Capillary Bundle Research Articles

A NEW FRACTAL APPARENT PERMEABILITY MODEL FOR LIQUID FLOW IN TORTUOUS NANOPORES FROM LATTICE BOLTZMANN SIMULATIONS TO THE THEORETICAL MODEL

Tortuous pores are ubiquitous in natural porous media; however, the linear effects of tortuosity on the liquid flow behaviors are usually considered through capillary bundle models, which lead to inaccurate permeability prediction. Additionally, in the nanopores, due to the existence of heterogeneous viscosity and boundary slip, the effects of tortuosity on nanoconfined liquid flow behaviors are more complicated. In this paper, we comprehensively use the theoretical models and a nanoscale multi-relaxation-time lattice Boltzmann method (MRT-LBM) to characterize water flow behaviors in the tortuous nanopores, where heterogeneous viscosity and boundary slip are considered. The results show that the increase of tortuosity causes more negative effects, which results in a decreasing apparent permeability. The conventional model of the influence of tortuosity on the apparent permeability is linear[Formula: see text], which greatly underestimates the effect of tortuosity on apparent permeability. Then, a new fractal apparent permeability model [Formula: see text] based on modified tortuous effects is obtained by fitting the results from the MRT-LBM simulations. Based on the new fractal apparent permeability models, the results show that with an increasing fractal tortuosity dimension, the apparent permeability decreases rapidly first and then this trend becomes moderate. Our works can provide a more accurate basic model for studying liquid flow in porous media based on the capillary bundle model or pore network model.

Laminar flowmeter for mechanical ventilator: Manufacturing challenge of Covid-19 pandemic

The rapid and sudden attack of the covid-19 pandemic has emerged the urgent need for pulmonary resuscitation devices (ventilators). The airflow sensor is a main element in the ventilator. Sensing very low airflow rates is an essential requirement to meet the least significant bit of the analogue to digital converter included in the ventilator. This short communication describes the fabrication and test of five flow sensors using basic and the 3D printing techniques to overcome the severe challenge arising from the pandemic under strict quarantine. The principle of these five flow sensors is based on Fleisch pneumotachograph technology, which creates a pseudo-laminar flow within a bundle of capillary tubes. Amongst the five tested sensors, those fabricated by 3D printing technique were the most accurate and reliable. Results show that the 3D printed sensor of 33 trapezoidal capillary tubes and displaced pressure taps meet the requirement of sensing flowrates with less resistance to patient at exhalation and more linearity figure. The experimental data were correlated using a sophisticated MMF correlation with an R-squared factor of 0.9999 and a percentage error of 1.68%.

An Integrated Imaging Study of the Pore Structure of the Cobourg Limestone—A Potential Nuclear Waste Host Rock in Canada

With the development of imaging technology, tools to quantitatively describe pore structure, morphology, and connectivity have been widely applied on low permeable rocks; however, it is still questionable to what extent this information can be used to predict permeability. Applicability and comparability of different techniques are discussed here for the Middle Ordovician Cobourg limestone (Canada), a rock dominated by calcite grains of variable sizes (µm–cm) and heterogeneously distributed quartz, dolomite, pyrite, and meshy clay minerals. Absolute porosities determined by helium pycnometry (HP) in literature are approximately 1.6% (±0.9%), and gas permeabilities range from 10−20 to 10−19 m2. Porosities obtained from BIB-SEM are much smaller compared to those from HP (16–69% of HP). Pores found in clays are smaller, slit-shaped, and more densely spaced when compared to those in calcite minerals. Connectivity between pores could not be resolved with 3D micro-CT or FIB-SEM reconstructions, which have a resolution limit of 8 µm and 10 nm, respectively. However, assuming the pores to be connected, laboratory-derived permeability data could be fitted using a simple capillary bundle model, including information about the visible pore size distributions obtained from BIB-SEM images and a tortuosity range of 8 to 15.

Relationship Between Zeta Potential and Wettability in Porous Media: Insights From a Simple Bundle of Capillary Tubes Model

Hypothesis & MotivationExperimental data suggest a relationship between the macroscopic zeta potential measured on intact rock samples and the sample wettability. However, there is no pore-scale model to quantify this relationship. MethodsWe consider the simplest representation of a rock pore space: a bundle of capillary tubes of varying size. Equations describing mass and charge transfer through a single capillary are derived and the macroscopic zeta potential and wettability determined by integrating over capillaries. Model predictions are tested against measured data yielding a good match. FindingsMixed- and oil-wet models return a macro-scale zeta potential that is a combination of the micro-scale zeta potential of mineral-brine and oil-brine interfaces and the relationship between macro-scale zeta potential and water saturation exhibits hysteresis. The model predicts a similar relationship between zeta potential and wettability to that observed in experimental data but does not provide a perfect match. Fitting the model to experimental data allows the oil-brine zeta potential to be estimated at conditions where it cannot be measured directly. Results suggest that positive values of the oil-brine zeta potential may be more common than previously thought with implications for surface complexation models and the design of controlled salinity waterflooding of oil reservoirs.

Modeling transport of soft particles in porous media.

Flow-driven transport of soft particles in porous media is ubiquitous in many natural and engineering processes, such as the gel treatment for enhanced oil recovery. In many of these processes, injected deformable particles block the pores and thus increase the overall pressure drop and reduce the permeability of the particle-resided region. The change of macroscopic properties (e.g., pressure drop and permeability) is an important indicator of the system performance, yet sometimes impossible to be measured. Therefore, it is desirable to correlate these macroscopic properties with the measurable or controllable properties. In this work, we study flow-driven transport of soft particles in porous media using a generalized capillary bundle model. By modeling a homogeneous porous medium as parallel capillaries along the flow direction with periodically distributed constrictions, we first build a governing differential equation for pressure. Solving this equation gives a quantitative correlation between the total pressure drop and measurable parameters, including concentration and stiffness of particles, size ratio of particle to pore throat, and flow rate. The resultant permeability reduction is also obtained. Our results show that the total pressure drop and permeability reduction are both exponentially dependent on the particle concentration and the size ratio of particles to pore throat. With no more than two fitting parameters, our model shows excellent agreements with several reported experiments. The work not only sheds light on understanding transport of soft particles in porous media but also provides important guidance for choosing the optimal parameters in the relevant industrial processes.

Spontaneous Imbibition in a Fractal Network Model with Different Wettabilities

In this work, we derived a mathematical model for spontaneous imbibition in a Y-shaped branching network model. The classic Lucas–Washburn equation was used for modeling the imbibition process occurring in the Y-shape model. Then, a mathematical model for the Newtonian fluid’s imbibition was derived to reveal the relationship between dimensionless imbibition time and length ratio, radius ratio, and wetting strength. The dimensionless imbibition time in the model was adopted to compare with that of the capillary bundle model. Different length and radius ratios were considered in the adjacent two-stage channels, and different wettabilities were considered in the different branches. The optimal radius ratio, length ratio, and wetting strength were calculated under the condition of the shortest imbibition time. In addition, the shortest dimensionless imbibition time of the three-stage Y-shaped branching network model was calculated when the wettability changes randomly. The results indicate that the imbibition time changed mostly when the wettability of the second branch changed, and the second branch was the most sensitive to wettability in the model.

Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

Immiscible two-phase flow in porous media with mixed wet conditions was examined using a capillary fiber bundle model, which is analytically solvable, and a dynamic pore network model. The mixed wettability was implemented in the models by allowing each tube or link to have a different wetting angle chosen randomly from a given distribution. Both models showed that mixed wettability can have significant influence on the rheology in terms of the dependence of the global volumetric flow rate on the global pressure drop. In the capillary fiber bundle model, for small pressure drops when only a small fraction of the tubes were open, it was found that the volumetric flow rate depended on the excess pressure drop as a power law with an exponent equal to 3/2 or 2 depending on the minimum pressure drop necessary for flow. When all the tubes were open due to a high pressure drop, the volumetric flow rate depended linearly on the pressure drop, independent of the wettability. In the transition region in between where most of the tubes opened, the volumetric flow depended more sensitively on the wetting angle distribution function and was in general not a simple power law. The dynamic pore network model results also showed a linear dependence of the flow rate on the pressure drop when the pressure drop is large. However, out of this limit the dynamic pore network model demonstrated a more complicated behavior that depended on the mixed wettability condition and the saturation. In particular, the exponent relating volumetric flow rate to the excess pressure drop could take on values anywhere between 1.0 and 1.8. The values of the exponent were highest for saturations approaching 0.5, also, the exponent generally increased when the difference in wettability of the two fluids were larger and when this difference was present for a larger fraction of the porous network.

Influence of Pore Size Distribution on the Electrokinetic Coupling Coefficient in Two-Phase Flow Conditions

Streaming potential is a promising method for a variety of hydrogeophysical applications, including the characterisation of the critical zone, contaminant transport or saline intrusion. A simple bundle of capillary tubes model that accounts for realistic pore and pore throat size distribution of porous rocks is presented in this paper to simulate the electrokinetic coupling coefficient and compared with previously published models. In contrast to previous studies, the non-monotonic pore size distribution function used in our model relies on experimental data for Berea sandstone samples. In our approach, we combined this explicit capillary size distribution with the alternating radius of each capillary tube to mimic pores and pore throats of real rocks. The simulation results obtained with our model predicts water saturation dependence of the relative electrokinetic coupling coefficient more accurately compared with previous studies. Compared with previous studies, our simulation results demonstrate that the relative coupling coefficient remains stable at higher water saturations but vanishes to zero more rapidly as water saturation approaches the irreducible value. This prediction is consistent with the published experimental data. Moreover, our model was more accurate compared with previously published studies in computing the true irreducible water saturation relative to the value reported in an experimental study on a Berea sandstone sample saturated with tap water and liquid CO2. Further modifications, including explicit modelling of the capillary trapping of the non-wetting phase, are required to improve the accuracy of the model.

AN ANALYTICAL MODEL FOR PORE AND TORTUOSITY FRACTAL DIMENSIONS OF POROUS MEDIA

Accurate characterization of pore-scale structures of porous media is necessary for studying their transport mechanisms and properties. An analytical model for pore and capillary structures of porous media is developed based on fractal theory in this study. The pore and tortuosity fractal dimensions are introduced to characterize the pore size distribution and tortuous flow paths. A power law scaling between fractal probability function and pore diameter is proposed, which can be applied to determine the pore fractal dimension. The explicit expression for tortuosity fractal dimension is derived based on exactly self-similar fractal set and fractal capillary bundle model. The present fractal model has been validated by comparison with that of experiments and numerical simulations as well as theoretical models. The results show that the tortuosity fractal dimension decreases as porosity and pore fractal dimension increase, it increases with the increment of tortuosity. Both the particle shape and pore size range take important effect on the tortuosity fractal dimension under certain porosity. The proposed pore-scale model can present a conceptual tool to study the transport mechanisms of porous media and may provide useful guideline for oil and gas exploitation, hydraulic resource development, geotechnical engineering and chemical engineering.

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

Hydraulic properties of unsaturated calcarenites by means of a new integrated approach

Most infiltration and water retention models for unsaturated porous media proposed in the literature often are based on simplified representations of the pore system and use the matric head as the main state variable.An integrated study on the hydraulic properties of homogeneous calcarenites with a complex pore network is presented, aimed at assessing water infiltration and retention mechanisms, starting from dry to wet conditions under high water inflow.Medium-grained grainstones and fine-grained packstones were used as material for laboratory testing and model set up. Petrophysical characterization and bimodal distribution of pore volume was obtained by standard and unconventional procedures. Permeability test under saturated conditions was performed with constant and falling head tests. Falling head infiltration tests at bench scale were carried out to estimate the hydraulic properties of the materials under unsaturated conditions.Unsaturated hydraulic relationships such as the soil water retention curve (SWRC) and hydraulic conductivity function were examined. The advection–diffusion form of Richard’s equation, together with the pore bundle model and dual porosity concept under equilibrium conditions represent the theoretical framework used to investigate the unsaturated hydraulic behavior of the calcarenites in the falling head infiltration test. The SWRC, relative hydraulic conductivity and celerity were determined through the capillary theory and pore bundle concept considering the bi-modal nature of the pore-size distribution. Theoretical solutions and model predictions were compared with experimental data, which demonstrated the dominant control of macro-porosity on water flow and infiltration rate. In particular, our experimental results indicate that the wetting front propagates mainly through the macropores with a gravity driven flow velocity higher than the diffusive flow through the micropores. The effect of texture, degree of saturation and boundary conditions on infiltration dynamics is discussed.

An improved saturation evaluation method of Chang 8 tight sandstone reservoir in Longdong West area of Ordos Basin, China

This study focus on saturation evaluation of Chang 8 tight sandstone reservoir in Longdong West area of Ordos Basin, China. An improved saturation calculation method was proposed based on the equivalent rock capillary bundle theory. Firstly, according to characteristics of reservoir pore structure and rock conductivity, the conductive space of reservoir rock is equivalent to the parallel conductive of micro capillary bundle representing the micro pores and the coarse capillary bundle representing the macro pores. Then, the variable cementation index(m) saturation model was deduced by using Poiseuille flow equation and Darcy's law. During the calculation of model parameters, the T2 spectrum data of nuclear magnetic resonance (NMR) was used to calculate the equivalent radius of reservoir micro pores and macro pores, which ensured the ability of model popularization and application. Finally, the proposed saturation calculation method is applied to reservoir evaluation of the study area, and compared with the classical Archie saturation model. The application effect shows that the calculated saturation from the proposed variable m model is much closer to the sealed coring data than that from classical Archie model, and the average relative error of saturation calculated by the variable m model is within 7%, which proves that the proposed saturation calculation method is applicable and effective.

An investigation on the robustness and accuracy of permeability estimation from 3D μ-CT images of rock samples based on the solution of Laplace's equation for pressure

This study aims to present a simple method to calculate the permeability of porous materials using μ-CT images and an approximation based on the solution of Laplace's equation for pressure. For this purpose, an in-house computer program was developed based on finite difference method to determine the distribution of pressure in voxelated pore space. Afterwards, approximate permeability was obtained using Euclidean distance map of the pore space and a simple upscaling scheme for a range of porous media including idealized channels of elementary cross sections, Boolean models of spherical grains, bundles of capillary tubes and digital rocks obtained from μ-CT imaging. Next, a comparison was made between the Laplace permeability approximation and the analytical solutions of idealized microstructure and digitally-computed permeability of a number of rock samples using the Stokes solver and the lattice-Boltzmann method. It has been revealed that the estimated permeability values are in good agreement over the investigated range of porosity. The developed Laplace permeability solver was also well matched with the results of experimental measurement on a real rock sample. As an illustration of the applicability of the proposed method, the anisotropy of permeability at pore scale and the cross-correlation between permeability and connected macro-porosity was analyzed for the experimentally investigated rock sample. In conclusion, the results of this paper suggest that the proposed permeability solver is suitable for rough estimation of permeability and hence rough evaluation of heterogeneity/anisotropy from μ-CT images of rocks, particularly for large datasets with high number of pore voxels.

On the applicability of viscosity-based capillary bundle concepts to predict the penetration behaviour of polymer solutions into sand

The increasing use of polymer solutions as support fluids in pile drilling, diaphragm walling or tunnelling applications demands a more detailed discussion of their penetration behaviour and prediction thereof. In this context, the capillary bundle approach can be a useful tool. However, while it is widely discussed in the oil and gas application, the subject is currently addressed only scarcely with regard to support fluid penetration targeting stagnation, where small flow velocities and non-cohesive soil environments are of relevance. In these boundary conditions, the applicability of capillary bundle approaches is not yet sufficiently confirmed and substantiated. The current paper thus reviews current capillary bundle models based on Hagen–Poiseuille in combination with a power-law rheological model and discusses their applicability with respect to support fluid application in the context of experimental soil permeation tests for small gradients (ile 10). Two granular materials of similar grain size, but different angularity (glass beads and sand), and four polymer solutions varying in polymer chain length and concentration are investigated, and the impact of model assumptions and bulk material input variables is systematically discussed. The experimental results show that the theoretical models are generally able to predict the filter velocity qualitatively for values above {bar{v}}=5times 10^{-7} m/s and also quantitatively, when an empirical shift factor alpha ^* is introduced and water permeability values are determined experimentally. With respect to the influence of soil parameters, it was found that the soil particle roughness decreases the flow velocity of the polymer solution despite similar hydraulic conductivity in water. Polymer chain length and concentration were observed to control the degree of possible dilution (alpha ^*<1) in the porous system compared to bulk rheological characteristics. It can therefore be concluded that capillary bundle models can indeed be applied in the targeted fields even though they are unable to predict a complete stagnation for i>0. However, rather than specific model assumptions for tortuosity, taking into account the specific soil-polymer interaction has shown to be of primary importance to ensure no under- or over-prediction of penetration velocities solely based on bulk rheology.

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Fractal Distribution of Tortuous Capillary Fractures

Electrokinetics methods have attracted increasing interest to characterize hydrogeological processes in geological media, especially in complex hydrosystems such as fractured formations. In this work, we conceptualize fractured media as a bunch of parallel capillary fractures following the fractal size distribution. This conceptualization permits to obtain analytical models for both the electrical conductivity and the electrokinetic coupling in water saturated fractured media. We explore two different approaches to express the electrokinetic coupling. First, we express the streaming potential coupling coefficient as a function of the zeta potential and then we obtain the effective charge density in terms of macroscopic hydraulic and electrokinetic parameters of porous media. We show that when the surface electrical conductivity is negligible, the proposed models reduces to the previously proposed one based on a bundle of cylindrical capillaries. This model opens up a wide range of applications to monitor the water flow in fractured media.

Analysis and Calculation of Threshold Pressure Gradient Based on Capillary Bundle

Oilfield water injection is one of the important means to supplement energy to the formation and enhance oil recovery in the process of oilfield development. The level of water injection technology determines the effect of oilfield development and also determines the length of oilfield development life. Research on seepage law of water injection development in low-permeability reservoir is the basis and important technical means of low-permeability reservoir development, and the key point of seepage law is to analyze the starting pressure gradient law. In previous studies, either static test or dynamic experimental value is used, so the error of pseudo starting pressure gradient derived from experimental value is too large, which makes people expand the starting pressure value in low-permeability reservoir in practical engineering application, and the starting pressure gradient obtained from laboratory test cannot be applied in actual reservoir. To accurately calculate the threshold pressure gradient for low-permeability reservoirs, the threshold permeability is proposed through the study of the seepage law and laboratory experiments. It is recognized that the threshold pressure gradient and the threshold permeability had been changing during the seepage. Through steady-state “flow rate-pressure difference” displacement experiment, with natural cores from a low-permeability reservoir, based on a capillary bundle model, the method for calculating the gradient is innovatively proposed. The experimental data show that the whole low-permeability seepage flow is nonlinear, divided into three stages according to the physical stages with obvious changes. Through processing and analyzing of the experimental results, first, it is showed that both threshold pressure gradient and threshold permeability increase with the rise of flow rate and the increasing amplitude is gradually decreasing. Second, the study proposes the permeability is the main controlling reason of the threshold pressure gradient, and the flow velocity is an important reason. Third, we obtain the formulas of the minimum threshold pressure gradient, the threshold pressure gradient, and the corresponding threshold permeability of different cores and the power function relationship between the threshold pressure gradient and the core permeability is obtained. And further, the one-dimensional experimental results are applied to the radial fluid flow, and the recognition that the threshold pressure gradient decreases with increasing distance and the ratio of the threshold pressure to the total displacement pressure difference are obtained. The ratio of starting pressure to total pressure drop is about 0.5, and the higher the permeability is, the lower the ratio is lower under 0.5. These findings significantly help in understanding how to effectively develop low-permeability reservoir by water injection. Through the dynamic macro experiment and microcapillary bundle principle, the experiment can be divided into several sections for analysis, which can be more accurate. The minimum start-up pressure gradient can not only guide the later development of the oilfield, but also enrich the theoretical study of non-Darcy low-velocity seepage. At the same time, the law of flow velocity and start-up pressure gradient indirectly proves the boundary layer theory of the generation mechanism of start-up pressure gradient and supports and guides the effective development of various development methods of low-permeability reservoir.

The influence of layer separation on multilayer mist coalescing filter performance

• Influence of small gaps between layers in a multilayer mist filter “sandwich” confirmed experimentally. • Gap size needed to induce onset of effect studied using pore network modelling. • Important implications for filter performance. • Parametric study to inform future research and design. This work experimentally and numerically examined the influence of micro-sized gaps between layers of filter media on the micro-physics of multilayer porous media commonly used in gas–liquid filter/coalescer applications. It had previously been assumed that if the layers are sufficiently closely packed then they will behave as a monolithic filter with equivalent properties, however no studies have been conducted on the micro-scale interstitial properties of multilayer filters to confirm this. High resolution micro-Computed Tomography ( μ -CT) carried out in this work, determined that even in closely packed “sandwiches” of media, the layers in the filter element behave more like individual filters than a monolithic entity, with each layer having a characteristic liquid saturation profile that repeats throughout the media. To further investigate and understand this phenomenon, simulations using a Dynamic Pore Network Model (DPNM) approach were undertaken to replicate the effect and investigate the influence of layer gap on the onset and magnitude of the effect. The DPNM simulations also revealed the presence of local minima in saturation in the gap, similar to the experiments. Such local reduction in saturation could be interpreted by the concept of capillary bundles. Both experiments and PNM predictions showed that the local minima is more pronounced at the lower velocities. It was also found that the monolith assumption breaks down at a gap thickness of 60 μ m for the micro-glass filter ( d = 4.5 μ m) for the range of parameters considered; however, this was likely larger than the gap width in the experimental cases.

Initial water imbibition of gas-saturated natural reservoir rock: A generalized multifactor geometry model with capillary bundles

The spontaneous imbibition in porous medium is of interest for many engineering problems particularly in the reservoir exploitation over several decades. So far, various analytical or numerical models have been proposed to simulate the imbibition, but none of them can fully take into account real microscopic geometry characteristics of pore structure. Therefore, assuming quasi-steady and completely developed laminar flow with no-slip boundary conditions when capillary bundles imbibe an incompressible Newtonian liquid, a generalized spontaneous imbibition model is proposed based on a fractal pore structure consisting of tortuous and nonuniform capillaries with different sizes and noncircular cross-sections. A theoretical analysis and experimental contrast demonstrate that the derived formulas enable the unification of several traditional and newly developed models available from the literature and have the better predicted trend with the relative error controlled within 100% in comparison to them. The obtained model is evaluated against previously reported data of water imbibition measured for various natural porous rocks in multiple directions. The validation results show that the generalized model can be utilized to characterize the imbibition behavior of porous rocks with little clay and even extend to other natural and engineering porous materials, including consolidated and unconsolidated media, and that the interconnected pores cannot always be assumed to be cylindrical or uniform. Moreover, the present model is applied to inversely estimate the pore size as a result of good agreement with experimental measurements. Simultaneously, in accordance with the new theoretical model, the difference in water imbibition is newly revealed for selected rock samples from the literature.

Determining Triaxial Stress Sensitivity of Oil Reservoir Rocks without Fluid Flooding

The sensitivity of oil reservoir rocks to stress is the basis for oilfield development, which determines the production method employed in the field. Therefore, it is critical to understand the stress sensitivity behavior of oil reservoir rocks in an oilfield. In this paper, a novel method for determining the stress sensitivity of oil reservoir rocks by triaxial stress testing without fluid flooding was proposed. It measures the triaxial stress and strain of the core rock samples, and based on which, the core porosity and permeability under stress can be evaluated by theoretical model. In the model, the pores of the core were assumed to be a bundle of capillaries and the necessary relationship was derived to calculate the changes of porosity and permeability of the core samples caused by the strain. Through comparison with and analysis of experimental results obtained for various rock core samples under different stress and strain conditions, it is observed that the theoretical model match well with that of the experiments. This method provides a new approach for the stress sensitivity analysis of oil reservoirs without fluid flooding.

Mercury cyclic porosimetry: Measuring pore-size distributions corrected for both pore-space accessivity and contact-angle hysteresis

We propose a set of simple formulae for interpreting “mercury cyclic porosimetry” measurements where multiple intrusion–extrusion cycles are carried out. By employing two parameters α∈[0,1] and κ∈[0,1], our theory quantitatively breaks down any hysteresis observed in cyclic porosimetry data into contributions due to connectivity effects and contact-angle hysteresis, respectively. In particular, the parameter α, called “pore-space accessivity”, characterizes any serial connectivity between different-size pores. It has long been recognized that the standard method for determining the pore-size distribution (PSD) from mercury intrusion data based on the capillary bundle assumption overestimates the fraction of smaller pores; that corresponds to the α→1 limit of our model. In contrast, for materials with α<1, our theory predicts a broadened PSD shifted toward larger radii, thus representing a simple way of rectifying PSDs for connectivity effects. The proposed model also establishes mercury cyclic porosimetry as a standard experimental procedure for measuring α, which can then be used in continuum models of porous media where connectivity effects play a significant role, such as in multiphase flow.