Dynamic Capillary Pressure Effects Research Articles

A review on measurement of the dynamic effect in capillary pressure

Studies have shown that multiphase flows in porous media are in a transient state with the dynamic effect in capillary pressure. The ignorance of the dynamic effect in capillary pressure might lead to some potential errors in engineering application. In this paper, recent advancements in the measurement of dynamic effect in capillary pressure are reviewed, focusing on the experimental setup, experimental method, and data interpretation method. The measuring technologies are developed both in accuracy and measurement range of porous media and fluids. State-of-the-art measurement technology can measure the dynamic effect in capillary pressure in tight rock and carbonate even with the existence of supercritical fluids. During the measurement process, it is essential to record the pressure difference between the wetting and the non-wetting phases and the in-situ fluid saturation. Besides, the end effect and the rapid change in the pressure at the flowing front need to be prevented. The fluid saturation can be measured through electrical resistivity under various injection pressures, which is applicable to determine the dynamic capillary pressure. The semipermeable elements are particularly the key material for testing the dynamic capillary pressure. Their installation site changes from the ends to the sides of the porous media domain. Additionally, the widely used mass balance-based method is not suitable to obtain the average fluid saturation for less permeable porous media, and calibration is required if the centroid-corrected phase average method and the intrinsic phase average method are used to compute the average dynamic capillary pressure. This paper suggests a reference for the evaluation of multiphase and unsaturated flow in porous media.

Dynamic capillary pressure analysis of tight sandstone based on digital rock model

In recent studies, dynamic capillary pressure has shown significant impacts on the flow behaviors in porous media under transient flow condition. However, the effect of dynamic capillary pressure effect on tight sandstone is still not very clear. Since lattice Boltzmann method (LBM) is a very promising and widely used method in analyzing flow behaviors, therefore, a two-phase D3Q27 LBM model is adopted in this paper to simulate the flow behaviors and analyze the dynamic capillary pressure effect in tight sandstone. Moreover, a new pore segmentation method for tight sandstone base on U-net deep learning model is implemented in this study to improve the pore boundary qualities of pore space, which is crucial for two-phase LBM simulation of tight sandstone. A total of 3800 3D sub-volume data sets extracted from computed tomography data of 19 tight sandstone samples are selected as ground truth data to train the network and segment the pore space afterward. The simulation results based on the segmented digital rock model, show that nonwetting phase fluid prefer the path with lower dynamic capillary pressure in the seepage process before breaking through the porous model. Furthermore, the increase of injection rate causes the saturation changes more quickly, injection rate also shows apparent positive correlation relationship with capillary pressure, which implies that dynamic capillary pressure effect also exists in tight sandstone, and LBM based two-phase flow simulation could be used to quantitatively analyze such effect in tight sandstone. Cited as : Cao, Y., Tang, M., Zhang, Q., Tang, J., Lu, S. Dynamic capillary pressure analysis of tight sandstone based on digital rock model. Capillarity, 2020, 3(2): 28-35, doi: 10.46690/capi.2020.02.02

A comprehensive modelling investigation of dynamic capillary effect during non-equilibrium flow in tight porous media

The dynamic capillary effect in capillary pressure plays a significant role during the non-equilibrium flow in porous media for various chemical, environmental and petroleum processes. A unified model is developed in this work to estimate the dynamic capillary effect in matrix during the non-equilibrium flow in tight porous media. Multiple influential parameters (especially fluid viscosity, surfactant and fracture with inconsistent effects) and the interplays between them are comprehensively considered. Firstly, a databank of the relationship between the dynamic capillary coefficient and the main controlling parameters is established through non-equilibrium flow experiments on the fractured and intact tight core samples. Secondly, the previously unclear correlations between the dynamic capillary coefficient and the influential parameters are determined individually, which are then incorporated into an overall model based on the Buckingham’s π-theorem. The proposed model is further validated and simplified, showing accurate matches with the R2 ≈ 0.95. At last, the sensitivity analysis of five different non-equilibrium flow conditions is conducted, through which effects of the influential parameters on the dynamic capillary effect are investigated. The proposed model can reasonably explain the porous media properties, the easiness and uniformity of the fluid flow, and the effect of viscous force for the non-equilibrium flow in tight porous media. The findings of this study can help for a better understanding of multiphase flow in tight porous media.

Impacts of dynamic capillary pressure effects in supercritical CO2-Water flow: Experiments and numerical simulations

Contrary to report that dynamic capillary pressure effect was insignificant in the supercritical CO2-water (scCO2-water) flow system, this work found the effect to be considerable in the displacement of water or brine by injected scCO2 in the geological carbon sequestration, especially prior to the attainment of equilibrium in the system. Series of controlled laboratory scale experimental measurements and numerical simulations of the dynamic capillary pressure effect and its magnitude (dynamic coefficient, τ) for supercritical CO2-water(scCO2-water) system are reported in unconsolidated silica sand. Novel measurement technique has been developed to achieve this purpose, by applying the concept of two-phase flow system in the context of geological carbon sequestration. This work considers the injection of scCO2 into storage aquifer as a two-phase flow system, where the CO2 displaces the resident fluid (brine or water). Using a high-pressure and high-temperature experimental rig, capillary pressure–saturation relationships (Pc-S) for this flow system and the saturation rate dependencies of the Pc-S relationships (quantified by dynamic coefficient, τ), known as dynamic capillary pressure effect were determined. This τ was previously unreported for scCO2-water system. In scCO2-water flow system, τ ranges from 2 × 105 to 6 × 105 Pa s at high water saturation and 1.3 × 106 to 8 × 106 Pa saround the irreducible saturation. τ increases with rising temperature but decreases with increase in porous medium permeability. Numerically determined τ-S relationships compare well with the corresponding experimental results for wide range of water saturation.The implication was that water saturation of the porous media will be considerably underestimated, if the dynamic capillary pressure effect was ignored in the characterization of the scCO2-water flow system, i.e., if only equilibrium Pcrelationship was used.

The dynamic effect in capillary pressure during the displacement process in ultra-low permeability sandstone reservoirs

The relationship between the capillary pressure and saturation is a primary factor to describe and simulate the multiphase flow. This relationship is also fundamental to understand the characteristics of oil and gas reservoirs and make the reservoir development plan. Traditionally, the capillary pressure is measured under the equilibrium process; however, this equilibrium is hard to establish when the multiphase flow is expected in low to tight permeability porous media, and the capillary pressure is dynamic. This laboratory study conducts specially designed dynamic displacement experiments to examine the dynamic effect in capillary pressure in ultra-low permeability sandstone oil reservoirs. The dynamic capillary pressure, the dynamic relative permeabilities, the dynamic coefficient and the change rate of water saturation are obtained. Results show that the dynamic coefficient is relatively larger in ultra-low permeability reservoirs compared with that in high to low permeability reservoirs. Difference between the dynamic and the steady capillary pressures becomes more significant for less permeable porous media, with a higher dynamic coefficient and a stronger dynamic effect. Wettability advancement has been triggered during the dynamic displacement process, which is responsible for the water-wet rock before the displacement to be oil-wet during the displacement process. The difference between the dynamic and the steady relative permeabilities becomes obvious, and the dynamic effect in capillary pressure cannot be neglected when the permeability reaches ultra-low. The dynamic coefficient can reveal the shape of the displacement front. Cited as : Li, Y., Li, H., Cai, J., Ma, Q., Zhang, J. The dynamic effect in capillary pressure during the displacement process in ultra-low permeability sandstone reservoirs. Capillarity, 2018, 1(2): 11-18, doi: 10.26804/capi.2018.02.01

The effect of a microscale fracture on dynamic capillary pressure of two-phase flow in porous media

Abstract Dynamic capillary pressure (DCP) effects, which is vital for predicting multiphase flow behavior in porous media, refers to the injection rate dependence capillary pressure observed during non-equilibrium displacement experiments. However, a clear picture of the effects of microscale fractures on DCP remains elusive. This study quantified the effects of microscale fractures on DCP and simulated pore-scale force and saturation change in fractured porous media using the multiphase lattice Boltzmann method (LBM). Eighteen simulation cases were carried out to calculate DCP as a function of wetting phase saturation. The effects of viscosity ratio and fracture orientation, aperture and length on DCP and DCP coefficient τ were investigated, where τ refers to the ratio of the difference of DCP and static capillary pressure (SCP) over the rate of wetting-phase saturation change versus time. Significant differences in τ values were observed between unfractured and fractured porous media. The τ values of fractured porous media were 1.1 × 104 Pa ms to 5.68 × 105 Pa ms, which were one or two orders of magnitude lower than those of unfractured porous media with a value of 4 × 106 Pa. ms. A horizontal fracture had greater effects on DCP and τ than a vertical fracture, given the same fracture aperture and length. This study suggested that a microscale fracture might result in large magnitude changes in DCP for two-phase flow.

A new numerical approach for investigation of the effects of dynamic capillary pressure in imbibition process

Capillary pressure is important in simulation of fluid flow in porous media at different scales. In ongoing simulation methods, capillary pressure is considered as a static process. However, recent researches have shown that capillary pressure is dynamic parameter. That is, its value directly depends on the rate of saturation changes. Including the effects of dynamic capillary pressure is especially important in prediction of imbibition process, which is an important mechanism in oil production from naturally fractured reservoirs. In this study, to investigate the effects of dynamic capillary pressure in two-phase flow process, an implicit and iterative method is proposed, and it is implemented in an open-source simulator named Matlab Reservoir Simulation Toolbox (MRST). The convergence results show that the proposed algorithm works well and the obtained results are acceptable. Furthermore, the analysis is made on the effects of dynamic capillary pressure functions in vertical imbibition process cases. The results confirm that considering dynamic capillary effects is critical in the simulation of two-phase flow in porous media. This is more important in imbibition process, where the capillary force is the dominant driving force. It is also found that at high permeability cases, considering dynamic capillary pressure effects is more crucial. Also, it is concluded that in high mobility ratios, due to low imbibition rates, effect of considering dynamic capillary pressure curves is not significant.

A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media

AbstractAn adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure effect in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive monitor function with directional control is applied to redistribute the mesh grid in every time step, then a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the proposed method.

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

Capillary pressure-saturation-relative permeability relationships (Pc-Sw-Kr) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic Kr-Sw relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, Krw, was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, Krnw, was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure Krw decreases while Krnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with Krnw decreasing as domain size increases. Effect of mea- surement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between Kr-Sw relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (s) were plotted as a function of water saturation (Sw), which showed that m decreases as s increases at a given saturation, or vice versa.

Artificial neural network modeling of scale-dependent dynamic capillary pressure effects in two-phase flow in porous media

A computationally efficient and simple alternative platform for the prediction of the domain scale dependence of the dynamic capillary pressure effects, defined in terms of a coefficient named as dynamic coefficient (τ), is developed using an artificial neural network (ANN). The input parameters consist of the phase saturation, media permeability, capillary entry pressure, viscosity ratio, density ratio, temperature, pore size distribution index, porosity and domain volume with corresponding output τ obtained at different domain scales. Different ANN configurations as well as linear and nonlinear multivariate regression models were tested using a number of performance criteria. Findings in this work showed that the ANN structures with double hidden layers perform better than those with a single hidden layer. In particular, the ANN configuration with 13 and 15 neurons in the first and second hidden layers, respectively, performed the best. Using this best-performing ANN, effects of increased domain size were predicted for three separate experimental results obtained from literature and our laboratory with different domain scales. Results showed increased magnitude of τ as the domain size increases for all the independent experimental data considered. This work shows the applicability and techniques of using ANNs in the prediction of scale dependence of two-phase flow parameters.

Scale dependent dynamic capillary pressure effect for two-phase flow in porous media

Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well.

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

Numerical simulations for core‐scale capillary pressure (Pc)‐saturation (S) relationships have been conducted for a supercritical carbon dioxide‐water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO2. As the Pc‐S relationships depend on both S and time derivative of saturation ( ) yielding what is known as the “dynamic capillary pressure effect” or simply “dynamic effect,” this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide‐water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO2 (scCO2)‐water flow is reached. The simulations in this work involved the solution of the extended version of Darcy's law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried out for three‐dimensional cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best‐fit straight line plotted between (1) the differences in dynamic and equilibrium capillary pressures against (2) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO2‐water system increases as the saturation decreases. From a practical point of view, it implies that the time to reach capillary equilibrium during geological sequestration of CO2 is an important factor and should be accounted for while simulating the flow processes, for example, to determine the CO2 storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for scCO2‐water flow as well as τ values. These issues are addressed in this article. © 2014 American Institute of Chemical Engineers AIChE J 60: 4266–4278, 2014

Dynamic Effect of Capillary Pressure in Tight Gas Reservoir

Standard theories for two-fluid flow in porous media assume capillary pressure to be in equilibrium. Numerical simulators often assume that equilibrium capillary pressure-saturation conditions are maintained as changes in fluid satu- ration are taking place. But recent theories indicate that capillary pressure is perhaps not only a function of saturation but also rate change, which is known as the dynamic effect. In order to investigate effects of the dynamic capillary pressure on fluid flow in tight gas reservoirs, standard theory and present novel pore-scale and Darcy-scale theoretical approaches that account for a dynamic capillary pressure were reviewed in this paper. A dynamic capillary pressure relationship was included in the mathematical and numerical schemes were proposed to simulate tight gas reservoir production, which al- lows one to identify previously unreported flow scenarios. The numerical schemes were also to modify the Gray and Has- sanizadeh equation for infiltration to account for a capillary pressure that depends on the flow velocity. This study is of great benefit to finding out the flow law of tight gas reservoir and the subsequent work of exploitation.

The Influence of Dynamic Capillary Pressure on the Seepage of Ultra-Low Permeability Reservoir

Capillary pressure has a great influence on the percolation of oil-water two-phase. We find that the seepage resistance of oil-water two-phase in ultra-low permeability reservoir is complex and the capillary pressure presents dynamic variation features through water flooding experiment. In this paper, first, we study the variation features of seepage resistance by mercury injection experiment. Second, we establish a percolation numerical model of oil-water twophase which considers the dynamic capillary pressure in ultra-low permeability reservoir. Finally, we analyze the sensitive factors of dynamic capillary pressure and the effects of dynamic capillary pressure on oil-water two-phase seepage. The results show that the capillary pressure and the dynamic effect of capillary pressure are obvious in ultra-low permeability reservoir. When the coefficient of dynamic capillary pressure or the injection rate is larger, the dynamic capillary pressure will be bigger. The existence of dynamic capillary pressure hinders the fltting speed of waterflood front and reduces the oil production. The dynamic capillary pressure makes the moisture content rise faster for water wetting ultra-low permeability reservoirs while it reduces the rising velocity of moisture content for oil wetting ultra-low permeability reservoirs. This study is of great benefit to finding out the percolation law of ultra-low permeability reservoir and the subsequent work of development.

Investigation of Dynamic Effect of Capillary Pressure in Ultra-Low Permeability Sandstones

Generally, an empirical relationship between capillary pressure and saturation obtained by means of laboratory experiments is used to describe capillary pressure. However, this relationship assumes equilibrium in the distribution of the phases in the porous medium. This assumption is valid in cases where saturation varies slowly, however it may not be appropriate for application in faster processes. In such cases, dynamic effects may have an influence on the system. In this study, an extended relationship of capillary pressure that includes the dynamic effect is chosen to be implemented into the percolation model of two-phase flow in ultra-low permeability (K is less than 1 × 10−3 μm2) sandstones. This model is used for the numerical simulation. The purpose of this study is to examine the influence of the inclusion of the extended relationship on two-phase flow. Firstly, the dynamic effect was investigated through laboratory tests and then the factors influencing on the dynamic capillary pressure were analyzed. Secondly, the percolation model of two-phase flow considering the dynamic effect was established. Finally, the influences of dynamic capillary pressure on two-phase flow were investigated. The results reveal that the dynamic effect of capillary pressure is obvious in ultra-low permeability reservoir. The inclusion of the dynamic capillary pressure relationship has a different influence compared to the cases without capillary pressure. The existence of dynamic effect has a significant influence on the water saturation distribution and oil production. The moisture content rises faster for water-wetting sandstones but the rising velocity is reduced for oil-wetting sandstones considering the dynamic effect.

Determination of dynamic relative permeability in ultra-low permeability sandstones via X-ray CT technique

Forced oil–water displacement is the crucial mechanisms of secondary oil recovery. The knowledge of relative permeability is required in the simulation of multiphase flow in porous media. Obvious dynamic effect of capillary pressure occurs in that the formation of ultra-low permeability reservoir (the permeability is <1 × 10−3 μm2) is tight and the pores and throats are very small. In addition, the significant capillary end effect causes serious errors when calculating relative permeabilities. For these reasons, the JBN method (neglecting capillary pressure) does not apply. Therefore, the dynamic capillary pressure and capillary end effects should be taken into account. This work focuses on calculating two-phase relative permeability of ultra-low permeability reservoir through considering the dynamic capillary pressure and eliminating the influence of capillary end effects. Firstly, laboratory core scale measurements of in situ water phase saturation history based on X-ray CT scanning technique were used to estimate relative permeability. Secondly, a mathematical model of two-phase relative permeability considering the dynamic capillary pressure was established. The basic problem formulations, as well as the more specific equations, were given, and the results of comparison using experimental data are presented and discussed. Results indicate that the dynamic capillary pressure measured at laboratory core scale in ultra-low permeability rocks has a significant influence on the estimation of unsteady-state relative permeability. The mathematical calculating method was compared with the history matching method and the results were close, suggesting reliability for ultra-low permeability reservoirs. Importantly, the proposed methods allow measurement of relative permeability from a single experiment. Potentially this represents a great time savings.

Experimental investigation of hysteretic dynamic effect in capillary pressure–saturation relationship for two‐phase flow in porous media

Well‐defined laboratory experiments have been carried out to investigate hysteretic dynamic effect in capillary pressure–saturation relationships for two‐phase flow in homogeneous and heterogeneous (layered) porous media. Conceptually, the dependence of the capillary pressure curves on the rate of change of saturation (dSw/dt) is defined as the dynamic effect in capillary pressure relationship, which is indicated by a dynamic coefficient, τ (Pa s) and it determines the rate at which two‐phase flow equilibrium is reached, i.e., dSw/dt = 0 where Sw and t are the water saturation and time, respectively. The dependences of τ on various fluid and porous materials properties have been studied in the context of drainage; but, there is limited study for imbibition and the hysteresis of τ−Sw relationships. As such, the emphasis in this article is on reporting τ−Sw curves for imbibition while also demonstrating the hysteresis in the τ−Sw relationships by comparing τ−Sw curves for drainage (previously reported) and imbibition (this study) in carefully designed laboratory experiments. Homogeneous sand samples composed of either fine (small particle size and lower permeability) or coarse (larger particle size and higher permeability) sand have been used for these experiments. Furthermore, a layered domain made of a find sand layer sandwiched between two coarse sand layers is used as a model of heterogeneous domain. The results of the study confirm that the τ−Sw relationships are hysteretic in nature and, as such, the speed to flow equilibrium should vary depending on whether drainage or imbibition takes place. At a particular water saturation, the magnitudes of the dynamic coefficient (τ) are found to be generally higher for imbibition, which imply that the speed to flow equilibrium at the same saturation will be slower for imbibition. © 2013 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 59: 3958–3974, 2013

Simulation of Infiltration Processes in the Unsaturated Zone Using a Multiscale Approach

We consider the infiltration of a wetting fluid into a homogeneous porous medium and the formation of preferential flow paths with saturation overshoots. These are caused by dynamic capillary pressure effects which can be modeled by the rate-dependent approach of Hassanizadeh and Gray. To track the overshoot wave numerically, we propose an extended Heterogeneous Multiscale Method. In the approach, the rate-dependent model takes the role of a microscale model. The algorithm is applied to several infiltration problems.

Dynamic effect of capillary pressure in low permeability reservoirs

Abstract The dynamic effect of capillary pressure in oil-water two-phase percolation flow in low permeability reservoirs was investigated by experiment and numerical simulation. An experimental apparatus was constructed to measure the relationship between the dynamic capillary pressure and water saturation change rate, and the dynamic capillary coefficient of low-permeability cores was calculated. A one-dimensional mathematical percolation model was established to analyze the effect of dynamic capillary pressure on waterflooding process. The dynamic capillary pressure effect is too significant to be neglected. The relationship between the dynamic capillary pressure and the change rate of wetting phase saturation is almost linear. The lower the rock permeability is, the greater the dynamic capillary coefficient and threshold pressure gradient are. One of the reasons for non-Darcy two-phase percolation flow is the dynamic capillary pressure effect. The dynamic capillary pressure in low permeability reservoirs has a significant influence on development indices such as the velocity of displacement front, water breakthrough time, pressure distribution, oil production rate, and recovery factor.

Universal scaling of spontaneous imbibition for water‐wet systems

Spontaneous, counter‐current imbibition (SI) is a key mechanism in many multiphase flow processes, such as cleanup of nonaqueous phase liquids (NAPLs), bioremediation, or CO2 storage. For interpreting and upscaling laboratory SI data, and modeling and prediction purposes, scaling groups are an essential tool. The question of how to formulate a general scaling group has been debated for over 90 years. Here we propose the first scaling group that incorporates the influence of all parameters on SI that are present in the two‐phase Darcy model. The group is derived rigorously from the only known exact analytical solution for spontaneous imbibition by relating the cumulative water phase imbibed to the normalized pore volume. We show the validity of the group by applying it to 42 published SI studies for water‐oil and water‐air experiments, for a wide range of viscosity ratios, different materials, different initial water saturations, and different length‐scales. In all cases, water was the wetting phase. Our group serves as a “master equation” whose generality allows the rigorous prediction of the validity of a large number of specialized scaling groups proposed during the last 90 years. Furthermore, our results give strong evidence that the Darcy model is suitable for describing SI, and that including dynamic effects in capillary pressure is not necessary for counter‐current SI, contrary to what has been hypothesized. Two key applications of the group are discussed: First, the group can serve as the long sought after general transfer rate for imbibition used in dual‐porosity models. Second, it is the so far missing proportionality constant in imbibition‐germination models for plant seeds.