline aquifer. We demonstrate that the interrelations between capillary pressure, salinity, dissolution and drying-out affect CO injectivity and storage capacity of a saline aquifer. High capillary forces require a high injection pressure for a given injection rate. Depending on salinity, the increase in injection pressure due to capillary forces can be offset by the dissolution of CO in formation water and its compressibility. Higher capillary forces also reduce gravity segregation, and this gives a more homogeneous CO plume which improves the dissolution of CO. The solubility of CO in formation water decreases with increasing salinity which requires an increased injection pressure. Higher salinity and capillary pressure can even block the pores, causing an increased salt precipitation. Simulations with various pressure-temperature conditions and modified salinity and capillary pressure curves demonstrate that, with the injection pressures similar for both cold and warm basins at a given injection rate, CO dissolves about 10% more in the warm basin water than in the cold basin. The increase in dissolution lowers the injection pressure compensating the disadvantage of low CO density and compressibility for storage in warm basins. [ABSTRACT FROM AUTHOR]

The effects of seismic stimulation on the flow of two immiscible fluids in an elastic synthetic porous medium is experimentally investigated. A wetting fluid is slowly evacuated from the medium, while a pressure oscillation is applied on the injected non- wetting fluid. The amplitude and frequency of the pressure oscillations as well as the evacuation speed are kept constant throughout an experiment. The resulting morphology of the invading structure is found to be strongly dependent on the interplay between the amplitude and the frequency of the applied pressure oscillations and the elasticity of the porous medium. Different combinations of these properties yield morphologically similar structures, allowing a classification of structures that is found to depend on a proposed dimensionless number. [ABSTRACT FROM AUTHOR]

In dentin restoration, collagen fiber network infiltration is an issue. Using data from the literature, we have constructed a relevant numerical geometrical model of the network. The specificity of our model is that the fibers are taken into account implicitly using a regularized Heaviside function. This function is either used to set the viscosity or to localize the contact line where capillary forces are applied. A level set technique with respect to fluid infiltration front tracking in five fiber networks using the level set method and Navier–Stokes equations with capillary terms is used to point out efficient critical infiltration parameters. A variational formulation which can be implemented in a finite elements model is proposed both for the infiltration front and the contact line. Because of lack of knowledge on fiber orientation, different configurations were tested through permeability assessment of the whole network. Fiber orientation, interfibrillar space and contact angle influence were investigated. [ABSTRACT FROM AUTHOR]

Use of a correct definition of average pressure is important in numerical modeling of oil reservoirs and aquifers, where the simulated domain can be very large. Also, the average pressure needs to be defined in the application of pore-network modeling of (two-phase) flow in porous media, as well as in the (theoretical) upscaling of flow equations. Almost always the so-called intrinsic phase-volume average operator, which weighs point pressure values with point saturation values, is employed. Here, we introduce and investigate four other potentially plausible averaging operators. Among them is the centroid-corrected phase-average pressure, which corrects the intrinsic phase-volume average pressure for the distance between the centroid of the averaging volume and the phase. We consider static equilibrium of two immiscible fluids in a homogeneous, one-dimensional, vertical porous medium domain under a series of (static) drainage conditions. An important feature of static equilibrium is that the total potential (i.e., the sum of pressure and gravity potentials) is constant for each phase over the whole domain. Therefore, its average will be equal to the same constant. It is argued that the correct average pressure must preserve the fact that fluid potentials are constant. We have found that the intrinsic phase-volume average pressure results in a gradient in the total phase potential, i.e., the above criterion is violated. In fact, only the centroid-corrected operator satisfies this criterion. However, at high saturations, use of the centroid-corrected average can give rise to negative values of the difference between the average nonwetting and wetting phase pressures. For main drainage, differences among various averaging operators are significantly less because both phases are present initially, such that the difference between the centroids of phases, and the middle of the domain are relatively small. [ABSTRACT FROM AUTHOR]

Radial capillary transport occurs, for example, when wine spreads in the tablecloth ink in paper, rain drops in textiles, or dye into yarn. It is of technical relevance for propellant and other liquid transport in space. We present a theoretical and experimental study on the more basic situation when liquid spreads radially from an infinite reservoir. Our theoretical model predicts both outward and inward radial transport in a porous screen. While the outward wicking is fed by a circular wick in the center, the inward wicking is fed by a ring-like wick from the outside. For both cases, an analytical solution is obtained in terms of time versus radius as well as radius versus time aided by the Lambert W function. In the experiments, we use four different filter papers combined with three cylindrical wicks for outward wicking and one ring wick for inward wicking, respectively. The wicking process is recorded by a digital camera. Afterward, the resulting image series are evaluated with Matlab routines to detect the wicking front line. From the wetted area, we derive the mean radius versus time. Beside radially outward and inward wicking, we consider also experimental reference data from horizontal and vertical wicking in a strip. [ABSTRACT FROM AUTHOR]

The liquid flow front during impregnation of non-crimp fabrics is considered. Irregularities in fibre bundle architecture lead to generation of bubbles at this front. The velocity of this interface is highly influenced by capillary forces mainly caused by the small fibres inside the bundles. In order to better understand which shapes the liquid front takes up at different conditions, a lattice gas model has been applied. First, the macroscopic properties of the solved gas in the liquid are discussed. Next, bubble inclusions are analyzed as to liquid–gas interface position and concentrations of minor component in each phase. The capillary effects at the fluid front are studied for systems both with and without gaps between the bundles. The flow in the interior of the fibre bundles is scrutinized, as well, by also considering the viscous stresses. The flow through unidirectional fabrics is considered by a one-dimensional model, which suggests that the liquid front inside bundles and gaps moves with the same speed when the liquid front inside the bundle has to catch up with the liquid front in the gap. [ABSTRACT FROM AUTHOR]

Flow modeling in fractured reservoirs is largely confined to the so-called sugar cube model. Here, however, we consider vertically fractured reservoirs, i.e., the situation that the reservoir geometry can be approximated by fractures enclosed columns running from the base rock to the cap rock (aggregated columns). This article deals with the application of the homogenization method to derive an upscaled equation for fractured reservoirs with aggregated columns. It turns out that vertical flow in the columns plays an important role, whereas it can be usually disregarded in the sugar cube model. The vertical flow is caused by coupling of the matrix and fracture pressure along the vertical faces of the columns. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach. As found previously for the sugar cube model, the Peclet number, i.e., the ratio between the capillary diffusion time in the matrix and the residence time of the fluids in the fracture, plays an important role. The gravity number plays a secondary role. For low Peclet numbers, the results are sensitive to gravity, but relatively insensitive to the water injection rate, lateral matrix column size, and reservoir geometry, i.e., sugar cube versus aggregated column. At a low Peclet number and sufficiently low gravity number, the effective permeability model gives good results, which agree with the solution of the aggregated column model. However, ECLIPSE simulations (Barenblatt or Warren and Root (BWR) approach) show deviations at low Peclet numbers, but show good agreement at intermediate Peclet numbers. At high Peclet numbers, the results are relatively insensitive to gravity, but sensitive to the other conditions mentioned above. The ECLIPSE simulations and the effective permeability model show large deviations from the aggregated column model at high Peclet numbers. We conclude that at low Peclet numbers, it is advantageous to increase the water injection rate to improve the net present value. However, at high Peclet numbers, increasing the flow rate may lead to uneconomical water cuts. [ABSTRACT FROM AUTHOR]

A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). [ABSTRACT FROM AUTHOR]

The concepts of relative permeability and capillary pressure are crucial for the accepted traditional theory of two phase flow in porous media. Recently, a theoretical approach was introduced that does not require these concepts as input (Hilfer, Physica A, 359:119–128, 2006a; Phys. Rev. E, 73:016307, 2006b). Instead it was based on the concept of hydraulic percolation of fluid phases. This paper presents the first numerical solutions of the coupled nonlinear partial differential equations introduced in Hilfer (Phys. Rev. E, 73:016307, 2006b). Approximate numerical results for saturation profiles in one spatial dimension have been calculated. Long time limits of dynamic time-dependent profiles are compared to stationary solutions of the traditional theory. The initial and boundary conditions are chosen to model the displacement processes that occur when a closed porous column containing two immiscible fluids of different density is raised from a horizontal to a vertical position in a gravitational field. The nature of the displacement process may change locally in space and time between drainage and imbibition. The theory gives local saturations for nonpercolating trapped fluids near the endpoint of the displacement. [ABSTRACT FROM AUTHOR]

We investigated the mechanism of residual gas trapping at a microscopic level. We imaged trapped air bubbles in a Berea sandstone chip after spontaneous imbibition at atmospheric pressure. The pore structure and trapped bubbles were observed bymicrofocused X-ray computed tomography. Distributions of trapped bubbles in Berea and Tako sandstone were imaged in coreflooding at a capillary number of 1.0 x 10-6. Trapped bubbles are of two types, those occupying the center of the pore with a pore-scale size and others having a pore-network scale size. In low-porosity media such as sandstone, connected bubbles contribute greatly to trapped gas saturation. Effects of capillary number and injected water volume were investigated using a packed bed of glass beads 600 µm in diameter, which had high porosity (38%). The trapped N2 bubbles are stable against the water flow rate corresponding to a capillary number of 1.0 x 10-4. [ABSTRACT FROM AUTHOR]

Abstract  Analysis of capillary-pressure distribution in single channels with sinusoidal profile shows that surface tension-driven flow in such channels is controlled by the pressure extrema at their “crests” and “troughs”. Formulating the geometric condition for the pressure in the troughs to exceed that in the crests leads to a simple criterion for the spontaneous break-up of the non-wetting fluid in the necks of the constrictions. The criterion reduces to the condition for the Plateau-Rayleigh instability as a limiting case. Similar pressure analysis is applicable to the case of a non-wetting fluid invading an open pore body. Computational-fluid-dynamics experiments have verified the validity of the break-up predicted from the capillary-pressure argument. Although the geometric criterion for the break-up is valid for small capillary numbers, it provides a common framework in which the results of various published studies of a non-wetting phase choke-off in capillary constrictions for a wide range of capillary numbers can be explained and understood. [ABSTRACT FROM AUTHOR]

Abstract  Different functions describing matrix-fracture transfer were tested for counter-current capillary imbibition interaction. The recovery curves obtained from capillary imbibition experiments were used to fit the transfer functions. The exponential coefficients yielding the best fit to the experimental data were obtained and correlated to the effective parameters such as viscosity, IFT, matrix length and diameter, matrix permeability and porosity, and wettability using multivariable regression analysis. In order to obtain the recovery curves, experiments were conducted on Berea sandstone and Indiana limestone samples. Cylindrical samples with different shape factors were obtained by cutting the plugs 1, 2.5, and 5 cm in diameter and 2.5, 5, and 10 cm in length. All sides were coated with epoxy except one end. More than fifty static imbibition experiments were carried out on vertically and horizontally situated samples where the imbibition took place upward and lateral directions, respectively. Brine–air, brine–kerosene, brine–mineral oil, and surfactant solution–mineral oil pairs were used as fluids. For many matrix shape factors (especially longer and small diameter ones), dividing the recovery curve into three parts were needed as the early, intermediate, and late times, which are typically distinguished by the time required for the imbibition front to reach the closed boundary at the end of the core. Correlations among the exponential coefficients and rock/fluid properties were developed. It was observed that different rock/fluid properties and transfer mechanisms (capillary imbibition and gravity drainage) govern the process for each part. Hence, the analyses done in this study were useful not only for developing explicit transfer functions but also identifying the physics of the counter-current imbibition recovery. [ABSTRACT FROM AUTHOR]

Abstract  A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes the nonlinear effects of the Forchheimer type is laid out by using variational solutions. It is shown that the five main parameters governing the propagation of sound waves in a fluid contained in rigid cylindrical tubes filled with a saturated porous media are: the shear wave number, $${s = R\sqrt{{\overline{\rho}\omega/\mu}}}$$ , the reduced frequency parameter, $${k = {wR}/\overline{a}}$$ , the porosity, ε, Darcy number, $${Da = R/\sqrt{K}}$$ , and Forchheimer number, $${C_F^\ast =2C_F}$$ . The manner in which the flow influences the attenuation and the phase velocities of the forward and backward propagating non-isentropic acoustic waves is deduced. It is found that the inclusion of the solid matrix increases wave’s attenuations and phase velocities for both forward and backward sound waves, while increasing the porosity and the reduced frequency number decreased attenuation and increased phase velocities. The effect of the steady flow is found to decrease the attenuation and phase velocities for forward sound waves, and enhance them for the backward sound waves. [ABSTRACT FROM AUTHOR]

Abstract  Counter-current spontaneous imbibition (COUCSI) in porous media is driven by capillary forces. Capillary action results in a high capillary imbibition pressure at the imbibition front and a low capillary drainage pressure at the outlet face. It is the difference between these two pressures that draws in the wetting phase and pushes out the non-wetting phase. A technique for measuring the capillary pressure at an imbibition front under restricted flow conditions has been developed and applied to Berea sandstone with a range of permeabilities. In the experiments, brine was the wetting phase and refined oil was the non-wetting phase. One end face of a sandstone core was butted to a short section of a finer-pored rock. The composite core surface was then sealed, apart from the end face of the low-permeability segment. A connection to a pressure transducer was set in the opposite end face of the core. Initially, the main core segment was filled with oil. In most cases, the finer-pored segment was filled with brine. Imbibition was started by immersing the core in brine. The purpose of the finer-pored segment was to prevent the escape of non-wetting phase from the open face. For some tests there was an initial period of co-current spontaneous imbibition (COCSI) created by allowing production of non-wetting phase through an outlet tapping in the sealed end face. The outlet was then connected to the transducer and the imbibition changed to COUCSI. There followed an increase in the monitored end pressure to a maximum as fluid redistributed within the core. For the tests in which the fine-pored segments were pre-saturated with brine, even without an initial period of co-current imbibition, limited invasion of the main core segment by brine resulted in an asymptotic rise of the end pressure to a maximum as the imbibition front dispersed. To confirm that the dispersing front did not reach the dead end of the core, the distance of advance of the wetting liquid was detected by a series of electrodes. The maximum value of the end pressure provides an estimate of the capillary pressure at an imbibition front for COUCSI. The maximum capillary pressure generated by the invading fluids ranged from 6.6 kPa to 42 kPa for sandstone with permeabilities between 1.050 (μm)2 and 0.06 (μm)2. [ABSTRACT FROM AUTHOR]

Abstract  To determine the permeabilities from a vertical interference test, earlier investigators proposed correlations or type curves based on point source solutions or partially penetrated well solutions. However, it is impossible for these correlations or type curves to cover all possible scenarios in the real world. In more recent years, people use regression analysis to simultaneously match the pressure responses at the source interval and the observation point. With regression analysis, we face the problem of non-unique solutions. Sometimes, estimated permeability could be outside a reasonable range when analyzing noisy data from real tests. In this paper, a new technique is presented to estimate horizontal and vertical permeabilities from the time-delayed response in a wireline vertical interference test. In a vertical test, a pressure drawdown test period is followed by a pressure buildup test period. Because of the delay in response, the pressure at the observation probe continues to drop for some time while the pressure at the source interval is being built up. The maximum pressure drop at the observation probe with regard to the maximum pressure drop in the source interval is time-delayed. Using this time delay and the maximum pressure drop at the observation probe, vertical and horizontal permeabilities can be estimated. A novel numerical scheme is used. The new technique is compared with the previous methods, and it shows its superiority in accuracy. In addition, it can be used in different test configurations. Application issues in real testing conditions are discussed. Finally, two field tests are analyzed using this technique, while an earlier effort to analyze the tests using a conventional method was not successful due to poor data quality. [ABSTRACT FROM AUTHOR]

Abstract  In the course of stimulation and fluid production, the chemical fluid–rock equilibrium of a geothermal reservoir may become disturbed by either temperature changes and/or an alteration of the fluid chemistry. Consequently, dissolution and precipitation reactions might be induced that result in permeability damage. In connection with the field investigations at a deep geothermal doublet, complementary laboratory-based research is performed to address these effects. The reservoir is located at a depth of 4100 to 4200 m near Groß Schönebeck within the Northeast German Basin, 50 km north of Berlin, Germany. Within the reservoir horizon, an effective pressure of approximately 45 MPa and a temperature of 150°C are encountered. Furthermore, the Lower Permian (Rotliegend) reservoir rock is saturated with a highly saline Ca–Na–Cl type formation fluid (TDS ≈ 255 g/l). Under these conditions we performed two sets of long-term flow-through experiments. The pore fluid used during the first and the second experiment was a 0.1 molar NaCl-solution and a synthetic Ca–Na–Cl type fluid with the specifications as above, respectively. The maximum run duration was 186 days. In detail, we experimentally addressed: (1) the effect of long-term flow on rock permeability in connection with possible changes in fluid chemistry and saturation; (2) the occurrence and consequences of baryte precipitation; and (3) potential precipitations related to oxygen-rich well water invasion during water-frac stimulation. In all substudies petrophysical experiments related to the evolution of rock permeability and electrical conductivity were complemented with microstructural investigations and a chemical fluid analysis. We also report the technical challenges encountered when corrosive fluids are used in long-term in situ petrophysical experiments. After it was assured that experimental artifacts can be excluded, it is demonstrated that the sample permeability remained approximately constant within margins of  ±50 % for nearly six months. Furthermore, an effect of baryte precipitation on the rock permeability was not observed. Finally, the fluid exchange procedure did not alter the rock transport properties. The results of the chemical fluid analysis are in support of these observations. In both experiments the electrical conductivity of the samples remained unchanged for a given fluid composition and constant p-T conditions. This emphasizes its valuable complementary character in determining changes in rock transport properties during long-term flow-through experiments when the risk of experimental artifacts is high. [ABSTRACT FROM AUTHOR]

Abstract  An unsaturated flow and non-passive transport model for water-soluble organic compounds has been implemented in cylindrical coordinates, with a top boundary condition that accounts for different zones of the surface that can be under infiltration or volatilization independently. We simulated two-dimensional infiltration of aqueous mixtures of methanol from a disk source, its redistribution and volatilization in both homogeneous and heterogeneous soils. Simulations showed that the incoming composition significantly affects volumetric liquid content and concentration profiles, as well as the fraction of infiltrated mass of methanol that is released to the atmosphere. Concentration-dependent viscosity had the major impact on the liquid flow. The differences in volumetric liquid content and normalized concentration of methanol became more pronounced during transport through a soil composed of a clay lens embedded within a main matrix of sandy clay loam texture. Dispersion in the liquid-phase was the predominant transport mechanism when dispersivity at saturation was set to 7.8 cm. However, for dispersivity of 1.0 cm, changes in composition led to changes in surface tension inducing significantly higher liquid flow. In this case, liquid-phase advection was the most active transport mechanism for homogeneous soils and highly concentrated infiltrating mixtures. [ABSTRACT FROM AUTHOR]

Abstract  Many reservoir simulator inputs are derived from laboratory experiments. Special core analysis techniques generally assume that core samples are homogeneous. This assumption does not hold for porous media with significant heterogeneities. This paper presents a new method to characterize core scale permeability heterogeneity. The method is validated by both numerical and experimental results. The leading idea consists in injecting a high viscosity miscible fluid into a core sample saturated with a low viscosity fluid. In such conditions, the fluid displacement is expected to be piston-like. We investigate the evolution of the pressure drop as a function of time. A continuous permeability profile is estimated along flow direction from the pressure drop assuming that the core sample is a stack of infinitely thin cross sections perpendicular to flow direction. Thus, we determine a permeability value for each cross section. Numerical and laboratory experiments are carried out to validate the method. Flow simulations are performed for numerical models representing core samples to estimate the pressure drop. The selected models are sequences of plugs with constant permeabilities. In addition, laboratory displacements are conducted for both low permeability and high permeability core samples. To investigate whether there is dispersion inside the porous medium, CT scan measurements are performed during fluid displacement: the location of the front is observed at successive time intervals. The results validate the methodology developed in this paper as long as heterogeneity is one dimensional. [ABSTRACT FROM AUTHOR]

Abstract  Hydrodynamic instability in immiscible porous media flows in the presence of capillarity is investigated here. The analysis and arguments presented here show that the slowdown of instabilities due to capillarity is usually very rapid which makes the flow almost, but not entirely, stable. The profiles of the stable and unstable waves in the far-field are characterized using a novel but very simple approach. [ABSTRACT FROM AUTHOR]

Abstract  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. [ABSTRACT FROM AUTHOR]

Abstract  Although there are a number of mathematical modeling studies for carbon dioxide (CO2) injection into aquifer formations, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study presents the results of computerized tomography (CT) monitored laboratory experiments to analyze permeability and porosity changes as well as to characterize relevant chemical reactions associated with injection and storage of CO2 in carbonate formations. CT monitored experiments are designed to model fast near well bore flow and slow reservoir flows. Highly heterogeneous cores drilled from a carbonate aquifer formation located in South East Turkey were used during the experiments. Porosity changes along the core plugs and the corresponding permeability changes are reported for different CO2 injection rates and different salt concentrations of formation water. It was observed that either a permeability increase or a permeability reduction can be obtained. The trend of change in rock properties is very case dependent because it is related to distribution of pores, brine composition and thermodynamic conditions. As the salt concentration decreases, porosity and the permeability decreases are less pronounced. Calcite deposition is mainly influenced by orientation, with horizontal flow resulting in larger calcite deposition compared to vertical flow. [ABSTRACT FROM AUTHOR]