Effect Of Capillary Pressure Research Articles

Determination of confined fluid phase behavior using extended Peng-Robinson equation of state

Phase behavior of confined fluids deviate significantly from that of bulk fluids because of the strong confinement effect in nanopores. The classical equation of state (EOS) based on bulk fluids is inapplicable for fluids in shale reservoirs because it cannot reflect the unique thermodynamic properties of confined fluids, such as the suppressed bubble-point pressure. The objective of this work is to extend the existing Peng-Robinson EOS (PR EOS) for unconventional reservoir fluids. In this work, techniques have been developed to compute the phase behavior of confined fluids by incorporating critical property shift and capillary pressure in the PR EOS, where a new term representing the molecule-wall interaction has been introduced. On the basis of data collected from both experiments and molecular simulations, a correlation which is a function of dimensionless pore size has been developed and incorporated in the extended PR EOS to correct the shifted critical properties. The capillary pressure effect is considered in phase equilibrium computation to account for the strong capillary force in nanopores, where the pressure in vapor phase is larger than that in liquid phase. The newly extended PR EOS is validated by reproducing the molecular simulation data from a previous literature, yielding an overall error of 7.71%. Both critical property shift and capillary pressure are found to be important factors influencing the phase behavior of confined fluids. The combined effect has been incorporated in the extended PR EOS which is successfully used to compute the phase behavior of three unconventional reservoir fluids. The bubble-point pressures under reservoir temperatures for Bakken, Eagle Ford, and Wolfcamp fluids at 10 nm are found to be reduced by 31.98%, 23.15%, and 37.77%, respectively.

Characterising the role of parametric functions in the van Genuchten empirical model on CO2 storage performance

In the application of two-phase flow in porous media within the context of CO2 sequestration, a non-wetting phase is used to displace a wetting phase residing in-situ to the maximum extent through a network of pore conduits. The storage performance of this physical process can be assessed through numerical simulations where transport properties are usually described using the Brooks & Corey (BC) or van Genuchten (vG) model. The empirical constant, namely the pore geometry index, is a primary parameter in both of these models and experimental evidence shows a variation in the value of this empirical constant. It is, therefore, essential to cast this empirical constant into a ternary diagram for all types of clastic porous media to demarcate the efficiency of two-phase flow processes in terms of the pore geometry index (PGI). In doing so, this approach can be used as a tool for designing more efficient processes, as well as for the normative characterisation of two-phase flow, taking into consideration the predominance of capillary pressure or relative permeability effects. This concept is based on the existence of a PGI estimation for clastic sediments, for which the value for 12 sediment mixtures fall between 1.01 and 3.00. Statistical data obtained from soil physics is used for developing and validating numerical models where a good match is observed in numerical simulations. In this context, a new methodology for the effective characterisation of PGI for different clastic rocks is proposed. This paper presents theoretical observations and continuum-scale numerical simulation results of a PGI characterisation for the prediction of the hydraulic properties of clastic reservoir rocks. The effect of key parameters in the vG empirical model, such as the pressure strength coefficient and the PGI, is incorporated into the simulation analysis. In particular, the model is used to investigate the effects of parameter representation on CO2 storage performance in a saline aquifer. Subsequent analysis shows that the PGI is a very important parameter for defining the flow characteristics of simulation models. It can also be flexibly changed for each rock type and this approach may thus be practical when simulating the evolution of CO2 plume in reservoirs with sedimentary heterogeneities, such as intra-aquifer aquitard layers or graded beds. The use of the realistic PGI boundaries promises a more precise description of the hydraulic behaviour in sandstones and shale when using either the BC or vG model.

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.

Compositional simulation of fractured shale reservoir with distribution of nanopores using coupled multi-porosity and EDFM method

Shale reservoir contains highly heterogenous pore systems due to the wide-range distributions of nanopores in shale matrix and hydraulic/natural fractures. To explicitly include pore size distribution in simulation of shale reservoir, a multi-porosity model is applied to subdivide the matrix into multiple continua based on experimental pore size data. Each continuum has its own pore size, porosity and permeability, as well as other petrophysical properties. Besides, the embedded discrete fracture model (EDFM) is coupled with multi-porosity model to describe the complex fractures networks with any angles and intersections. To evaluate effects of pore size distribution on production, compositional simulation is conducted in a fractured shale reservoir using different number of continua in shale matrix. Simulation results show that the use of multiple continua results in lower oil and gas production. Different pressures, oil and gas saturations and compositions are observed in different continua. To further investigate the effects of distribution of nanopores, oil-gas capillary pressure is rigorously calculated in every continuum. The existence of large capillary pressure leads to different fluid properties in different size of nanopores. Moreover, capillary pressure reduces oil and gas recovery and alters compositions of residuals. The effects of capillary pressure are more significant in the low permeable continua due to smaller pore sizes.

Impact of Injecting CO2 and Light Hydrocarbon Fractions in a Condensate Reservoir

Greenhouse gas emissions have grown significantly in recent times globally. One of the most prevalent greenhouse gases is carbon dioxide (CO2). Over the years, pilot projects along with reservoir simulations have sought to strengthen our confidence in the use of geologic storage as a mitigation strategy, but a lot more related research still has to be done. One of the key issues when producing condensate reservoirs is that of liquid dropout as the reservoir drops below the dew point pressure. Condensate can therefore become trapped in the reservoir due to the effect of capillary pressure. As a result, flow within porous media can become restricted, thus reducing the efficiency of condensate and gas recovery. CO2 injection can assist with both these challenges, i.e. pressure maintenance and the sequestering of the CO2. The depleted hydrocarbon pore spaces in the reservoir provide suitable storage sites for the injected CO2. Current technologies involve injecting produced natural gas from source wells into other wells to help increase reservoir pressure and improve recovery efficiency. This paper examined the effects of injecting both CO2 and light hydrocarbon fractions (C1-C2) into condensate reservoirs to optimize condensate recovery and CO2 sequestration. The results from the associated simulation studies show that the use of CO2 to increase condensate recovery from the reservoir is feasible with the additional benefit of CO2 sequestration. It also demonstrated that it is highly possible to increase condensate production by injecting CO2 with some percentages of lighter fractions (C1-C2), with these lighter fractions assisting to increase condensate recovery. It is possible to store between 11 and 15% of injected CO2 using the different injection compositions. The injection of CO2 had a positive effect on the re-vaporization of condensate dropout in the reservoir. Increasing the injection pressure yielded higher condensate recoveries. More than 95% of the injected CO2 stored in the reservoir was trapped in the supercritical phase, whilst 3-5% was stored due to hysteresis. As the injection pressure increased, the amount of CO2 stored by hysteresis decreased in all cases. Once the reservoir seals were not breached, the CO2 will remain trapped for over 1000 years.

A Mechanistic Model for Relative Permeability of Gas and Water Flow in Hydrate‐Bearing Porous Media With Capillarity

AbstractLack of mechanistic models to describe petrophysical properties of mobile phases in gas hydrate‐bearing sediments is one of the key challenges in accurately predicting gas production. The major drawback of empirical models that are used to fit a relative permeability curve for mobile phases in gas hydrate‐bearing sediments is that they are based on experimental data, which are limited, and not able to account for hydrate morphology in pore space. This study proposes a relative permeability model that is mechanistic in nature and developed to account capillarity by building on the original nonempirical relative permeability model that assumes negligible capillary pressure. The proposed model implicitly accounts for capillarity with the help of four empirical parameters (two for each mobile phase) that incorporate each mobile phase pressure. It is shown that the proposed model provides an improved match to relative permeability data (derived from pore‐scale simulation of gas hydrate‐bearing sediments) than nonempirical relative permeability by accounting for the effect of capillary pressure. Additionally, unlike fully empirical models that can predict relative permeabilities reliably only at gas hydrate saturations for which experimental data are available, the proposed model only requires fitting the empirical parameters once with experimental data at any single gas hydrate saturation and then it can then be used to predict relative permeability at any gas hydrate saturation. The mechanistic nature of the proposed model allows studying relative permeability of hydrate‐bearing sediments as a function of hydrate morphology and wettability (fluid phase distribution) besides other physical parameters of the model (e.g., porosity, gas, and water residual saturation). Based on the sensitivity analysis of different hydrate morphologies on gas/water relative permeability, it is found that gas relative permeability is sensitive to hydrate morphologies, while water relative permeability shows little dependency on hydrate localization in pore space.

Volume-based phase stability analysis including capillary pressure

The effect of capillary pressure on phase equilibrium is very important in tight formations, such as shale oil and gas reservoirs. In confined fluids, the capillary pressure induced by highly curved interfaces causes bubble points suppression and an inflated dew point locus, with a shift of cricondentherm points towards higher temperatures, as compared to the bulk fluid. In the conventional phase stability testing including capillary pressure, the problem is solved using the classical tangent plane distance (TPD) function (related to the Gibbs free energy surface) and mole numbers as primary variables. In this work, a volume-based approach (in which the equation of state needs not to be solved for volume) is used to solve this problem, as a bound and linear inequality constrained minimization of a TPD function with respect to the component molar densities. A modified Cholesky factorization (to ensure a descent direction) and a two-stage line search procedure (to ensure that iterates remain in the feasible domain and the objective function is decreased) are used in Newton iterations; a proper change of variables strengthens the robustness. The Weinaug-Katz equation (widely used in chemical and petroleum industry), which is a function of molar densities only, is used for interfacial tensions; the additional partial derivatives in the gradient vector and Hessian matrix have very simple expressions, unlike in conventional formulations. The proposed method is tested for two hydrocarbon mixtures (an oil and a gas condensate) in a wide range of pressures, temperatures and curvature radii, with a special attention paid to the convergence behavior near the singularities, that is, the stability test limit locus (STLL) and the spinodal. The method proves to be highly robust and exhibits fast convergence, showing a similar convergence behavior and almost the same computational effort as in the case of a bulk fluid. The results are only slightly different from conventional methods (except at high curvatures near the cricondentherm and at low pressures); differences are due to the fact that the dependence of capillary pressure on composition is taken into account in deriving the stationarity conditions, unlike in the conventional approach. The proposed method is not dependent on the thermodynamic model and can be used with any capillary pressure representation in which the interfacial tension model is explicit in molar densities.

Assessing Left Ventricular Unloading and Wall Tension to Predict the Need for Durable Mechanical Circulatory Support after Peripheral VA-ECMO

Purpose Peripheral veno-arterial extracorporeal membrane oxygenation (pVA-ECMO) has gained increasing value in the management of advanced cardiogenic shock. Unloading the left ventricle (LV) while reducing myocardial oxygen consumption (MVO2) are crucial for myocardial recovery during pVA-ECMO. To study the effects of a pulmonary capillary wedge pressure (PCWP)-directed protocol in patients on pVA-ECMO (goal: PCWP Methods Following IRB approval, we identified 99 patients with advanced cardiogenic shock undergoing pVA-ECMO and at least one formal transthoracic echocardiography study (TTE) during pVA-ECMO. We analyzed demographic data, routine laboratory data, hemodynamic parameters, and TTE results. We used PCWP measurements and calculations of LV systolic wall tension (LVSWT) to assess LV unloading and MVO2 during pVA-ECMO, respectively. Statistical analyses included Mann-Whitney-U test and logistic regression modeling. Data are given as median (interquartile range). Results Survival to hospital discharge was 60.6%. 27.3% of all patients required transition to dMCS to be weaned off pVA-ECMO. 10.1% of all patients developed refractory LV distention with pulmonary edema despite maximum medical treatment and required either atrial septostomy or additional mechanical support. Minimum PCWP readings during pVA-ECMO were 12.8 mmHg (11.0-14.4) in patients without and 10.0 mmHg (8.0-17.0) in patients with need for dMCS (p=0.236). Minimum LVSWT during pVA-ECMO were 2.7 × 105 dynes/cm (2.0-3.5) in patients without and 3.5 × 105 dynes/cm (3.1-4.0) in patients with need for dMCS (p=0.002). Adjusting for age and race in a logistic regression model revealed that only post-cardiotomy pVA-ECMO and LVSWT, but not minimum PCWP were independently associated with need for dMCS after pVA-ECMO. Conclusion We show that strict medical management can lead to LV unloading, i.e. minimum PCWP

Chebyshev wavelets collocation method for simulating a two-phase flow of immiscible fluids in a reservoir with different capillary effects

At least in the last 10 years, considerable effort has been given to studying the dynamics of fluid flow in porous media. The phenomena is widely applicable in many areas of science and engineering. In many cases, the effect of capillary pressure and discontinuities in the two-phase flow dynamics is not fully clear, especially in petroleum reservoirs. In this paper, we introduce a new method based on the Chebyshev wavelets collocation method and the so-called operational matrices of integration. The method was implemented specifically for an oil–water-phase flow in heterogeneous reservoir using different capillary pressure treatments. Convergence and accuracy of this method were established and used to simulate the partial differential equations governing the two-phase model. The method incorporates the various conditions of the complex governing equations as a single system. The system is subsequently reduced into a simple set of algebraic equations making the problem easier to solve. Numerical results showed that the method is able to account for the expected discontinuities occurring in the flow process. It was also found that these discontinuities or jumps in the two-phase flow are caused by the capillary pressure as expected physically.

ЕЛЕМЕНТАРНА МОДЕЛЬ ПРЯМОГО З’ЄДНАННЯ МАТЕРІАЛІВ ПРИ НИЗЬКІЙ ТЕМПЕРАТУРІ

The simplest model of the joining kinetics at the stage of isolated interface voids shrinking is developed. The model basic assumptions are described, as well as also the kinetic equations in the mono-size approximation are derived. There are tThree main stages of the process can be represented distinguished when two surfaces with a small roughness are in contact with each other (tens-of-nanometer-order irregularities) and fall under pressure: 1. At the first stage, several isolated contacts are formed. Their number and contact area increases with time due to the capillary pressure and external pressure effect. 2. At the next stage, the formation of a two-phase quasi-directional contact zone, consisting of two interpenetrating percolation clusters – a contact cluster and a pore cluster – can be expected. 3. At the third stage, one can expect the formation of almost complete contact aside from a certain number of isolated pores at the interface. These pores ripen and selfheal (recover) withover time, mainly due to the capillary pressure effect. The present article is devoted to a simple model of the third stage. The Gibbs-Thomson equations for capillary effect is reformulated for the case of rectangular voids. Chemical potentials for various facets of finite sizes are found. Difference of the surface diffusivities along different facets is taken into account. Balance of grain-boundary diffusion fluxes and surface diffusion fluxes are also taken into account. The proposed model is only the first step to describe the compound joining kinetics at its last stage. Subsequent research will focus on: 1. Accounting for evolving pore size distribution. The ripening of interfacial poresPore coalescence proceeds due to vacancy exchangeexchange by by diffusion via theacross their outer surface (cont contact interface.) 2. Designing a model with a rigorous solution for the ‘real’ stress distribution (the real contact stress distribution) around realistic pore structures (irregular, nont-rectangular shape) 3. Detailed and comprehensive three-stage compound analysis.

Study on the productivity of the multi-stage fractured horizontal wells in tight oil reservoirs

In this paper, a comprehensive dual-porosity and dual-permeability oil/water flow model that uses experimentally determined reservoir properties to simulate well performance of a multi-stage fractured horizontal well in tight oil reservoirs was established. The numerical simulation results was validated by the commercial simulator Eclipse and field production data. Besides, the effect of threshold pressure gradient, stress-sensitive matrix permeability, stress-sensitive fracture conductivity, and capillary pressure was conducted, revealing that those factors affect the well productivity in different degrees. The results indicate that the threshold pressure gradient can significantly reduce the well productivity. The impact of stress-sensitive coefficient should be significant to oil production in high stress-sensitive tight oil reservoirs. Also, the effects of fracture conductivity and capillary pressure on oil production was studied. This study provides a basis for long-term tight oil production analysis of hydraulically fractured tight oil wells. [Received: October 8, 2016; Accepted: January 28, 2017]

Coupled hydro-thermal-mechanical analysis for cold CO2 injection into a deep saline aquifer

This study investigated the thermal effects of thermal stress and Joule-Thomson cooling on CO2 migration in a deep saline aquifer through a hydro-thermal-mechanical model. Firstly, the temperature variation of injected CO2 was analyzed through the coupling of two-phase flow, deformation of porous medium and heat transfer with Joule-Thomson effect. Then, the effect of capillary entry pressure on CO2 plume was numerically investigated and compared. It is found that injection temperature and Joule-Thomson effect can significantly affect the distributions of CO2 mass and temperature, particularly in the upper zone near the injection well. The reduction of capillary entry pressure accelerates the upward migration of CO2 plume and increases the CO2 lateral migration distance.

Effect of moisture content and porosity on compressive strength of concrete during drying at 105 °C

Concrete structures can at times be exposed to temperatures of up to 105 °C. In this study, the compressive strength of concretes with different water–cement ratios during drying at 105 °C is measured. The results indicate that, with increasing moisture content, the compressive strength decreases initially and then increases. The effect of moisture content on compressive strength increases with the increasing porosity. In addition, the competitive effects of capillary pressure and microcracks on the evolution of the compressive strength during the drying process are discussed through mercury intrusion porosimetry (MIP) and the fluorescent epoxy impregnation method (FEIM). Finally, based on the strength–porosity model reported by Ryshkewitch, a strength–porosity–saturation model, which considers the effect of moisture content and porosity on the compressive strength, is proposed.

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.

Performance Evaluation of Gas Production With Consideration of Dynamic Capillary Pressure in Tight Sandstone Reservoirs

In this paper, a pragmatic and consistent framework has been developed and validated to accurately predict reservoir performance in tight sandstone reservoirs by coupling the dynamic capillary pressure with gas production models. Theoretically, the concept of pseudo-mobile water saturation, which is defined as the water saturation between irreducible water saturation and cutoff water saturation, is proposed to couple dynamic capillary pressure and stress-induced permeability to form an equation matrix that is solved by using the implicit pressure and explicit saturations (IMPES) method. Compared with the conventional methods, the newly developed model predicts a lower cumulative gas production but a higher reservoir pressure and a higher flowing bottomhole pressure at the end of the stable period. Physically, a higher gas production rate induces a greater dynamic capillary pressure, while both cutoff water saturation and stress-induced permeability impose a similar impact on the dynamic capillary pressure, though the corresponding degrees are varied. Due to the dynamic capillary pressure, pseudo-mobile water saturation controlled by the displacement pressure drop also affects the gas production. The higher the gas production rate is, the greater the effect of dynamic capillary pressure on the cumulative gas production, formation pressure, and flowing bottomhole pressure will be. By taking the dynamic capillary pressure into account, it can be more accurate to predict the performance of a gas reservoir and the length of stable production period, allowing for making more reasonable development schemes and thus improving the gas recovery in a tight sandstone reservoir.

A Collection of Analytical Solutions for the Flash Equilibrium Calculation Problem

We describe an interesting family of closed-form solutions for the flash equilibrium calculation problem. These solutions can be used as benchmark solutions for verification of numerical solvers of the flash equilibrium problem for multicomponent mixtures. To obtain a problem possessing an analytical solution, we consider a special form of the free energy. Although this form of the free energy is artificial, it captures qualitatively several features that are present in the realistic cases too. The procedure is first illustrated on a 1-D two-phase case and is further generalized to multicomponent mixtures in two and more phases, and also to a problem including the capillary pressure effect.

A New Three-Phase Flash Algorithm Considering Capillary Pressure in a Confined Space

Tight/shale reservoirs are extensively containing nanopores, and the confined space in nanopores can greatly alter the phase behavior of reservoir fluids due to the strong capillarity effect. Many researches have been recently conducted to investigate the effect of capillary pressure in nanopores on altering the oleic-vapor two-phase equilibria. Few attempts have been made to describe the effect of capillarity on the aqueous-oleic-vapor three-phase equilibria. This work proposes a new algorithm for performing three-phase pressure-temperature (P-T) flash coupled with capillary effect. This algorithm considers two capillary pressures that exist across the two interfaces dividing the three phases in a nanopore. When describing the three-phase equilibria, two types of reservoir wettability are considered: water-wet formation and oil-wet formation. In each case, distribution of the three phases in a nanopore is determined based on the spreading coefficient which refers to the spreading ability of an oleic phase over the spreading ability of an aqueous phase. Example calculations are conducted to show the robustness of the new algorithm as well as to study the effect of capillarity on the three-phase equilibria. Computation results show that the three-phase P-T envelope for a given hydrocarbons/water mixture in a nanopore can be significantly altered by capillary pressure, but how the envelope moves will depend on the wettability of the nanopore and the spreading coefficient. The general trend is that both the upper branch (i.e., the oleic-aqueous/vapor-oleic-aqueous boundary) and the lower branch (i.e., the liquid-vapor/liquid-liquid-vapor boundary) of the three-phase envelope tend to move downward. Compared to the water-wet case, the oil-wet nanopore will shift the three-phase boundaries in a much larger degree. In addition to the alteration of the three-phase envelope, the presence of capillarity will also lead to the alteration of the phase fractions and phase compositions in the nanopore. Nanofluidic experiments should be conducted in the future to verify the findings obtained from the calculations.

A parametric analysis of capillary pressure effects during geologic carbon sequestration in a sandstone reservoir

AbstractDuring carbon capture and sequestration, capillary forces and buoyancy effects strongly influence CO2 migration and plume geometry. To understand interactions between these processes, we implement a numerical modeling experiment of CO2 injections in a sandstone reservoir to understand how parametric variability reported in the literature affects numerical predictions of CO2 migration. We simulate ten years of supercritical CO2 (scCO2) injections for 189 unique parameter combinations (entry pressure, Po, and van Genuchten fitting parameter, λ) that control the van Genuchten capillary pressure model. Results are analyzed on the basis of a dimensionless ratio, ω, which is a modified Bond number that defines the relationship between buoyancy pressure and capillary pressure. When ω > 1, buoyancy governs the system and CO2 plume geometry is governed by upward flow. In contrast, when ω < 1, then buoyancy is smaller than capillary force and lateral flow governs CO2 plume geometry. We show that the ω ratio is an easily implemented screening tool for qualitative assessment of CO2 distribution characteristics. We also show how parametric variability affects the relationship between buoyancy and capillary force, and thus controls CO2 plume geometry: (1) small entry pressure Po encourages vertical flow and large entry pressure Po inhibits vertical flow; and (2) the van Genuchten fitting parameter λ exhibits minimal control on the spatial distribution of CO2, as evidenced by the 2 × difference between the ∂ω/∂Po and ∂ω/∂λ gradients quantified using response surface analysis of the ω ratio. © 2018 Society of Chemical Industry and John Wiley & Sons, Ltd.

Segmented two-phase flow analysis in fractured geological medium based on the numerical manifold method

Abstract A segmented two-phase flow model is developed to describe immiscible two-phase flow in discrete fracture networks; i.e., there is an abrupt interface separating the two immiscible fluids. The capillary pressure on the fluid material interface and gravity are considered. For two-phase flow in fracture networks it is inevitable to form a mixed fluid in some fracture segments. The mixed fluid is described by a homogeneous model, and parameter γ is introduced as a critical value controlling new fluid formation in mixed fluid. The governing equations for two-phase flow are solved with a developed numerical manifold method (NMM) which is verified using the finite element and analytical methods with two examples. Two-phase flow through a single fracture intersection acting as one of the basic elements for complex fracture networks is then analysed. Different inlet and outlet configurations are considered including one-inlet/two-outlets, two-inlets/one-outlet and one-inlet/multi-outlets. For the second configuration, parametric studies of defined parameter γ and boundary conditions are carried out. In the third configuration, capillary pressure and gravity effects are discussed. The developed NMM is applied to the analysis of two-phase flow in a complicated fracture network showing that it is an efficient method for simulating segmented two-phase flow in fracture networks. Complex two-phase flow characteristics in the fracture networks that cannot be addressed in continuum models, e.g., the change in flow direction and transition from static to flow, are also revealed and analysed.

Thermodynamic Analysis of Phase Behavior at High Capillary Pressure

Summary High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs because of the small pores in the rock, so understanding the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale-gas and tight-oil reservoirs. As the main finding of this paper, first we show that the tangent-plane-distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis of the problem of phase stability with capillary pressure. Second, we demonstrate that there is a maximum capillary pressure (Pcmax) where calculation of capillary equilibrium using bulk-phase thermodynamics is possible and derive the necessary equations to obtain this maximum capillary pressure. We also briefly discuss the implementation of the capillary equilibrium in a general-purpose compositional reservoir simulator. Two simulation case studies for synthetic gas condensate reservoirs were performed to illustrate the influence of capillary pressure on production behavior for the fluids studied.