Average Capillary Pressure Research Articles

Multiphase flow simulation in hybrid porous structure

Recent research has primarily focused on creating biporous and hybrid porous structures with multiple pore sizes and length scales to optimize capillary pressure and permeability. Despite numerous experimental investigations on biporous and hybrid media, there is a noticeable absence of numerical simulations that explore the multiphase flow within these media. Therefore, the present study aims to conduct a pore-scale numerical simulation of two-phase flow in a biporous structure. The biporous structure is proposed by arranging clusters of solid particles in a staggered regular pattern, with each cluster consisting of closely packed particles. The dimensions and characteristics of the simulated structure are based on previous experimental literature on biporous and hybrid media. A monoporous structure simulation is also included for comparison with biporous results. ANSYS Fluent is utilized to carry out the numerical simulations of capillary pumping flow. The simulation results indicate that the permeability and average capillary pressure of the biporous media are four times and over one and a half times higher, respectively, compared to those of the monoporous media. The presence of smaller pathways within each cluster of a biporous and hybrid porous media enhances the capillary effect in comparison to conventional monoporous structures. Additionally, the larger pores between the clusters contribute to a higher permeability of the hybrid porous structure. As a result, the combined effect of increased capillary action and higher permeability leads to improved performance of the hybrid porous structure. Overall, the proposed simplified biporous geometry accurately models fluid flow in real, complex biporous and hybrid structures.

A novel method for evaluation of the spontaneous imbibition process in tight reservoir rocks: Mathematical model and experimental verification

Spontaneous imbibition driven by capillary forces is essential for the development of oil and gas resources because it can significantly influence the oil recovery of tight reservoirs. But limited by traditional experimental methods, the existing mathematical models lack applicability to complex tight reservoir rocks. Therefore, to better predict water imbibition in tight reservoirs, this paper proposes a new spontaneous imbibition model based on modifications of the classical Handy model. Two important parameters, the average capillary pressure, and the imbibition permeability are derived using a nuclear magnetic resonance spectroscopy method to quantify the macroscopic driving force and percolation ability of the complex pore network. Furthermore, combined experiments of co-current spontaneous imbibition experiments and transverse relaxation time analysis on four shale core plug samples are conducted to verify the new model. Results show the imbibition process can be modeled successfully before the imbibition volume reaches 85% of the maximum imbibition volume, and two continuous stages: the early/free imbibition stage and the later/limited imbibition stage, are then subdivided according to the applicability of our model. Considering the heterogeneity of the pore network in shale samples, it can be inferred that an uneven imbibition front occurred during the imbibition process. In all, this model enriches the classical imbibition theory and provides a new approach to analyzing the imbibition of fracturing fluids in complex tight reservoirs.

Three-dimensional numerical simulation of Ostwald ripening characteristics of bubbles in porous medium

Ostwald ripening behaviors of bubbles in porous medium are observed commonly in various fields, including CO<sub>2</sub> geological storage, preparation of porous materials, and fuel cells. A three-dimensional pore network model based on concentration coupling calculation has been developed to investigate the ripening characteristics of bubbles in porous medium on a pore scale. This model takes into account the shape of bubble, the structure of porous medium, and mass transfer between gas and liquid. By solving the gas phase concentration of each pore body in the three-dimensional pore network, the model can track the evolution process of each bubble. A microfluidic chip with a four-pore structure is used to validate the reliability of the model through visual experiments. To analyze the effect of porous medium heterogeneity on the bubble ripening process, two different three-dimensional pore network structures with varying pore sizes are constructed and the ripening processes of bubbles in two regions are simulated numerically. The results show that the initial distribution of bubbles can affect the ripening process of porous medium. When bubbles are uniformly distributed, in the ripening process, they exhibit regular and systematic changes in their spacing. However, in the case of uneven bubble distribution, as the bubbles transfer from smaller pore region to larger pore region, they also undergo individual mass transfer towards the larger bubble region in their respective areas. Consequently, the remaining bubbles no longer maintain a spaced distribution pattern. Additionally, the differences in initial size among bubbles can accelerate the ripening process, resulting in a significantly shorter ripening time than that in a uniform distribution. The choice of pore number has a significant influence on continuous-scale equivalent parameters, such as average capillary pressure and saturation. As the number of pores increases, the capillary pressure and saturation exhibit a more regular, nonlinear variation. A relationship between capillary pressure and saturation in the small pore region and in the large pore region are established, which deviate from the assumptions made in the existing literature. This result provides important guidance for constructing the continuous-scale ripening model that can be used to predict the evolution process of CO<sub>2</sub> during geological storage and provide guidance for studying the influence mechanism of heterogeneity during long-term CO<sub>2</sub> storage.

Upscaling unsaturated flows in vertically heterogeneous porous layers

Characterising interfacial and unsaturated flows in heterogeneous porous layers is of both fundamental and practical interest. Under the assumption of vertical gravitational–capillary equilibrium, we present a theoretical model to describe one-dimensional flows in a porous layer with vertical variations in average pore size, porosity, intrinsic permeability and capillary pressure jump between invading and displaced fluids. The model leads to asymptotic solutions for the saturation distribution and outer envelope of the invading fluid, and for the background pressure drop across the porous layer. Eight dimensionless parameters are recognised after appropriate non-dimensionalisation of the governing equations, the influence of which is demonstrated through a series of example calculations. In particular, four asymptotic regimes are identified, representing unconfined sharp-interface flows, confined sharp-interface flows, unconfined unsaturated flows and confined unsaturated flows. Finally, in the context of flow upscaling, analytical solutions are derived for the effective relative permeability curves on the basis of exact solutions of the saturation field and interface shape, shedding light on the subtle influence of competition between injection/pumping and gravitational forces, wetting and capillary effects, viscosity contrast between the invading and displaced fluids and vertical heterogeneity of the porous layer.

Numerical studies of spontaneous imbibition in porous media: Model development and pore-scale perspectives

Spontaneous imbibition is a crucial two-phase flow process in a variety of subsurface and industrial applications. Due to the lack of an efficient and reliable pore-scale model, however, how pore-filling events in spontaneous imbibition influence average transport properties (i.e., capillary pressure and relative permeability curves) and entrapment of the nonwetting fluid has not been fully understood. In this work, we first experimentally verify an image-based dynamic pore-network model of spontaneous imbibition that is computationally efficient. Then, case studies of a Nubian sandstone are conducted. We demonstrate that average capillary pressure in cocurrent spontaneous imbibition is significantly overestimated by the widely used Young-Laplace equation. This is because the effects of dynamic pore-filling and air entrapment on average capillary pressure are not parameterized in the equation. Based on our pore-scale numerical results, we elaborate on the competition of pore-filling events under different viscosity ratios of the wetting to the nonwetting fluids. It is found that the filling mode evolves from the co-filling of neighboring pores to the preferential filling of small pores as the nonwetting viscosity increases. Our model will be a useful numerical tool for quantitatively predicting spontaneous imbibition in geological formations. Our findings will help us bridge the gap between pore-scale flow dynamics and the Darcy theory of spontaneous imbibition.

In situ 3D observations of capillary-driven flows in parallel arrangements of rigid fibres using X-ray microtomography

Capillary-driven impregnation phenomena occurring in fibre bundles during the processing of composite materials are complex and still not fully understood. Hence, synchrotron X-ray microtomography was used to characterise the longitudinal propagation of the flow front within a parallel arrangement of rigid fibres. The analysis of 3D images enabled the fluid-air interface curvatures, triple line lengths, and local contact angles to be quantified during wetting and dewetting experiments. The results showed that even in quasi-static situations, local contact angles exhibited significant variations along the fibres. These variations also depended on the wetting/dewetting state. The transverse capillary forces measured at the fibre scale from the analysis of 3D images were shown to be of the same order of magnitude as the longitudinal capillary forces. Local curvatures of the fluid-air interface and the resulting estimate of the average capillary pressure proved the relevance of a mesoscale capillary pressure model adapted for fibre bundles.

An integral method for calculation of capillary pressure based on centrifuge data of tight sandstone

The traditional Hassler-Brunner (HB) interpretation method of centrifuge capillary pressure is widely used in materials, soil, biotechnology, and especially in the petroleum industry. However, the assumptions of the traditional method cannot be simultaneously satisfied, the traditional method has been known to lead significant errors in some cases. In this paper, a new double integral method is proposed to evaluate the centrifuge capillary pressure of long tight sandstone samples. Both the changes of capillary length and interface of wetting phase and non-wetting phase fluids are considered by the new integral method, thus the average pressure and saturation derived from the proposed double integral method is more sufficient in theoretic foundation and clearer on physical meaning. By comparing with the measured capillary pressure of long tight sandstone core samples from porous plate, the capillary pressure calculated from traditional HB method is obviously smaller than the measured value, and the discrepancy increases with the decreasing core porosity. However, the average capillary pressure obtained by the proposed double integral method is remarkably consistent with the measured value. The findings of this study can help for better understanding of distribution of wetting phase fluid and average centrifuge capillary pressure in the core during centrifugal process.

A review on measurement of the dynamic effect in capillary pressure

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

Machine Learning for Capillary Pressure Estimation

Summary Capillary pressure plays an essential role in controlling multiphase flow in porous media and is often difficult to be estimated at subsurface conditions. The Leverett capillary pressure function J provides a convenient tool to address this shortcoming; however, its performance remains poor where there is a large scatter in the scaled data. Our aim, therefore, was to reduce the gaps between J curves and to develop a method that allows accurate scaling of capillary pressure. We developed two mathematical expressions based on permeability and porosity values of 214 rock samples taken from North America and the Middle East. Using the values as grouping features, we used pattern-recognition algorithms in machine learning to cluster the original data into different groups. In each wetting phase saturation, we were able to quantify the gaps between the J curves by determining the ratio of the maximum J to the minimum J. Graphical maps were developed to identify the corresponding group for a new rock sample after which the capillary pressure is estimated using the average J curve of the identified group and the permeability and porosity values of the rock sample. This method also provides better performance than the flow zone indicator (FZI) approach. The proposed technique was validated on six rock types and has successfully generated average capillary pressure curves that capture the trends and values of the experimentally measured data by mercury injection. Moreover, the proposed methodology in this study provides an advanced and a machine-learning-oriented approach for rock typing. In this paper, we provide a reliable and easy-to-use method for capillary pressure estimation in the absence of experimentally measured data by mercury injection.

A New Experimental Approach for Hydraulic Fracturing Fluid Damage of Ultradeep Tight Gas Formation

The unconventional resources from an ultradeep tight gas reservoir have received significant attention in recent decades. Hydraulic fracturing is the main method for tight gas reservoir development because of its extremely low permeability and porosity. During hydraulic fracturing, high hydraulic fracturing fluid (HFF) that invaded the zone near the fracture face may reduce gas relative permeability significantly and impede gas production. The sources of this damage can be the high capillary pressure (HCP) and the presence of water-sensitive clays (PWC). For tight rock, it is usually infeasible to identify the primary damage mechanism using the traditional steady-state measurement method due to long measurement time and gauge accuracy. In this paper, we present a new experimental approach to identify the primary mechanism of the fracture face damage (FFD) through the application of the pressure transmission method and pressure decay method. Both rock matrix and naturally fractured tight samples (depth 18,000 ft, Tarim field, China) were tested. The experimental results showed that the average high capillary pressure damage indexes ( D HCP ) of rock matrix cores and naturally fractured cores are 94.9% and 92.4%, respectively, indicating severe damage caused by HCP. The average clay-swelling and mobilization (CSM) damage indexes ( D CSM ) of rock matrix cores and naturally fractured cores are 29.6% and 38.4%, respectively, indicating that the damage caused by CSM is lighter than that by HCP. HCP is the primary damage mechanism for the tight sandstone. And the damage degree of the rock matrix cores is higher than that of the naturally fractured core. The proposed procedures can be applied to identify the FFD mechanism of other tight and shale formation and provide insightful fundamental data for HFF optimization.

A FRACTAL-MONTE CARLO APPROACH TO MODEL OIL AND WATER TWO-PHASE SEEPAGE IN LOW-PERMEABILITY RESERVOIRS WITH ROUGH SURFACES

The capillary pressure and relative permeability are the key parameters to affect the transport properties of low-permeability reservoirs. In this paper, the Fractal-Monte Carlo technique is applied to predict the oil and water relative permeabilities of low-permeability reservoirs with rough surfaces by considering the effect of tortuosity of capillaries and capillary pressure as well as roughness of capillary walls. The oil and water relative permeabilities are expressed as a function of the pore size, the area fractal dimension of pores, porosity, the water saturation, the capillary pressure, the relative roughness, the tortuosity fractal dimension and the microstructural parameters of low-permeability reservoirs with rough surfaces. It is observed that the average capillary pressure for water phase decreases with the increase of water saturation. On the other hand, it is found that the average capillary pressure for water phase increases with tortuosity fractal dimension and relative roughness. It can be found that the oil relative permeability of low-permeability reservoirs with rough surfaces increases with the increase of driving pressure. On the contrary, it can be observed that the oil and water relative permeabilities of low-permeability reservoirs with rough surfaces decrease with the increase of tortuosity fractal dimension and relative roughness. The predicted oil and water relative permeabilities obtained by the proposed Fractal-Monte Carlo simulation are shown to have a good agreement with the available experimental results. The proposed probability models for capillary pressure and relative permeability well revealed the physical mechanisms of transport properties of low-permeability reservoirs with rough surfaces.

Pore-network modeling and determination of rock and two-phase fluid flow properties

Pore-scale modeling is becoming widely applied in the oil industry. The objective of pore-scale imaging and modeling is to predict the properties of multiphase flow in porous media. Pore-network model construction of geologically realistic samples and determination of rock and two-phase fluid flow properties are described and discussed in this paper. Pore-network models were constructed using published micro-computed tomography images of different rock samples. Effective porosity, average absolute permeability, capillary pressure, tortuosity (in 3 directions), and relative permeability were calculated for 2 types of displacement (drainage and imbibition). Avizo® Software and two-phase code were used for volume rendering of rock samples and calculations of rock and two-phase fluid flow properties, since it is a valuable and reliable tool for prediction of petrophysical properties and has advances in visualization of the pore space. Created 3D models of core samples based on micro-computed tomography scan data will allow oil and oilfield service companies to create a digital core database on a computer instead of storing physical cores in warehouses, which in turn greatly facilitates access to cores for further work with them.

Determining Characteristic Relative Permeability From Coreflooding Experiments: A Simplified Model Approach

AbstractRelative permeability measurements from drainage coreflooding experiments are effective properties that vary with injection rate when capillary heterogeneity effects are present. It is therefore important to estimate the fine‐scale characteristic relative permeability ( ), which is independent of flow rate and can be used for accurate reservoir simulation and numerical modeling of coreflooding. Previous methods for estimation are based on two‐phase flow simulations with fine‐scale heterogeneous permeability and capillary pressure. These are computationally complex and prone to error. This work presents a reduced method, based on a simplified model, requiring only solutions of steady state single‐phase flow equations. The simplified model is used to study a number of synthetic 2‐D permeability realizations and 3‐D core models constructed based on experimental data from previous literature. The estimation method is tested on these examples and shown to be generally accurate. Cases where estimation error is significant are characterized by low injection rates, large nonwetting phase fractional flow, strong capillary heterogeneity, and small capillary number (ratio between core average pressure drop and capillary pressure drop). The estimation error is believed to be related to errors in the full‐model (two‐phase flow) simulations; that is, we find that for low injection rates, our simulator presents significantly different results compared to a commercial simulator. This could explain the source of mismatch between full and simplified methods and calls for further investigation of inaccuracy in numerical simulations at low flow rates, which could have implications for coreflood modeling and low rate reservoir simulation.

Quantification of Uncertainty and Best Practice in Computing Interfacial Curvature from Complex Pore Space Images.

Recent advances in high-resolution three-dimensional X-ray CT imaging have made it possible to visualize fluid configurations during multiphase displacement at the pore-scale. However, there is an inherited difficulty in image-based curvature measurements: the use of voxelized image data may introduce significant error, which has not—to date—been quantified. To find the best method to compute curvature from micro-CT images and quantify the likely error, we performed drainage and imbibition direct numerical simulations for an oil/water system on a bead pack and a Bentheimer sandstone. From the simulations, local fluid configurations and fluid pressures were obtained. We then investigated methods to compute curvature on the oil/water interface. The interface was defined in two ways; in one case the simulated interface with a sub-resolution smoothness was used, while the other was a smoothed interface extracted from synthetic segmented data based on the simulated phase distribution. The curvature computed on these surfaces was compared with that obtained from the simulated capillary pressure, which does not depend on the explicit consideration of the shape of the interface. As distinguished from previous studies which compared an average or peak curvature with the value derived from the measured macroscopic capillary pressure, our approach can also be used to study the pore-by-pore variation. This paper suggests the best method to compute curvature on images with a quantification of likely errors: local capillary pressures for each pore can be estimated to within 30% if the average radius of curvature is more than 6 times the image resolution, while the average capillary pressure can also be estimated to within 11% if the average radius of curvature is more than 10 times the image resolution.

Optimizing the particle size distribution of drill-in fluids based on fractal characteristics of porous media and solid particles

Drill-in fluid loss will lead to severe formation damage, and the particle size distribution (PSD) of lost circulation material is one of the most essential factors to control the drill-in fluid loss and protect the formation. In this paper, a fractal model for optimal solid PSD in drill-in fluids is developed for porous reservoir protection. The proposed model presents the following features: It demands particle size should be determined based on the “d90 Rule”, it requires the average capillary pressure curve to characterize the whole porous reservoir, and it allows for the microstructure characteristics of porous media and solid particles. The core dynamic damage experiments to verify this fractal model are carried out. Experimental results indicate that the loss of drill-in fluids designed by the proposed fractal model can be controlled within 10 min, and the permeability recovery rate after dynamic damage is above 90%, which means that formation damage is mitigated and well-controlled by the proposed fractal model. It is preliminarily proved that the proposed fractal model is of great validity and more suitable for formation damage control.

A New Method for Obtaining the Average Oil-Bearing Rock Capillary Pressure

Recent modification of the J-function model for obtaining the average oil-bearing rock capillary pressure based on the Leverett J-function have not fundamentally improved this technique, and modifications based on the rock pore-network model remain challenging. Because of this, a new method based on filling in 3-D curvilinear surfaces was developed for obtaining the average capillary pressure. The accuracy of the new method was verified by comparing the calculated results with the experimental data, which are in agreement. These findings suggest that the new method can be used to obtain the accurate average capillary pressure.

Dynamics of Microscale Liquid Propagation in Micropillar Arrays.

Understanding the dynamics of microscale liquid propagation in micropillar arrays can lead to significant enhancement in macroscopic propagation modeling. Such a phenomenon is fairly complicated, and a fundamental understanding is lacking. The aim here is to estimate three main parameters in liquid propagation, capillary pressure, average liquid height, and contact angle on the pillar side, through modeling and experimental validation. We show that the capillary pressure is not constant during liquid propagation, and the average capillary pressure is evaluated using its maximum and minimum values. The average liquid height influences the permeability of such a structure, which is challenging to determine as a result of the complicated three-dimensional (3D) meniscus shape. A simple physical model is provided in this paper to predict the average liquid height with less than 7% error. The contact angle on the micropillar side, which has considerable impact on the capillary pressure and the average liquid height, has been debated for a long time. We propose a model to predict this contact angle and validate it against experimental values in the literature. Our findings also indicate that the microscopic motion of the liquid front is significantly affected by the ratio of the pillar height to edge-to-edge spacing, and a correlation is provided for quantification. The proposed models are able to predict the droplet spreading dynamics and estimate spreading distance and time reasonably.

基于J函数的含油饱和度建模方法—以陆丰A油田为例

随着注水开发的进行，油层各项参数随之发生变化。由于水淹的影响，测井解释的含油饱和度与油藏原始含油饱和度在数值和分布上都有显著差异，不能代表油藏的原始分布状态。依据平均化后的毛管压力曲线，分流动单元对各类型储层进行原始含油饱和度的计算，建立基于J函数的含油饱和度模型，减小不同钻井时期测井解释含油饱和度的误差，对储量复算、油藏数值模拟等工作具有重要意义。 With the development of water injection, the parameters of the reservoir change accordingly. Because of the influence of flooding, there is a significant difference between the oil saturation of logging interpretation and the original oil saturation of reservoir, and it cannot represent the original distribution of oil reservoir. According to the average capillary pressure curve, the original oil saturation of each type of reservoir is calculated by flow unit, and a model of oil saturation based on J function is established. The error of oil saturation in logging interpretation at different drilling periods is reduced. Therefore, this work is important for reserves recalculation and reservoir numerical simulation.

Evaluation of TrueCell program for estimating point capillary pressure — saturation parameters for Flint sand

The purpose of this paper is to compare inverse estimates of point capillary pressure–effective saturation, Se(ψ), parameters and functions with independently measured Se(ψ) parameters and functions. Average capillary pressure–effective saturation functions, <Se>(ψ), were measured for Flint sand using a hanging water column setup and 9 packed columns, with heights varying between 4.3cm and 55.0cm. TrueCell, a Fortran program, was employed to inversely estimate point Se(ψ) parameters and functions from the <Se>(ψ) data sets. The TrueCell estimates were then compared with point Se(ψ) parameters and functions determined by neutron radiographic imaging of a single hanging water column setup. One sample t-tests indicated that there were no significant differences (at p<0.05) between the mean values of the inversely estimated point parameters and the corresponding neutron imaging values. However, the individual TrueCell predictions produced variable results compared to the measured point parameter set. Relatively few parameter estimates fell within the 95% confidence intervals of the neutron imaging estimates, and some deviations were quite large. These deviations were related to subtle variations in column packing, rather than differences in column height. Although this study has produced support for inverse modeling with TrueCell, it is important to note that individual predictions of Se(ψ) parameters and functions were often at odds with the independent measurements. Thus, TrueCell should be used with caution. In future studies of a similar nature, it would be desirable to independently determine point parameters and functions on multiple columns, rather than on a single column as was done here. Additionally, future research might want to examine the relationship between variations among individual parameters within a parameter set and the resulting predicted function.

Asymmetry Characteristics of Oil Production by Spontaneous Imbibition from Cores with Two Ends Open

Spontaneous imbibition experiments with two ends open (TEO) boundary condition showed that oil production from each open face of core is asymmetrical while the invasion of water is symmetrical. Investigating the asymmetry characteristics of oil production is helpful to understand the imbibition displacement mechanisms. In this paper, a mathematical model considering the difference in capillary back pressure for TEO imbibition is established by assuming piston-like advance of the imbibition front. Based on the model, the reason for asymmetry in oil production is discussed and the effect of the viscosity ratio, relative permeability ratio, average capillary back pressure and the difference in capillary back pressure on the asymmetry in oil production is investigated as well. The simulated results show that asymmetry in oil production depends on the ratio of the difference in capillary back pressure to the pressure drop in oil between the imbibition front and the open face of the core. As capillary driving pressure dissipated in oil is very small, a small difference in capillary back pressure will cause a significant asymmetric production of oil. Furthermore, the asymmetry in oil production decreases with increasing viscosity ratio (\(\mu _{\mathrm{o}}/ \mu _{\mathrm{w}})\) and relative permeability ratio \((k_{\mathrm{rw}}/k_{\mathrm{rnw}})\) and increases with increasing average capillary back pressure and the difference in capillary back pressure. This work gives us a comprehensive insight into the spontaneous imbibition with TEO boundary condition.