Influence Of Capillary Pressure Research Articles

Role of capillary pressure on carbon dioxide sequestration: mathematical analysis

ABSTRACT Geological disposal of CO2 after capturing the gas from large emitting sources is one of the safest and most prominent methods to eliminate CO2 from the atmosphere and mitigate climate change. The heterogeneities in porosity, permeability and capillary pressure in various underground formations impact gas distribution, affecting their storage capacity. Therefore, a numerical model is developed to study the plume migration under various physical heterogeneities by upscaling the variation in capillary pressure. Accordingly, homogeneous, heterogeneous and layered formations have been considered. The influence of capillary pressure and field-scale heterogeneities, such as porosity and permeability, is incorporated using the Leverett J function. The impact of variations in capillary pressure on gas migration is calibrated in different formations for ten years of injection. The analysis project that plume evolution in different formations highly deviates and a plume length of 3410 m is obtained for layered formation. A sensitivity analysis was conducted to understand the influence of interfacial tension in formations with differing heterogeneity. The change in interfacial tension impacts the average saturation of CO2, ranging from 0.287 to 0.155 in heterogeneous aquifers. The plume migration decreases in layered and increases in homogenous and heterogeneous media with decreased interfacial tension.

The Influence of Wettability Effect and Adsorption Thickness on Nanoconfined Methane Phase Behavior: Vapor-Liquid Co-Existence Curves and Phase Diagrams

Research interest in the behavior of methane inside nanopores has been growing, driven by the substantial geological reserves of shale gas and coalbed methane. The phase diagram of methane in nanopores differs significantly from its bulk state, influencing its existing form and pertinent physical properties—such as density and viscosity—at specific pressures and temperatures. Currently, there is a lack of effort to understand the nanoconfinement effect on the methane phase diagram; this is a crucial issue that needs urgent attention before delving into other aspects of nanoconfined methane behavior. In this study, we establish a fully coupled model to predict the methane phase diagram across various scales. The model is based on vapor-liquid fugacity equilibrium, considering the shift in critical pressure and temperature induced by pore size shrinkage and adsorption-phase thickness. Notably, our proposed model incorporates the often-overlooked factor of capillary pressure, which is greatly amplified by nanoscale pore size and the presence of the adsorption phase. Additionally, we investigated the impact of surface wettability, correlated to capillary pressure and the shift in critical properties, on the methane phase diagram. Our results indicate that (a) as pore size decreases, the methane phase diagram becomes more vertical, suggesting a transition from a gaseous to a liquid state for some methane molecules, which is contrary to the conventional phase diagram; (b) enhancing surface wettability results in a more vertical phase diagram, with the minimum temperature corresponding to 0 MPa pressure on the phase diagram, increasing by as much as 87.3%; (c) the influence of capillary pressure on the phase diagram is more pronounced under strong wettability conditions compared to weak wettability, and the impact from the shift in critical properties can be neglected when the pore size exceeds 50 nm.

A MODEL FOR CAPILLARY PRESSURE INTERMEDIATED LIQUID-GAS TWO-PHASE FLOW IN SINGLE FRACTURES

The liquid-gas two-phase flow in rock fractures is of great significance in the community of civil engineering. The flow velocity of a fluid through a rock fracture depends on both the hydraulic conductivity of the fracture and the applied pressure drop along the fracture. The capillary pressure intermediates the liquid-gas two-phase flow in fractures by altering the "effective" pressure drop acting on both gas and liquid phases flowing in fractures. This paper presents a liquid-gas two-phase flow model, into which the influence of capillary pressure was introduced to quantify the interaction between the liquid phase and the gas phase. The liquid-gas two-phase flow was found to exhibit different patterns at different flow rates, i.e., bubble flow, slug flow, annular flow, and droplet flow. The contact angle, capillary pressure, and relative permeability at different liquid-gas flow rates were calculated. Numerical simulation data and experimental data were used to compare the predictions using the capillary pressure model with those using the existing liquid-gas two-phase flow models. It is found that the capillary pressure model prevails over the existing models in describing the characteristics of complex flow patterns. The effect of capillary pressure on relative permeability was discussed as well.

Oscillations of free surface at the edge of short capillary tubes

Liquid gets imbibed into the capillary tube under the influence of capillary pressure. If capillary tube is shorter than Jurin height, oscillations of free surface are observed when contact line is confined by the edge of tube. Through numerical simulations and theoretic analyses, the velocity at the tube edge is determined, and the morphologies of meniscus at different stages of oscillation are identified. Finally, the oscillation period is found to be linearly correlated to rρL/γ through scale analysis, which is also verified by the simulation results. Discoveries in this paper show that new dynamics exists during the conversion between inertia and surface energy.

A Calculation Model of the Dimensionless Productivity Index Based on Non-Piston Leading Edge Propulsion Theory in Multiple Oilfield Development Phases

The dimensionless productivity index is an important indicator for measuring the oil production capacity of oilfields. The traditional calculation method of the dimensionless productivity index is not suitable for the continuous multiple development phases of oilfields. In this study, based on Darcy’s Law and the theory of non-piston leading edge propulsion, we considered the influence of capillary pressure and derived a differential equation for leading edge propulsion distance. We established a calculation model of the dimensionless productivity index that is suitable for the multiple development phases of oilfields, including water flooding, polymer flooding, and binary compound flooding. The model was applied to the W block of the JZ9-3 oilfield, and the calculation results of the model were compared with the actual statistical results. The results show that the calculation error rates of the dimensionless productivity index in three phases of oilfield development are 4.67%, 17.65%, and 18.50%, respectively, and the average error rate is 10.38% in the overall development phase. The dimensionless productivity index curve shows a trend of first rising, then falling, and finally stabilizing when the pore volume number is included. This calculation model expands the field application scope of the theoretical dimensionless productivity index, which is convenient for application in oilfields, and improves the efficiency of the comprehensive evaluation of oilfields during multiple development phases.

Plastic Shrinkage Cracking of Self-compacting Concrete: Influence of Capillary Pressure and Dormant Period

Abstract This research investigates the effect of capillary pressure and the length of the hydration dormant period on the plastic shrinkage cracking tendency of SCC by studying specimens produced with different w/c ratios, cement types and SP dosages. A relationship between the capillary pressure rate and the length of the hydration dormant period is defined, which can explain the cracking severity of the concrete when the volumetric deformation is unknown. The results show, that the cracking tendency of SCC was the lowest in case of w/c ratio between 0.45 and 0.55, finer and more rapid hardening cement, and lower dosage of SP. The dormant period was prolonged by increasing the w/c ratio, using coarser cement, and higher SP dosage. It was concluded that the cracking tendency of concrete is a function of the capillary pressure buildup rate and the length of the dormant period.

A comprehensive model for calculating relative permeability based on spontaneous imbibition and CT scanning measurement

Relative permeability plays an essential role in evaluating reservoir characteristics in reservoir engineering. However, due to the tight reservoirs of low permeability and low porosity, conventional methods cannot accurately measure the relative permeability curves, even in a long time. The objective of this work is to develop an analytical model of spontaneous imbibition considering the influence of capillary pressure, which can be used to obtain the relative permeability curves for tight reservoirs. We derived an equation about fractional flow function (F(Sw)) and nonlinear coefficient (D(Sw)). Then combined with an empirical relative permeability model with uncertain parameters, a numerical method is used to calculate the fractional flow function, and an analytical water saturation curve can be drawn. After that, fitting CT scanning data with the analytical water saturation curves, a detailed relative permeability curves were acquired. The results show that relative permeability curves can be obtained by this method, and only use a spontaneous imbibition and CT scanning data, avoiding waste of time for testing relative permeability curves. The proposed model provides a more efficient tool for evaluating the relative permeability of the tight reservoirs.

An investigation of remediation and recovery of oil spill and toxic heavy metal from maritime pollution by a new absorbent material

The extremely serious effects of the marine environment pollution due to oil spill, oil slick and toxic heavy metals on the human, ecosystem, and society are clearly seen. Findings of absorbent materials with high absorption capacity and high usage efficiency are being much interested by several researchers. In this work, four samples of absorbent material fabricated after adding, respectively, 5%, 25% of rice straw mass percentage along with 0.5 and 3 mm of rice straw size, four oil types including crude oil, fuel oil (FO), diesel oil (DO), kerosene, and a solution containing toxic heavy metals such as Cd2+, Pb2+, Hg2+ are used for the experimental purposes related to the evaluation of the oil absorption capacity (OAC) and toxic heavy metal, and the oil removal efficiency (ORE) during 120–150 min. As a result, the as-used sample with 25% of rice straw mass and 0.5 mm of rice straw size shows the highest absorption capacity. In addition, the influence of capillary pressure on the OAC and ORE is analysed, the assistance of Scanning Electron Microscope (SEM) for observation of porous structure of rice straw, pristine PU, and the as-fabricated absorbent are also conducted and presented in this study.

Influence of Water–Oil Saturation on the Fracture Process Zone: A Modified Dugdale–Barenblatt Model

The wetting and nonwetting fluid saturations in porous reservoirs always change during long-term injection and production. The fracture process zone (FPZ) is a prominent feature in the rock fracture process. If the FPZ properties are influenced by pore fluids, the process of hydraulic fracturing will change greatly. The existing models do not consider the role of pore fluid when characterizing the FPZ. In this paper, a modified Dugdale–Barenblatt (D–B) model with capillary pressure is proposed. The model reflects the fact that the FPZ length decreases nonlinearly with the increase in capillary pressure, and it reveals the mechanism of capillary pressure on the equivalent fracture cohesion in the FPZ, which affects the FPZ length. Three-point bending tests were carried out on sandstone under various fluid saturations through digital image correlation (DIC), acoustic emission (AE), and scanning electron microscope (SEM). It was found that the FPZ length of the water–oil-saturated samples was 30–50% smaller than that of water-saturated/oil-saturated samples due to the capillary pressure effect, and the modified D–B model was well consistent with the experiments. The AE behaviors of different saturated samples were not the same: The cumulative AE signals changed abruptly at 90% of the peak load for the water–oil-saturated samples and at 50% of the peak load for water-saturated samples. This demonstrated that the effect of capillary pressure was more obvious than the weakening effect of microstructural damages. The significant influence of capillary pressure on FPZ requires continuous recognition in hydraulic fracturing design.

Examination of unconventional phenomena in naturally fractured liquid-rich gas reservoirs: single-block compositional model

During the depletion of liquid-rich gas reservoirs, the gas condenses as the pressure inside the reservoir reduces below the hydrocarbon dew-point pressure, which introduces retrograde condensate. In such conditions, the productivity experiences a reduction in recovery due to the appearance of condensate near the production channels. This work is aimed to provide insight on productivity characteristics of a liquid-rich gas system in unconventional environments and extend the scrutiny on the propagation of condensate while activating capillary forces and diffusion. The impact of capillary pressure on phase behavior was explored using an in-house generated coupled phase behavior model with a capillary pressure equation. The influence of capillary pressure was examined against different sets of composition combinations in different reservoir settings. Capillary force extents were highly dependent on composition combinations and pore throat radiuses. Mixtures with higher volatile concentrations showed the highest capillary forces. The enhancement in condensate propagation, resistance to gas flow, and impact on recovery were explored at 10- and 20-nm pore throat sizes. The investigation suggested that interfacial tensions implied greater influence on the flow behavior in oil-dominated systems than in gas-dominated conditions. Evaluating the flow performance of unconventional phenomena in liquid-rich gas reservoirs was extended to include diffusion while activating capillary forces. The results showed higher domination of diffusion on reservoir performance, which provided additional fluid recovery. Subsequently, the enhanced withdrawal of fluid dismissed the impact of capillary forces on gas flow and the impact of condensate blockage.

Fundamental aspects of the interaction between hardened cement paste and water applied to improve prediction of shrinkage and creep of concrete: A Critical Review

In this contribution, selected fundamental properties of concrete are presented and discussed. Basic mechanisms of shrinkage are first described in some detail. With increasing age of concrete different mechanisms of shrinkage become activated. During the first few hours after mixing, dissolution of cement is the main shrinkage mechanism. Depending on the humidity of the surrounding air, capillary pressure in the pore water may cause serious damage in the first few hours. After this initial loss of water, the remaining aqueous solution is retreated in the pores between fine aggregates and first hydration products. At this scale, the role of disjoining pressure is pointed out in detail and it becomes clear that the influence of capillary pressure on shrinkage of hardened concrete can be neglected. Additionally, at relative humidity lower than 50%, the dominating mechanism is the increasing surface energy of the drying gel particles. Shrinkage of high-strength concrete has a totally different time evolution. The moisture distribution n aging high-strength concrete is completely different. If high-strength concrete is exposed to an environment with RH higher than 80%, there will be no shrinkage at all but swelling. These fundamental aspects of shrinkage have to be taken into consideration when long-term shrinkage is to be predicted. Creep of concrete can be described in a realistic way by means of rate theory. Elements of rate theory are briefly described. The influence of temperature and applied stress is outlined. Most important, however, is the influence of humidity content. As the humidity content of high-strength concrete is comparatively low, creep is significantly reduced as compared to normal concrete. Prediction of creep can be significantly improved if these fundamentals are taken into consideration.

An adaptive multiscale approach for modeling two-phase flow in porous media including capillary pressure

[2] Many important applications in porous media require the large-scale simulation of complex physical processes. Due to the limitations of computational resources, huge model domains often have to be simulated on relatively coarse grids. However, depending on the application, a high spatial resolution may be necessary to capture important effects, for example due to small-scale heterogeneities. One solution strategy is multiscale modeling. The idea is to decrease the number of global degrees of freedom while preserving important fine-scale features. In this work, we present a multiscale approach for modeling two-phase flow in porous media, which is applicable in a wide range of flow regimes, but especially if the influence of capillary pressure is significant. In this case, many existing upscaling or multiscale techniques, originally developed and successfully used for advection-dominated systems, fail or are not able to yield sufficiently accurate results. We combine an adaptive grid method based on multipoint flux approximation with various local upscaling techniques. In particular, the numerical method has to be able to treat complex effective parameters like anisotropic phase permeabilities. A crucial point is the development of suitable grid-adaptation strategies to account correctly for important effects. The method is tested and proven to work for various examples including varying heterogeneous parameter fields and different flow regimes.

Influence of capillary pressure and trapping hysteresis on large-scale CO<SUB>2</SUB> migration

Influence of capillary pressure and trapping hysteresis on large-scale CO<SUB>2</SUB> migration

Influence of capillary pressure in bubbles on their attachment to particles during froth flotation: Part two

The calculation of the energy possibility of the transfer of spherical bubble A into adhered bubble M or the A → M transition (AMT) shows how large the influence of the capillary pressure (Pc) on the results of calculation is and how, as bubbles A and M diminish and Pc in them increases, the range of the possible variation of PcM in bubble M abruptly narrows. The influence of PcM on the energy barrier on the path to the adherence of the bubble to a hydrophilic surface drops almost to zero, but the preference to the adherence of the bubbles to a hydrophobic surface is retained, although the difference noticeably decreases compared with large bubbles. The data of the practice of the first processes of froth flotation by microbubbles are the confirming experimental base of the results of this precision calculation. A decrease in wetting angle θM to 0.02° and the beginning increase in the spreading coefficient of the adhered bubble over the substrate particle apparently also promotes the adherence process in practice.

Influence of Capillary Pressure and Injection Rate as well as Heterogeneous and Anisotropic Permeability on CO2 Transport and Displacement Efficiency in Water-Saturated Porous Media

Greenhouse gas emission from industrial production and human living has been widely recognized as one of the primary reasons which cause global climate warming. CO2 sequestration in saline aquifers plays an important role in effectively reducing the greenhouse gas emission. Numerical modeling can be used to quantitatively analyze the effect of some formation properties on the storage processes of CO2 in saline aquifers. Magnetic resonance imaging (MRI) technology may be used to observe the evolution of CO2 plume through time in porous rocks and hence provide an effective means for validate the reliability of the numerical modeling. Based on a combined use of the numerical modeling and the MRI measurement of the vertical injection of the supercritical CO2 into water-saturated rock cores, this study presents a lab-scale investigation on the influence of the heterogeneous and anisotropic permeability, the CO2 injection rate and capillary pressure on the transport of CO2 plume as well as the CO2 utilization efficiency of subsurface space in saline aquifers. Our results indicate: 1) both the heterogeneity and the anisotropy of permeability can enhance the CO2 displacement efficiency. Ignoring these two permeability properties can cause the obvious deviation in the predicted CO2 saturation and transport processes by the model; 2) the enhanced sequestration efficiency by the anisotropy depends on the degree and spatial extension of itself. If the approximately stochastically distributed permeability anisotropy represents natural conditions, specifying the constant ratio of the vertical permeability to the horizontal one in the model to mimic the real permeability can lead to the obvious over-estimation of the CO2 displacement efficiency. Besides, the displacement front of the CO2 plume tends to pass through the region with the higher vertical permeability, thus forming the anomalistic shape of the displacement front; 3) the capillary pressure can influence the CO2 utilization efficiency in the rock core significantly, and tends to inhibit the movement of pore water, which accordingly lowers the CO2 displacement efficiency; 4) the CO2 injection rate can largely affect the CO2 displacement efficiency. The final CO2 saturation of CO2 in the rock core is notably enhanced with the increasing injection rate.

The influence of capillary pressure on the phase equilibrium of the CO2–water system: Application to carbon sequestration combined with geothermal energy

We quantify the capillary-pressure effect on the phase equilibrium of the CO2–water system and subsequently on the CO2 storage capacity and heat-energy recovery for CO2–water injection into geothermal reservoirs. Our interest is in the capillary-pressure range between 0 and 100bars for temperatures between 293 and 372K and wetting-phase pressures between 25 and 255bars. For this purpose, we have implemented capillary pressure in the PRSV equation of state.The results show that capillary pressure promotes interfacial evaporation. Capillary pressure reduces the CO2 solubility in water and the aqueous-phase density up to 64% and 1.3%, respectively, whereas it increases the water solubility in the CO2-rich phase and the CO2-rich-phase density up to 1172% (1.0+11.7=12.7 times) and 13%, respectively. If the CO2-rich-phase properties were calculated as a function of the wetting-phase pressure, capillary pressure would shift the CO2 liquid–vapor transition and consequently the upper critical point of the CO2–water system to a lower pressure. Therefore, the CO2-rich-phase properties must be calculated using the non-wetting-phase pressure to avoid this shift.For mixed CO2–water injection into a geothermal reservoir, the influence of capillary pressure on the phase equilibrium reduces both the heat recovery up to 37% and the CO2-storage capacity up to 37%. We construct a plot of the recuperated heat energy versus the maximally stored CO2 for a variety of conditions; we compare the results including and excluding the effect of capillary pressure in the phase-equilibrium calculations. We also provide a cursory evaluation of the energy and economics of mixed CO2–water injection into a geothermal reservoir.

Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two‐phase flow

We derive a set of semianalytical solutions for the movement of solutes in immiscible two‐phase flow. Our solutions are new in two ways: First, we fully account for the effects of capillary and viscous forces on the transport for arbitrary capillary‐hydraulic properties. Second, we fully take hydrodynamic dispersion for the variable two‐phase flow field into account. The understanding of immiscible two‐phase flow and the simultaneous miscible displacement and mixing of components within a phase is important for many applications, including the location of nonaqueous phase liquids in the subsurface, the design of contaminant cleanup procedures, the sequestration of carbon dioxide, and enhanced oil‐recovery techniques. For purely advective transport we combine a known exact solution for the description of immiscible two‐phase flow with the method of characteristics for the advective transport equations to obtain solutions that describe cocurrent flow and countercurrent spontaneous imbibition and advective transport in one dimension. We show that for both cases the solute front can be located graphically by a modified Welge tangent. For the advective‐dispersive solute transport, we derive approximate analytical solutions by the method of singular perturbation expansion. On the basis of this, we obtain analytical expressions for the growth of the dispersive zone for the case with and without the influence of capillary pressure. We show that for the case of spontaneous countercurrent imbibition the order of magnitude of the growth rate is far smaller than that for the viscous limit. We give some illustrative examples and compare the analytical expressions with numerical reference solutions.

An analytic model for air drying of impermeable wood

An analytic model for the process of air drying of boards of impermeable wood was developed in the light of some new experimental results. The work includes a new and informative way of plotting the data, a formula for the drying time and a derivation for the diffusion coefficient function within the wood. It was found necessary to take into account the aspect ratio of the board, and that the correction term for evaporative cooling was also significant. The notion of impermeability implies that there is no movement of cell lumen water under the influence of capillary pressure.

Influence of capillary pressure on the evaporation of thin liquid films

A model is presented that considers the influence of capillary pressure on the evaporation of a liquid film on a vertical that plate. The governing equations are derived and numerically integrated with a step-variable Runge-Kutta method. The numerical results are compared with the analytical solution from Nusselt's film condensation theory. The deviation from the Nusselt film theory become very prominent when the liquid film becomes thin enough. This can be attributed to the fact that the Nusselt film theory does not consider the influence of capillary pressure on the shape of the liquid film.

Analysis of Gas-Cap or Dissolved-Gas Drive Reservoirs

Abstract A numerical method of solving the partial differential equations which describe the one-dimensional displacement of oil by gas has been presented. Possible extension of the method to treat multidimensional flow is discussed, and the limitations of this extension are indicated. Using this method, it is possible to allow for the existence of a gas cap, the presence of any number of gas-injection or oil-production wells and the evolution of dissolved gas from the oil. It is also possible to allow for variation in the cross-sectional area, elevation, porosity and permeability of the reservoir. The influence of relative permeability and the force of gravity in the direction of flow upon the displacement is considered. The influence of capillary pressure upon the flow and the effect of gravity in the direction perpendicular to flow are neglected. The physical properties of the fluids are considered to be functions of pressure only, and equilibrium between contiguous phases is assumed. The numerical calculations can be readily carried out by the use of a digital computer. Several example analyses have been performed using the IBM 704 computer, and about one-third of an hour of computing time was required per case. Reservoir behavior predicted by use of this numerical method was compared to data obtained by other methods for three cases - complete pressure maintenance, dissolved. gas drive and gas-cap drive. The independent solutions to these problems were obtained by analytical solution, laboratory experiment and field data, respectively. Agreement of the numerical solution with data from these sources was good; this agreement establishes the convergence and accuracy of the numerical method. Introduction Most petroleum reservoirs can be produced by any one of several alternative programs. When a reservoir is produced by primary methods, production economics can be influenced by controlling the number and location of wells and the flow rate of each well.