Presence Of Capillary Pressure Research Articles

Analytical Solution for Predicting Salt Precipitation During CO2 Injection Into Saline Aquifers in Presence of Capillary Pressure

AbstractSalt precipitation within pores of the reservoir is an important phenomenon occurring during CO2 injection into saline aquifers. The phenomenon results in permeability reduction and injectivity impairment. Salt precipitation mainly happens because of water vaporization inside the CO2‐saturated (dry‐out) region. For water‐wet systems, the capillary pressure acts toward the lower water saturation regions in the reservoir, thereby displacing a film of brine backward to the dry‐out region. This results in more precipitation. Overlooking this phenomenon, referred to as capillary‐driven backflow, results in over‐estimations of injectivity in the dried region. Here, we have developed an analytical solution based on fractional flow theory and shock waves for CO2‐brine systems considering the effect of capillary pressure. The validity of the solution is verified by comparing the outputs of our model with those of numerical results from a commercial numerical simulator for a hypothetical reservoir. An equation is derived to calculate the distance at which capillary pressure is most influential, and also the injectivity impairment at injection well due to salt precipitation was reasonably accurately estimated. The results emphasize that effects of capillary pressure should not be ignored.

Towards the vulnerability assessment of low-code RC frame buildings at precarious slopes subjected to rainfall induced landslide hazard

The presence of capillary pressure in unsaturated soils may, under certain circumstances, significantly affect the stability of a slope and the safety of a structure standing in the vicinity of its crest. More specifically, the change in saturation induced by a rainfall event may directly influence the value of apparent soil cohesion potentially resulting in excessive permanent slope displacements and subsequent structural damages for the structure standing on it. Under these considerations, this study aims at the vulnerability assessment of typical reinforced concrete (RC) buildings on precarious slopes subjected to rainfall induced landslide hazard. The proposed methodology is based on a two-step numerical analysis procedure. First, the permanent absolute and differential ground displacement time histories at the assumed building location within the landslide zone are evaluated performing coupled mechanical-flow analysis of a generic initially unsaturated natural slope configuration considering the employment of different rainfall events of increased intensity at the surface of the slope model. Different soil properties of the surface layer are considered to represent silty and soft clayey soil material. Appropriate analytical relationships between the rainfall intensity and its duration and the computed permanent displacements are extracted. Then, a series of nonlinear static time history analyses are performed for reference low and mid-rise, low-code RC bare and infilled frame buildings located next to the slope's crest to assess their fragility. The buildings’ response assessed using appropriate engineering demand parameters (EDPs) to account for both the global flexural and local shear demand are statistically correlated with predefined damage limit states to construct the fragility functions. To facilitate the applicability of the proposed methodology within a quantitative landslide risk assessment framework, vulnerability curves are finally developed to quantify the expected direct losses in normalised cost terms.

Two-phase flash for tight porous media by minimization of the Helmholtz free energy

Thermodynamic modeling of phase behavior is one of the most fundamental components in the study of enhanced oil recovery by gas injection. Robust algorithms exist for multiphase equilibrium problems with no capillary pressure as commonly used in compositional reservoir simulation. However, various convergence problems have been reported even for simple two-phase split problems in the presence of capillary pressure by using the traditional algorithm based on minimization of the Gibbs free energy. In this research, the phase-split problem with capillary pressure is formulated by using the Helmholtz free energy for a given temperature and total volume. The algorithm is based on the successive substitution (SS) for updating K values, which is coupled with the volume update by using the pressure constraint equation. The robustness of the SS algorithm is improved by using the convexity information of the Helmholtz free energy and using an under-relaxation method. Case studies present phase-split problems with capillary pressure by using the developed algorithm and highlight several advantages of using the Helmholtz free energy over the Gibbs free energy. The improved robustness comes mainly from the involvement of a single energy surface regardless of the number of phases. The pressure variability that occurs during the phase-split calculation with capillary pressure is inherent in the Helmholtz free energy in volume space.

Phase stability analysis for tight porous media by minimization of the Helmholtz free energy

This paper presents a new method of phase stability analysis in the presence of capillary pressure by minimization of the Helmholtz free energy. The thermodynamic consistency of phase stability is rigorously preserved between the Helmholtz and Gibbs free energy.Case studies demonstrate the main advantages of the new method over the conventional methods using the Gibbs free energy. The effect of capillary pressure on phase stability is inherently considered in the new method using the Helmholtz free energy. The most fundamental reason for various issues associated with using the conventional methods is that the Gibbs free energy in composition space requires a pressure to be specified; i.e., the conventional methods involve two Gibbs free energy surfaces and their relative location changes during the iterative solution with capillary pressure.Case studies further show that there exist indefinite solutions in phase stability analysis with capillary pressure, in which the fluid is unstable, but no two-phase solution exists. Also, it is demonstrated that the shadow-phase region in the presence of capillary pressure can be defined with the Helmholtz free energy, but not with the Gibbs free energy.

Water—Ice Phase Transition in Unsaturated Soil in the Presence of Capillary Pressure

The problem of ice formation in unsaturated soil in the presence of pressure gradient and capillary forces is formulated. The complete system of conditions on the crystallization surface is derived. The one-dimensional problem is investigated in the self-similar formulation. The dependence of the amount of the ice formed on the problem parameters is also investigated. It is found that the ice saturation increases as the pressure on the cooling wall that initiates water inflow to the front decreases and also in the regime of more intense cooling. Increase in the pressure leads to water outflow from the front and decrease in the ice saturation.

Phase equilibrium calculations in shale gas reservoirs

Compositional multiphase flow in subsurface porous media is becoming increasingly attractive due to issues related with enhanced oil recovery, CO 2 sequestration and the urgent need for development in unconventional oil/gas reservoirs. One key effort to construct the mathematical model governing the compositional flow is to determine the phase compositions of the fluid mixture, and then calculate other related physical properties. In this paper, recent progress on phase equilibrium calculations in unconventional reservoirs has been reviewed and concluded with authors’ own analysis, especially focusing on the special mechanisms involved. Phase equilibrium calculation is the main approach to investigate phase behaviors, which could be conducted using different variable specifications, such as the NPT flash and NVT flash. Recently, diffuse interface models, which have been proved to possess a high consistency with thermodynamic laws, have been introduced in the phase equilibrium calculation, incorporating the realistic equation of state (EOS), e.g. Peng-Robinson EOS. In the NVT flash, the Helmholtz free energy is minimized instead of the Gibbs free energy used in NPT flash, and this thermodynamic state function is decomposed into two terms using the convex-concave splitting technique. A semi-implicit numerical scheme is applied to the dynamic model, which ensures the thermodynamic stability and then preserves the fast convergence property. A positive definite coefficient matrix is designed to meet the Onsager reciprocal principle so as to keep the entropy increasing property in the presence of capillary pressure, which is required by the second law of thermodynamics. The robustness of the proposed algorithm is demonstrated by using two numerical examples, one of which has up to seven components. In the complex fluid mixture, special phenomena could be captured from the global minimum of tangent plane distance functions and the phase envelope. It can be found that the boundary between the single-phase and vapor-liquid two phase regions shifts in the presence of capillary pressure, and then the area of each region changes accordingly. Furthermore, the effect of the nanopore size distribution on the phase behavior has been analyzed and a multi-scale scheme is presented based on literature reviews. Fluid properties including swelling factor, criticality, bubble point and volumetrics have been investigated thoroughly by comparing with the bulk fluid flow in a free channel. Cited as : Zhang, T., Li, Y., Sun, S. Phase equilibrium calculations in shale gas reservoirs. Capillarity, 2019, 2(1): 8-16, doi: 10.26804/capi.2019.01.02

VT-Based Phase Envelope and Flash Calculations in the Presence of Capillary Pressure

Phase-envelope construction and isothermal flash are two widely used phase-equilibrium calculations. Because of the increasing importance of oil and gas production from shale, there is a need to perform these calculations in the presence of capillary pressure. Such calculations are also important for other processes inside porous media. Classical phase-equilibrium calculations usually use pressure and temperature based (PT-based) thermodynamics that requires the solution of the equation of state for the molar volume or density to calculate the desired thermodynamic properties. An alternative to this formulation is volume and temperature based (VT-based) thermodynamics, in which repeated molar volume or density solutions are avoided by co-solving the equality of phase pressures in the equilibrium calculation. The formulation is particularly advantageous for equilibrium calculation with capillary pressure. It can naturally handle the negative pressures in the wetting phase (usually the liquid) caused by the...

Coupled Capillary-Pressure and Three-Phase Flash Models Simulate Liquid Blockage

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 190242, “Simulation of Water and Condensate Blockage and Solvent Treatments in Tight Formations Using Coupled Three-Phase Flash and Capillary-Pressure Models,” by Sajjad S. Neshat, SPE, Ryosuke Okuno, SPE, and Gary A. Pope, SPE, The University of Texas at Austin, prepared for the 2018 SPE Improved Oil Recovery Conference, Tulsa, 14–18 April. The paper has not been peer reviewed. Water and condensate blockage near production wells in unconventional reservoirs can reduce oil- and gas-production rates significantly. This paper presents a new approach for more-accurate modeling of liquid blockage in tight oil and gas reservoirs and investigates the use of solvents for blockage removal. Introduction In this paper, coupled three-phase flash and capillary-pressure models are presented for simulation of tight oil and gas reservoirs. The capillary pressure between each phase pair (e.g., oil/gas or oil/aqueous) is calculated with a general three-phase capillary-pressure model that integrates the effect of important petrophysical properties including pore-size distribution, phase saturations, and different wettability conditions. The capillary-pressure function is integrated with three-phase flash calculations to define the equilibrium state between oil, gas, and aqueous phases under reservoir conditions. The criterion for selection of cubic equation-of-state (EOS) roots is extended for three-phase mixtures. This method minimizes the global Gibbs free energy (GFE) of the whole mixture instead of minimizing the free energy of each phase separately. The models are then used for simulation of primary production and solvent enhanced-oil-recovery (EOR) processes in tight formations. Using rock and fluid properties for tight oil and gas reservoirs, the effect of water and condensate blockage and capillary pressure on production is simulated. The use of solvents to remove liquid blockage and to increase production rates is extended to tight formations with high capillary pressure. Coupled Three-Phase Flash and Capillary-Pressure Models At three-phase equilibrium conditions, the chemical potential of each component must be equal in all three phases. In the presence of capillary pressure, the chemical potentials are calculated at corresponding phase pressures. Capillary pressure across a two-phase interface is a function of the surface curvature and interfacial tension (IFT). The variation in pore size and interfacial curvature can be accounted for by saturation-dependent functions. In the presence of a third phase, the interface between any two phase pairs would shift toward either larger or smaller pores depending on wettability conditions. A general three-phase model that can be used to define the capillary pressure between any phase pairs under the entire range of wettability conditions has been coupled with a three-phase relative permeability model with three-phase hysteresis and compositional consistency and was validated through measured three-phase relative permeability data. For the applications discussed in this study, it is assumed that the gas phase is always the most nonwetting phase, while a mixed wetting condition for oil and aqueous phases is assumed.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ПРОМЕРЗАНИЯ НЕНАСЫЩЕННОГО ГРУНТА ПРИ НАЛИЧИИ КАПИЛЛЯРНЫХ СИЛ

Сформулирована математическая модель промерзания грунта, насыщенного гетерогенной смесью воды и воздуха, при наличии капиллярного давления. Представлен вывод уравнения диффузии влаги, следующий из законов сохранения масс и импульса, позволяющий выразить коэффициент диффузии через параметры среды. Выведены балансовые соотношения и предложено замыкающее соотношение на фронте кристаллизации воды. В линейном приближении получено автомодельное решение задачи. A mathematical model of freezing of soils saturated with a heterogeneous mixture of water and air in the presence of capillary pressure is proposed. The derivation of the diffusion equation for the redistribution of moisture from the laws of conservation of mass and momentum is given. This allows us to define the diffusion coefficient through the parameters of the porous medium and fluids. Balance relations through the water crystallization front is derived. A self-similar solution of the problem in the linear approximation is obtained. It is shown that the growth of capillary forces reduces the amount of ice formed, and a more intensive freezing regime leads to an increase in the saturation with ice.

The capillary instability of the evaporation surface in soil

The stability of the evaporation surface of subsoil waters is investigated in the presence of capillary pressure, when a light liquid (a mixture of air and vapor) is above a heavy liquid (water). It is found that the instability arises in non-wettable and wettable soil with the capillary-pressure gradient.

Effect of capillary pressure and salinity on CO2 solubility in brine aquifers

CO2 storage is a process in which CO2 is injected into depleted oil and gas reservoirs or deep aquifers to store CO2 through several mechanisms. Since supercritical CO2 phase and saline brine are immiscible at a wide range of pressure and temperature in a permeable medium, capillary pressure exists between the CO2 and saline brine. Although there have been many efforts to study solubility of CO2 in brine aquifers, the most published models neglect the capillary pressure effect during phase behavior calculations to investigate the amount of dissolution trapping. This work focuses on effects of capillary pressure and salinity on solubility of CO2 in the region, where brine saturation increases from a dried zone and/or below residual saturation toward a 100% water saturated zone at the transition zones of CO2 saturations. For this purpose, we developed a new model accounting for inequalities of aqueous and gas phase pressures to calculate the solubility of CO2 in the brine phase. Peng-Robinson equation of state and criterion for local equilibrium are applied. The capillary pressure is a function of phase saturation. We verified the proposed method against the experimental measurement. Subsequently, we performed the case studies including the capillary pressure effect on the solubility of CO2, water vaporization and K-values. The results indicate that increasing capillary pressure leads to a reduction in CO2 solubility. The importance of this effect on CO2 solubility depends on the capillary pressure curve which represents petrophysical properties. In a case considered in this paper, the decrease of CO2 solubility is 23% when the capillary pressure increases from 0.48 to 9.45MPa. Additionally, effects on equilibrium constant (K-values) and water vaporization were also investigated in the presence of capillary pressure, which can be used to obtain accurate simulation results in commercial reservoir simulators. Furthermore, we analyzed the influence of salinity on CO2 solubility and compared the results with and without the capillary equilibrium. Comparisons between different salinities reveal that CO2 solubility decreases nearly 49% when the salinity increases from 0 to 4mol aqueous NaCl solutions. It is the first attempt to theoretically investigate the capillary pressure effect on the subject of CO2 geological storage.

Carbon Nanotube Balls and Their Application in Supercapacitors

We have provided a design of the macroscopic morphology of carbon nanotubes (CNTs) using emulsion droplet confinement. The evaporation of CNT-dispersed aqueous emulsion droplets in oil produces spherical CNT assemblies, i.e., CNT balls. In this emulsion-assisted method, compact packing of CNT was obtained by the presence of capillary pressure during droplet evaporation. The size of the CNT balls could be controlled by changing the concentration of the CNT dispersion solution; typically, CNT balls with an average size in the range of 8-12 μm were obtained with a Brunauer-Emmett-Teller (BET) specific area of 200 m(2)/g. Heat treatment of the CNT balls, which was required to remove residual solvent, and cement CNTs was followed, and their effect has been characterized; the heat treatment at high temperature desorbed surface oxygenated groups of CNTs and created defective carbon structures, but did not change pore structure. The dispersion of CNT balls was applied to form CNT ball-assembled film for a supercapacitor electrode. The specific capacitance of 80 F/g was obtained at 500 °C heat treatment, but the CNT balls prepared at a higher temperature actually decreased the capacitance, because of the removal of surface oxygenated groups, thereby decreasing the pseudo-capacitance. The capacitive properties of CNT ball-assembled electrodes were compared to CNT films; the CNT ball electrodes showed 40% higher specific electrochemical capacitance and higher rate performance, which is attributed to the compact packing of CNTs in the CNT ball and the hierarchical porous structures in the ball assemblies.

Dynamic foam behavior in the entrance region of a porous medium

In foam EOR, complex dynamics of bubble creation and destruction controls foam properties. Here we reconsider whether and when non-equilibrium effects are important, focusing specifically on the entrance region, where injected gas and liquid are transformed into foam. We solve for water saturation and foam texture in the entrance region using the population-balance foam model of Kam (2008), which features three steady states (no foam, strong foam, and an unstable intermediate state) at some injection rates, as seen in experiments. We derive and solve equations for water saturation and foam properties along the entrance region at steady state. Mathematical conditions on the entrance region itself can control which of the several possible steady states is ultimately taken downstream by foam. For instance, if foam is not pre-generated, and capillary-pressure gradients are neglected, as in many published simulation studies, the final steady state downstream is the one with highest water saturation – the weakest foam. Simulations neglecting capillary pressure therefore may lead to inference of the wrong foam state in the formation or core. In some cases, in the presence of capillary pressure, analysis of the asymptotic dynamic behavior in the vicinity of possible downstream steady states may rule out some possible steady states. We show that the apparent length of entrance region can be quite different if one measures water saturation or pressure gradient. Finally, we fit foam kinetic parameters to the length of the entrance region seen in some experiments; a companion paper [18] investigates the effect of these parameters on the traveling wave at the shock front downstream.