Capillary Pressure Correlation Research Articles

Capillary pressure profile estimation using numerical method and centrifuge test data

Capillary pressure is a crucial parameter that affects the displacement of two or more immiscible fluids in porous media. Measuring capillary pressure as a function of saturation is essential for simulating the process of immiscible flooding in porous media, especially in oil reservoir rocks. The centrifuge method is one of the most widely used techniques for estimating capillary pressure in reservoir rock porous media. This study applied a numerical method to a one-dimensional equation with boundary conditions to simulate the flow of two immiscible fluids in the core plug for a centrifuge experiment. The study also tested oil-water and air-oil systems across various core plugs using a centrifuge device. It involved analyzing the experimental data output through a numerical calculation method to derive the capillary pressure correlation as a function of saturation. The correlation obtained for capillary pressure demonstrates an acceptable match with the experimental data and is applicable in other simulation software.

Analytical solutions of critical oil film thickness of negative spreading coefficient in a capillary corner

In this paper, by combining applications of minimum surface free energy with capillary force balance equations, and considering that the total free energy change is zero at thermodynamic equilibrium, an analytical equation of the oil film critical thickness to spread over a water film in a three-dimensional capillary corner is derived. The derivation is based on the analysis proposed by Dong et al. [Journal of Colloid and Interface Science 172 (1995) 21–36]. This analytical solution allows the critical oil film thickness in three-phase systems to be calculated conveniently without lengthy calculation and be readily applied in simulation of three-phase systems in porous media using predictive models. The equation was examined by comparing the analytical solutions with the numerical results by Dong et al. Using the analytical solution, the reason why the oil phase spreads between the gas and water phases in three-phase systems in porous media was analyzed. The spreading of oil phase is controlled by the free energy change, and the spreading of oil phase only occurs in the system when the free energy change during the oil spreading process is negative. Also, there is a critical oil film thickness controlling this process that is a function of interfacial tension, contact angles, and corner angles. This analytical solution of critical oil film thickness can also be utilized to find the correlation of three-phase capillary pressure when the system is in thermodynamic equilibrium for water-wet porous media. This correlation should be useful in pore-scale simulation of three-phase flow of spreading oil.

Enhancement of permeability estimation by high order polynomial regression for capillary pressure curve correlation with water saturation

Suggesting a cost-effective and straightforward approach is indispensable for obtaining permeability estimates in carbonate reservoirs utilizing available well logs. In this study, several procedures were conducted to reach an optimum approach, primarily by constructing a correlation between capillary pressure and water saturation using core data plotted and utilized a good polynomial regression to obtain a better relationship, which leads to calculating the permeability. The second step is to use different theoretical models which Tixier introduces, Timur, Coats, and Dumanior, which resulted not good matching with the permeability from core analysis and modified Brown and Husseini correlation which used and gave better matching than others correlations by comparing the results with the calculated permeability depending on core data. The proposed approach in this study based on modified Husseini equation using the well logs data by applying Statistical regression techniques within capillary pressure prediction to enhance reservoir characterization can potentially advantage reservoir simulation efforts. Obtained results of permeability prediction based on capillary pressure correlation was examined for a certain well and compared with the measured permeability value of cores. There was a good matching between the predicted and measured permeability.

THE CORRELATION OF RELATIVE WALL THICKNESS, LV MASS/LV MASS INDEX, CARDIAC INDEX AND PCWP IN RELATION TO SERUM FERRITIN IN TRANSFUSION DEPENDENT BETA THALASSMEIC CHILDREN IN NORTH WEST RAJASTHAN

Objective: Regular blood transfusions used for long term survival in ß-thalassemia major patients cause a secondary state of tissue iron overload. Myocardial iron deposition can result in cardiomyopathy, and heart failure remains the leading cause of death. This study was planned to see the correlation of Relative Wall Thickness (RWT), LV Mass, Cardiac Index(CI) and pulmonary capillary wedge pressure(PCWP) in relation to Serum Ferritin in transfusion dependent Beta Thalassemia children.
 Methods: Patients of ß thalassemia major above 2 years of age received regular blood transfusions at least for 1 year duration, attending OPD in the Department of Pediatrics, S.P. Medical College, Bikaner were enrolled. Echo findings of 50 cases were correlated with serum ferritin level(SFL).
 Result: Mean RWT in SFL group <2500ng/ml was 0.40±0.09, in SFL group 2500-5000 ng/ml, it was 0.41±0.08 and in SFL group >5000 ng/ml, it was 0.49±0.09; p value>0.05. Mean LV mass in SFL group <2500 was 68.76±24.32, in SFL group 2500-5000, it was 90.07±24.18 and in SFL group >5000, it was 123.06±42.42. The difference was found statistically highly significant (p<0.001). Mean PCWP in SFL group <2500 was 11.55±1.53, in SFL group 2500-5000, it was 12.02±2.06 and in SFL group >5000, mean PCWP was 13.31±2.09;p value>0.05. Mean CI in SFL group <2500 was 5.24±0.99, in 2500-5000 group was 5.79±1.07 and in SFL group >5000, it was 5.91±1.26 ; p value>0.05.
 Conclusion: There was significant positive correlation of serum ferritin level only with LV Mass.Relative Wall thickness, PCWP and cardiac index were insignificantly correlated. .
 Keywords: ß-thalassemia major; Relative wall thickness, LV mass/ LV mass index, cardiac index, PCWP, Echocardiogram; Tissue Doppler Imaging

Petrophysical attributes of the middle zone of the Bahariya Formation as a producing reservoir using core analysis correlations and log evaluation, Abu Sennan area, Egypt

A total of 78 sandstone core samples were obtained from the NES-2 well of the SWS field in the Abu Sennan area to assess the reservoir properties of the Middle Zone of the Bahariya Formation. It comprises carbonate, silt, and shale with sandstone interbeds, where the sandstone was targeted as it represents the main production zone in the studied area. The studied samples were subjected to porosity and permeability measurements, where the relationship between them showed the reservoir heterogeneity in terms of flow properties. Capillary pressure correlations displayed four hydraulic flow units with different performances within the studied samples in accordance with r35 parameter classification. The very permeable flow unit (megaport) constitutes 92% of the total flow capacity. Other petrophysical parameters such as apex, pore throat radii, reservoir quality index (RQI), and turbulence factor (β) were used to confirm the previous results and deeply evaluate the studied reservoir samples. Petrographically, the Middle Zone of the Bahariya Formation is represented by intercalations of siltstone, quartz arenite (the common facies), quartz wacky, and sandy siltstone facies from base to top. These microfacies represent the different petrophysical flow units.In terms of log evaluation, the middle zone of the Bahariya sandstone reservoir is characterized by a net pay thickness of about 6.9 m in the NES-2 well and marked by (Vsh = 0.05, φE = 0.24, and Sw = 0.4) as an oil producer. All the results were consistent and confirmed that the Middle Zone of the Bahariya Formation has excellent reservoir capabilities. Megaport flow units of the highest flow rate nature are predominant and nearly constitute the flow capacity, hence the reservoir may suffer some productivity loss under the turbulence flow conditions or the moving fines.

Multiphysics NMR correlation spectroscopy

One hallmark of modern nuclear magnetic resonance spectroscopy is the use of multi-dimensional correlation experiments typically with only spin Hamiltonians. However, spin systems may be affected by interactions and processes that are not controlled through the spin degree of freedom. This paper demonstrates a correlation spectroscopy between two different physical processes, one is NMR spin dynamics, and the other capillary drainage for the study of porous materials. We show that such a correlation experiment produces a joint capillary pressure (Pc) and NMR relaxation (T2) correlation function, Pc-T2 map that probes how pores are connected, an insight not available in conventional NMR or capillary experiments.

Pore structure characterization and permeability estimation with a modified multimodal Thomeer pore size distribution function for carbonate reservoirs

Pore structure of carbonate reservoirs is complex and multimodal. In order to characterize the pore structure of complex carbonate, a modified multimodal Thomeer pore size distribution (PSD) function was developed, which was based on the multimodal Gaussian density function and three controlling parameters including peak position, peak height and full width at half maximum (FWHM). The Expectation-Maximization algorithm for Gaussian mixture model was utilized to obtain three controlling parameters for the calculation of Thomeer parameters, namely the extrapolated displacement pressure, the percent bulk volume occupied by mercury at infinite capillary pressure and the pore geometrical factor. Three permeability models were proposed based on the Thomeer parameters and compared with the previous models. The results show that PSD curve of 55% samples need more than two Gaussian density function, which illustrates the multimodal characteristic. Thomeer parameters relate to the controlling parameters of Gaussian density function. The peak position moved toward larger capillary pressure with the increase of extrapolated displacement pressure and pore geometrical factor. The peak height has positive correlation with the percent bulk volume occupied by mercury at infinite capillary pressure and negative correlation with pore geometrical factor respectively. FWHM has positive correlation with pore geometrical factor. The extrapolated displacement pressure derived from the first Gaussian density function has a high correlation with permeability, which demonstrates that permeability is mainly controlled by the maximum pore throat radius. We found that when the sample has the percentage occupied by the first porous system larger enough than 21.64%, its permeability is dominated by the first porous system with the maximum pore throat radius; otherwise, it would be influenced by the second porous system. The comparative study shows that permeability models that has considered the influence of second porous system could improve the accuracy of permeability estimation for the complicated carbonate samples.

Pore saturation model for capillary imbibition and drainage pressures

BackgroundLeaching and transport of radionuclides from cementitious waste forms and from waste tanks is a concern at the Savannah River Site and other Department of Energy sites. Computer models are used to predict the rate and direction for migration of these through the surrounding soil. These models commonly utilize relative permeability and capillary pressure correlations to calculate migration rates in the vadose (unsaturated) zone between the surface and the water table. The most commonly used capillary pressure models utilize two parameters to relate the pressure to the relative saturation between the wetting (liquid) and nonwetting (gas) phases. The correlation typically takes the form of a power law relation or an exponential equation.ResultsA pore saturation model is used to derive the secondary drainage pressure and the bounding imbibition pressure as functions of a characteristic pore pressure and the liquid saturation. The model utilizes singularity analyses of the total energies of the liquid and gas to obtain residual saturations for the two phases.ConclusionsThe model successfully correlates a selected set of laboratory imbibition and drainage data for sand. The capillary pressure model utilizes a single fitting parameter, a characteristic pore pressure, which is related to a characteristic pore diameter by the Laplace equation. This pore diameter approximately equals the diameters predicted by two different geometric pore models based on the particle diameter.

Reconstruction and prediction of capillary pressure curve based on Particle Swarm Optimization-Back Propagation Neural Network method

Abstract Capillary pressure curve plays a critical role in the reservoir evaluation. It is essential to reconstruct and predict capillary pressure curve properly. Many traditional capillary pressure correlations have been suggested in the literature. However, their major limitation is mainly applicable to homogenous reservoir, and the larger error will be caused when heterogeneous reservoir is dealt by using these mathematical correlations. This study aims at providing an important method based on Particle Swarm Optimization-Back Propagation Neural Network (PSO-BP neural network) to represent and predict capillary pressure curve for homogenous and heterogeneous reservoir. The combination of PSO algorithm and BP neural network converges quickly, which improves the accuracy and efficiency of simulation. In this paper, core samples from three blocks of the same marine-sand reservoir, whose porosity is between 0.6% and 20.0% and permeability is between 0.1mD and 6117mD, are investigated by PSO-BP neural network method and J-Function method respectively. The reconstruction and prediction results are compared with the results obtained by mercury intrusion method in laboratory. The results show that capillary pressure curves reconstructed and predicted by PSO-BP neural network method are in better agreement with mercury intrusion curves than J-Function method, with 0.1%–5% and 5%–8% relative error respectively, which can totally meet the in-situ requirements. It is also demonstrated that PSO-BP neural network method is more suitable for homogenous and heterogeneous reservoir.

Capillary pressure and relative permeability correlations for transition zones of carbonate reservoirs

A sizable oil reserves are held in a thick oil/water capillary transition zones in the carbonate reservoirs, but it is an ongoing challenge to accurately describe the relationship between capillary pressure, relative permeability and oil/water saturation due to the complex wettability variation, pore geometry and heterogeneity throughout the reservoir column. It has been shown that a proper interpretation of relative permeability and capillary pressure including hysteresis has a substantial influence on the prediction and optimization of field production, especially for a heterogeneous carbonate reservoir with a thick transition zone. The conventional models, such as Corey method and Leverett J-function, cannot precisely present the behaviors of capillary pressure and relative permeability of transition zones in carbonate reservoirs. In the present work, a study has been conducted to provide an improved understanding of capillary pressure and relative permeability of the transition zones in carbonate reservoirs by implementing and optimizing recently developed models considering mixed-wet property and geological heterogeneity. For single core plug and each reservoir rock typing classified on the basis of petrophysical properties, the applicability to generate bounding drainage and imbibition curves of the models was tested with fitting parameters by comparing with experimental data. Also, a comprehensive assessment was provided about the feasibility and efficiency of the models along with an evaluation of the hysteresis between bounding drainage and imbibition curves. The results showed excellent matches in the case of Masalmeh model (SPE Reserv Eval Eng 10(02):191–204, 2007) with a correlation coefficient value of 0.95, in which mixed-wet and pore size distribution are taken into account. Therefore, it can be stated that the work conducted in this study could be used as a guide for further investigation and understanding of transition zones in carbonate reservoirs.

Experimental Validation of a Pore-Scale-Derived Dimensionless Capillary Pressure Function for Imbibition Under Mixed-Wet Conditions

Summary We validate experimentally a dimensionless capillary pressure function for imbibition at mixed-wet conditions that we developed recently on the basis of pore-scale modeling in rock images. The difference from Leverett's traditional J-function is that our dimensionless function accounts for wettability and initial water saturation after primary drainage through area-averaged, effective contact angles that depend on the wetting property and distribution of oil- and water-wet grain surfaces. In the present work, we adopt the dimensionless function to scale imbibition capillary pressure data measured on mixed-wet sandstone and chalk cores. The measured data practically collapse to a unique curve when subjected to the dimensionless capillary pressure function. For each rock material, we use the average dimensionless curve to reproduce the measured capillary pressure curves and obtain excellent agreement. We also demonstrate two approaches to generate different capillary pressure curves at other mixed-wettability states than that available from the data used to generate the dimensionless curve. The first approach changes the shape of the spontaneous- and forced-imbibition segments of the capillary pressure curve whereas the saturation at zero capillary pressure is constant. The second approach shifts the vertical level of the entire capillary pressure curve, such that the Amott wetting index (and the saturation at zero capillary pressure) changes accordingly. Thus, integrating these two approaches with the dimensionless function yields increased flexibility to account for different mixed-wettability states. The validated dimensionless function scales mixed-wet capillary pressure curves from core samples accurately, which demonstrates its applicability to describe variations of wettability and permeability with capillary pressure in reservoir-simulation models. This allows for improved use of core experiments in predicting reservoir performance. Reservoir-simulation models can also use the dimensionless function together with existing capillary pressure correlations.

Correlation of pulmonary capillary wedge pressure with left atrial pressure in patients with mitral stenosis undergoing balloon valvotomy

AimsWe sought to evaluate the correlation between PCWP and LAP and to compare transmitral gradients obtained with LAP and PCWP in MS, before and after balloon mitral valvotomy (BMV). MethodsConsecutive patients with MS for BMV were included in this prospective cohort study. Simultaneous PCWP and LAP were recorded followed by simultaneous left atrium–left ventricular (LA–LV) and pulmonary capillary wedge pressure–left ventricular (PCWP–LV) gradients before and after BMV. ResultsThere were 30 patients with a mean age of 41 yrs (males 10 (33.3%), females 20 (66.7%)). There was no significant difference between mean LAP and mean PCWP before BMV (21.3mmHg and 22.3mmHg, respectively) or after BMV (15.3mmHg and 17.3mmHg, respectively). There was excellent correlation between mean PCWP and mean LAP before BMV (r=0.95) (p<0.001) and after BMV (r=0.85) (p<0.001). The phasic components of the pressures (a and v waves) of LAP and PCWP also showed good correlation before and after BMV. Further, transmitral gradients assessed by LA–LV and PCWP–LV pressures showed excellent correlation before BMV (r=0.95) (p<0.001) and after BMV (r=0.95) (p<0.001). ConclusionIn patients with MS undergoing balloon valvotomy, PCWP shows good correlation with LAP. Transmitral gradients obtained with PCWP and LAP also correlate well after correction of phase lag in PCWP tracing. Hence, PCWP can be used for reliable measurement of transmitral gradient.

Numerical and dimensional analysis of nanoparticles transport with two-phase flow in porous media

Abstract In this paper, a mathematical model and numerical simulation are developed to describe the imbibition of nanoparticles–water suspension into two-phase flow in a porous medium. The flow system may be changed from oil-wet to water-wet due to nanoparticles (which are also water-wet) deposition on surface of the pores. So, the model is extended to include the negative capillary pressure and mixed-wet relative permeability correlations to fit with the mixed-wet system. Moreover, buoyancy and capillary forces as well as Brownian diffusion and mechanical dispersion are considered in the mathematical model. An example of countercurrent imbibition in a core of small scale is considered. A dimensional analysis of the governing equations is introduced to examine contributions of each term of the model. Several important dimensionless numbers appear in the dimensionless equations, such as Darcy number Da, capillary number Ca, and Bond number Bo. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles using numerical experiments.

Correlation of pulmonary capillary wedge pressure with left atrial pressure in patients with mitral stenosis before and after balloon mitral valvotomy

Correlation of pulmonary capillary wedge pressure with left atrial pressure in patients with mitral stenosis before and after balloon mitral valvotomy

Proton exchange membrane fuel cell modeling with diffusion layer-based and sands-based capillary pressure correlations: Comparative study

Although the Leverett–Udell correlation has been proven inaccurately to describe the capillary pressure-saturation (pc-s) characteristics of a gas diffusion layer (GDL), this correlation is still extensively applied in the modeling of proton exchange membrane (PEM) fuel cells. The question of how much error is introduced into the determination of the cell current-voltage performance by using Leverett–Udell correlation has not been answered satisfactorily. This study numerically evaluates cell performance using a three-dimensional, two-phase, and non-isothermal fuel cell model, which incorporates the Leverett–Udell correlation and the experimentally measured pc-s correlation. The performances predicted by the two models were compared for various model parameters – GDL porosity (0.6 and 0.9), GDL tortuosity (1.5 and 2.5), and coefficient of water vapor condensation rate (500s−1 and 5000s−1). Numerical results indicate that introducing the cosine of the contact angle into the Leverett–Udell correlation inaccurately represents the effect of wettability on the capillary pressure. The Leverett–Udell correlation with a contact angle far larger than the actual contact angle can nevertheless yield a cell performance that is close to that obtained from the experimentally measured pc-s correlation. Quantitative modeling using the Leverett–Udell correlation is not recommended. However, qualitatively, the comprehensive PEM fuel cell model with the Leverett–Udell correlation can be used for preliminary screening in cell design and performance estimation.

Estimation of Imbibition Capillary Pressure Curves from Spontaneous Imbibition Data

A closed-form solution for calculating imbibition capillary pressure from experimental data has been derived on the basis of the assumption of a constant capillary diffusion coefficient combined with Corey functions for the relative permeability curves. The solution is almost similar to the capillary pressure correlation reported by Skjaeveland et al. (Skjaeveland, S. M., Siqveland, L. M., Kjosavik, A., Hammervold Thomas, W. L. and Virnovsky, G. SPE Reservoir Eval. Eng. 2000, 3 (1), 60−67), but it allows for calculation of the empirical fit parameters from experimental data. Calculated imbibition capillary pressure curves show the correct qualitative behavior because of variations in the curvature of the relative permeability curves, the end-point values on the relative permeability curves, the absolute permeability, and the capillary diffusion coefficient. Capillary pressure threshold values calculated from the model are in accordance with experimental data, assuming reasonable input data. The model, how...

Physically Based Capillary Pressure Correlation for Mixed-Wet Reservoirs From a Bundle-of-Tubes Model

Summary It is shown that the main characteristics of mixed-wet capillary pressure curves with hysteretic scanning loops can be reproduced by a bundle-of-triangular-tubes model. Accurate expressions for the entry pressures are employed, truly accounting for the mixed wettability and the diverse fluid configurations that arise from contact-angle hysteresis and pore shape. The simulated curves are compared with published correlations that have been suggested by inspection of laboratory data from core plug experiments.

Dynamic optimization for the core-flooding problem in reservoir engineering

Relative permeability and capillary pressure correlations are required for reservoir simulation and hence for proper exploitation of petroleum resources. These flow functions are typically estimated from laboratory scale two-phase flow displacement experiments. This work aims at estimating these flow functions from multi-fractional-flow experiments. The system is governed by partial differential equations (PDEs). The PDEs are discretized spatially giving rise to a differential-algebraic equation (DAE) system. The DAE optimization problem is then solved using a simultaneous approach wherein the differential and the algebraic variables are fully discretized leading to a large-scale nonlinear programming (NLP) problem. This core-flooding problem is also governed by the “outlet-end effect”, which is an on–off condition relating capillary pressure, flow rates and pressures of individual phases at the outlet. This effect is modeled using a complementarity formulation. The multi-fractional-flow experiment is modeled by appending several blocks of models, each corresponding to a given fractional flow. The resulting optimization problem is solved using an interior point algorithm capable of handling large-scale NLPs. Our methodology is reliable and robust and is demonstrated on several cases with good parameter estimates.

Relative Permeability From Thermodynamics

Summary A new theory is reviewed for single-component, two-phase flow in porous media. It integrates thermodynamics with fluid mechanics and includes wettability in the thermodynamic description. It does not make use of the relative permeability concept. Wettability is included through a function that is part of the input to the model, together with an equation of state. A dialogue between this new model and the existing one has been established with the purpose of obtaining some of the input functions of both models. First, we have used information available in the existing model so as to calculate the function necessary for the description of wettability in the new model. The new model then being complete, we use it to find the two central functions necessary to the existing model, the relative permeabilities. We show that these are well defined when flow is characterized as a traveling wave, and we give a formula for their calculation. The formula assumes that a capillary pressure correlation and an equation of state are known, in addition to a constant related to the thickness of the transition region between the two phases.

Relative Permeability Correlation for Mixed-Wet Reservoirs

SummaryA two-phase relative permeability correlation for mixed-wet rock is presented and validated. It includes provisions for bounding drainage and imbibition processes and scanning hysteresis loops, and is inferred from a capillary pressure correlation.The well-known Corey-Burdine relative permeabilities were developed for water-wet rock from a Brooks-Corey power-law capillary pressure correlation and a bundle-of-tubes network model. We have extended this correlation to mixed-wet rock and now propose the ensuing relative permeability correlation for mixed-wet reservoirs. The functional form is symmetric with respect to fluid-dependent properties, because neither fluid has precedence in a mixed-wet environment. It reverts to the standard Corey-Burdine correlation for the completely water- or oil-wet cases, and exhibits the following characteristics in agreement with reported experiments: first, water-wet behavior at low water saturations and oil-wet behavior at low oil saturations; second, an inverted S-shape oil relative permeability curve with an inflection point; and, third, closed hysteresis scanning loops.