Pore Body Size Distributions Research Articles

Augmenting X-ray micro-CT data with MICP data for high resolution pore-scale simulations of flow properties of carbonate rocks

Pore-scale modeling is essential in understanding and predicting flow and transport properties of rocks. Generally, pore-scale modeling is dependent on imaging technologies such as Micro Computed Tomography (micro-CT), which provides visual confirmation into the pore microstructures of rocks at a representative scale. However, this technique is limited in the ability to provide high resolution images showing the pore-throats connecting pore bodies. Pore scale simulations of flow and transport properties of rocks are generally done on a single 3D pore microstructure image. As such, the simulated properties are only representative of the simulated pore-scale rock volume. These are the technological and computational limitations which we address here by using a stochastic pore-scale simulation approach. This approach consists of constructing hundreds of 3D pore microstructures of the same pore size distribution and overall porosity but different pore connectivity. The construction of the 3D pore microstructures incorporates the use of Mercury Injection Capillary Pressure (MICP) data to account for pore throat size distribution, and micro-CT images to account for pore body size distribution. The approach requires a small micro-CT image volume (7–19 mm3) to reveal key pore microstructural features that control flow and transport properties of highly heterogeneous rocks at the core-scale. Four carbonate rock samples were used to test the proposed approach. Permeability calculations from the introduced approach were validated by comparing laboratory measured permeability of rock cores and permeability estimated using five well-known core-scale empirical model equations. The results show that accounting for the stochastic connectivity of pores results in a probabilistic distribution of flow properties which can be used to upscale pore-scale simulated flow properties to the core-scale. The use of the introduced stochastic pore-scale simulation approach is more beneficial when there is a higher degree of heterogeneity in pore size distribution. This is shown to be the case with permeability and hydraulic tortuosity which are key controls of flow and transport processes in rocks.

Critical pressure (Pc) and critical temperature (Tc) of Midra shale

The critical pressure (Pc) and critical temperature (Tc) of shale gas depend on the characteristic pore size because of the importance of fluid–rock interactions in the matrix. This size dependency is neglected in highly permeable formations, where gas composition is only implemented because the fluid–fluid interactions are dominant. This study determines the critical properties by accounting for the characteristic pore size in the shale matrix and gas composition. The analyzed components are carbon dioxide, ethane, methane, n-butane, nitrogen, pentane, and propane. It shows that the bulk properties overestimate the actual critical properties. The overestimation varies between 15 and 26% in a uniform 5 nm conduit with a circular cross section, and it increases nonlinearly when decreasing the conduit size. Overestimation versus size is presented to provide a convenient tool for correcting the existing data. This study also determines the critical properties of Midra shale by accounting for the pore-throat size and pore-body size distributions. The former distribution is based on the mercury injection capillary pressure measurements of eight samples, whereas the latter is based on the nitrogen adsorption measurements of six samples. This study indicates that common bulk properties overestimate the critical properties of the studied shale between 5 and 22%. The results have applications in characterizing multiphase transport in shale gas reservoirs.

Analysis of the length scale characterized by the yield stress fluids porosimetry method for consolidated media: comparison with pore network models and mercury intrusion porosimetry

Substantial progress has been recently achieved in the development of a clean alternative to mercury intrusion porosimetry (MIP) based on single-phase flow measurements in porous samples using yield stress fluids. However, no study to date has examined the scale of the pore length actually provided by the yield stress fluids porosimetry method (YSM) in consolidated porous media. Indeed, while the results of YSM were compared to those provided by MIP in the past, the relationships between the characterized pore size distribution (PSD) and the actual pore geometry have still not been addressed for this type of porous media. This issue is of special interest to geoscientists involved in seeking relevant information from core characterization operations. With this aim in mind, the objective of the present paper is to evaluate the agreement between the PSDs characterized by YSM, the pore-opening size distributions provided by MIP tests, and the pore-throat and pore-body size distributions obtained from X-ray computed microtomography. For this purpose, a set of artificial and natural porous samples with permeability values extending over two magnitudes were characterized by using both YSM and MIP laboratory tests. Then, the results were matched to the model pore geometries extracted from digital images of the real microstructure. This analysis led to the main conclusion that YSM can be reliably used as an adequate substitute for MIP in the case of the investigated consolidated media, given the general agreement observed between these methods.

Comprehensive pore size characterization of Midra shale

Although the Middle East's carbonate reservoirs were the first and most studied rocks in the world, Middle Eastern shale reservoirs are still poorly understood compared with other unconventional formations in the US. We investigate the pore-throat size and pore-body size distributions of Midra shale in Qatar to quantify the pore-scale features that control transport properties at the core scale. We measured the capillary pressure by injecting mercury into samples in drainage. The capillary pressure variation with wetting phase saturation exhibits a plateau-like trend, which differs from the linear trend observed in most shales in the US. The capillary pressure measurements quantify the pore-throat size distribution. We also measure nitrogen adsorption and analyze the measurements to determine the pore-body size distribution. This study shows that the pore-throat size has a narrow distribution, and its average is close to 22 nm. In addition, the pore-body size has a wide distribution, and its average is 18 nm. Thus, the transport properties dependent on the pore-throat size require modifications to account for the pore proximity to represent subsurface conditions. The transport properties, such as density, relevant to the pore volume in the matrix can be estimated with reasonable accuracy from the gas composition in wider conduits. The presented results have applications for the development of unconventional gas, which is the cleanest fossil fuel.

Effects of gas pressurization on the interpretation of NMR hydrocarbon measurements in organic rich shales

The estimation of total hydrocarbons (HCs) in place is one of the most important economic challenges in unconventional resource plays. Nuclear magnetic resonance (NMR) has proven to be a valuable tool in directly quantifying both hydrocarbons and brines in the laboratory and the field. Some major applications of NMR interpretation include pore body size distributions, wettability, fluid types, and fluid properties. However, for tight formations, the effects of the factors on NMR relaxation data are intertwined. One purpose of this study is to review the interpretation of NMR response of HCs in a tight rock matrix through illustrated examples. When comparing NMR data between downhole wireline and laboratory measurement, three important elements need to be considered: 1) temperature differences, 2) system response differences, and 3) pressure (mainly due to the lost gasses.) The effect of temperature on HCs would be presented with experimental results for bulk fluids. Whereas, the effect of pressure is investigated by injecting gas back into rock matrix saturated with original fluids. The experiments were performed within an NMR transparent Daedalus ZrO2 pressure cell, which operates at pressures up to 10,000 psi. The results show that, at ambient temperature and pressure, NMR responds to a fraction of HCs, which is volatile enough to be observed as an NMR relaxation sequence. The invisible fraction of HCs to NMR sequence at ambient condition can be up to 20% of the total extractable HCs. Molecular relaxation is impacted by fluid viscosity, pore size, and surface affinity. In other words, the fluid with higher viscosity (either due to temperature or gas loss), presenting in smaller pore, or highly affected by the pore surface, will relax faster, and would be partially invisible to NMR, especially in the field. This is critical to the interpretation of NMR response for liquid rich source rocks, in which all of the above molecular relaxing restrictions can be found. Thus, engineers can underestimate movable HCs by using routine core analysis data.

Pore structure and fractal characteristics of Ordovician Majiagou carbonate reservoirs in Ordos Basin, China

Fractal analysis was performed on carbonate core plug samples from the Ordovician Majiagou carbonate reservoirs in the Ordos Basin using mercury intrusion capillary pressure (MICP), nuclear magnetic resonance (NMR), and the x-ray computed tomography (CT) measurements to improve our understanding of the pore structure characteristics. The relationships between pore structure parameters and the fractal dimensions were investigated. The pore systems are dominated by secondary intercrystalline pores and enlarged dissolution pores as well as microfractures. The fractal curves from MICP analysis break into two segments at the Swanson’s parameter. The small pore-throat systems can be described by the fractal theory, whereas pores connected by relatively large throats (greater than the pore-throat radius at the Pittman’s hyperbola’s apex) are not cylindrical in shape, cannot be described by a capillary tube model, and tend to have apparent fractal dimensions larger than 3.0. The fact that the entirety of the capillary curve cannot be fit by a single fractal dimension implies that there are multiple pore systems present with different fractal dimensions. The CT analysis shows that the pores are dispersed in the three-dimensional spaces mainly with elliptical shapes. The NMR measurements are sensitive to pore-body size and MICP probes pore-throat dimensions, the latter being complementary to the pore-body–size distribution. None of the CT, MICP, and NMR techniques provide “right” or “wrong” answers to the pore-throat systems, but they probe different aspects of the pore systems. This study assumes the pore shapes to be spherical in general, and then the fractal dimension is calculated from the NMR transverse relaxation time (T2) spectrum. The fractal dimensions of all the samples are calculated, and the accuracy of the fractal model is verified by the high regression coefficients. Almost all the pore systems can be described by fractal theory, and the fractal dimensions are strongly correlated with the T2 values separating the immovable fluid and the free fluid. Microfractures may bias T2 toward larger values, making it hard to derive fractal dimensions from NMR measurements. The coexistence of small pores (pore radius 50 μm) results in a heterogeneous pore distribution and a high fractal dimension. Reservoir quality increases with the complexity degree of the microscopic pore structure. Conversely, samples that are dominated by small pore systems tend to have a lower fractal dimension and a less complex pore structure.

Clarifying pore diameter, pore width, and their relationship through pressure measurements: A critical study

Abstract Understanding geometrical and topological properties of the pore space in permeable media is of paramount importance, particularly in oil and gas production. Pore space characteristics such as pore sizes and their probability distributions, as well as pore's connectivity are main factors in the modeling of fluid flow and chemical transport in soils and rocks. A common method to determine the pore size is to convert an implemented pressure via either the Young-Laplace or Kelvin equation by assuming a specific pore shape. Simple geometries such as cylindrical and slit-shaped have been frequently used in the literature, particularly to represent pores and to derive theoretical models estimating permeability from pore-throat size distribution. In this study, we clarify the relationship between pore diameter (d) and pore width (w), two terms interchangeably used in the literature. The former corresponds to a cylindrical pore, while the latter to a slit-shaped one. We emphasize that d = 2w, in contrast to previously published studies claiming that the diameter of a cylindrical pore is equal to the distance between sides of a slit-shaped pore (i.e., d = w). In addition, we discuss that comparing/combining pore size distribution derived from mercury intrusion porosimetry and that determined from nitrogen adsorption isotherm is not supported, unless the effect of hysteresis is trivial, as most probably the former represents pore-throat while the latter pore-body size distributions.

Critical properties (Tc, Pc) of shale gas at the core scale

The transport properties of gas deviate from the nominal values, reported without confinements, when it is confined inside a nano-size conduit. This is because the interactions between the gas molecules and the conduit become more important than do those of the gas molecules with each other. The deviation is relevant to shale gas because of the ultra-narrow pore size in the matrix. With this in mind, we determine the critical temperature (Tc) and critical pressure (Pc) for shale formations in North America at the core scale. The shale formations are the Bakken, Barnett, Eagle Ford, Haynesville, Marcellus, Monterey, New Albany, Niobrara, Utica, Wolfcamp, and Woodford. The present study uses the acyclic pore model to account for the effective connectivity of shale samples at the core scale. It also differentiates between the pore-throat and pore-body size distributions. The former is used to derive the critical properties relevant to the fluid flow (displacement), and the latter is used to determine the effective properties relevant to the storage. Our study shows that the displacement-critical properties change significantly, whereas the storage-critical properties do not require modifications. Quantitative corrections of the critical properties for various formations are presented. The results have major applications in developing a realistic reservoir model for shale formations.

Pore Size of Shale Based on Acyclic Pore Model

The transport properties inside a nanosize conduit, such as viscosity and density, deviate from those reported at unconfined conditions with an identical pressure and temperature. The deviation from the nominal value is well studied for the simple topology in nanofluidics. A straight circular tube is an example of a simple topology. The pore space inside the matrix of a shale formation is also a nanofluidic system, because its characteristic size is smaller than or equal to 100 nm, but it includes a complex structure. With this in mind, we determine the pore-throat and pore-body size distributions of different shales whose data are available in the literature. The main objective is to quantitatively distinguish the two sizes, whose importance is overlooked in the study of shale formations. The pore-throat size distribution is determined from mercury injection capillary pressure measurements, and the pore-body size distribution is derived from nitrogen adsorption–desorption. The acyclic pore model, which is physically representative of the pore space at the core scale, allows us to interpret the petrophysical measurements. Our study of different shales shows that the average pore-body size is usually larger than 20 nm; thus, there is no need to account for the pore proximity (confinement). The pore-throat size distributions of different shales usually fall below 20 nm, which entails the modification of a transport property that is relevant to the formation resistance against the flow.

Numerical Simulation of Yield Stress Fluid Flow in Capillary Bundles: Influence of the Form and the Axial Variation in the Cross Section

In this paper, we investigate possible improvements that can be made to the bundle of capillaries model in order to better represent the flow of yield stress fluids through porous media. This was examined by performing extensive and progressive numerical simulations and by introducing the non-circularity of channels’ cross section and/or its variability along the channels’ axis. It is shown that if only the non-circularity of channels’ cross section is taken into account, a moderate influence is observed on both critical pressure gradient for the flow onset and the flow rate/pressure gradient $${Q}({\nabla P})$$ relationship. However, the axial variation in capillaries’ cross section has proved to be more impacting the computed flow rate/pressure gradient data. We show hence that when available pore throat and pore body size distributions are used to construct the bundle of axially varying capillaries, the obtained $${Q}({\nabla P})$$ data do fit well experimental results corresponding to the flow of a Bingham-like fluid through a bed of randomly packed mono-sized spheres.

Combining nuclear magnetic resonance and rate-controlled porosimetry to probe the pore-throat structure of tight sandstones

Abstract Rate-controlled porosimetry (RCP), nuclear magnetic resonance (NMR) and micro CT tests were conducted on five tight sandstone samples, the results were compared to reveal the limitations of RCP in determining the pore size distribution (PSD) and pore to throat ratio (PTR), and then an effective method to test the pore-throat structure of tight sandstone by combining NMR and RCP was proposed. The quasi-PSD derived by RCP was bimodal, the left peak of which corresponding to throats was in good agreement with that of NMR, while the right peak corresponding to pore bodies had similar volume content and different distribution range with that of NMR. RCP reflected an equivalent spherical radius of pore body, and the calculation was significantly larger than the maximum inscribed radius (MIR) of the actual pore body with the same volume; whereas in NMR, the ratio of pore volume to surface area was used to estimate pore radius, and the pore radius calculated was close to MIR. The full-range pore body size distribution was determined by subtracting the RCP-derived throat size distribution from NMR-derived PSD, and then the pore throat connectivity was evaluated comprehensively. The mean value of PTR calculated by RCP was larger than 100.0 due to the differences in the calculation method between pore body size and throat size in RCP, while the mean value of PTR calculated by combining NMR and RCP ranged from 7.5 to 64.0. It is concluded that the combination of RCP and NMR experiment is an effective way to comprehensively reveal the size distribution of pore body and throat in tight sandstone.

Modeling adsorption–desorption hysteresis in shales: Acyclic pore model

Existing conventional measurements face challenges in characterizing transport properties of a shale because they are designed originally for formations with relatively wide pores and high permeability. The integrated analysis of such measurements helps us better understand the connected pore system of a shale formation when they are sensitive to the pore topology and cover a wider range of pore size. Here, we analyze nitrogen adsorption–desorption and mercury intrusion measurements to characterize the pore space of a shale. We determine pore-body size distribution by interpreting adsorption–desorption experiments. We also calculate pore-throat size distribution from mercury intrusion. We adopt the acyclic pore model, which embraces limited pore connectivity, and account for the connected path of the pores at the core scale. Our study distinguishes the pore size relevant to the storage and the flow conductance for the shale.

Quantifying fluid distribution and phase connectivity with a simple 3D cubic pore network model constrained by NMR and MICP data

A computer algorithm is implemented to construct 3D cubic pore networks that simultaneously honor nuclear magnetic resonance (NMR) and mercury injection capillary pressure (MICP) measurements on core samples. The algorithm uses discretized pore-body size distributions from NMR and pore-throat size versus incremental pore-volume fraction information from MICP as initial inputs. Both pore-throat radius distribution and body–throat correlation are iteratively refined to match percolation-simulated primary drainage capillary pressure with MICP data. It outputs a pore-throat radius distribution which is not directly measurable with either NMR or MICP. In addition, quasi-static fluid distribution and single-phase connectivity are quantified at each capillary pressure stage. NMR measurements on desaturating core samples are simulated from the quantitative fluid distribution in a gas-displacing-water drainage process and are verified with laboratory measurements. We invoke effective medium theory to quantify the single-phase connectivity in two-phase flow by simulating percolation in equivalent sub-pore-networks that consider the remaining fluid phase as solid cementation. Primary drainage relative permeability curves quantified from fluid distribution and phase connectivity show petrophysical consistency after applying a hydrated-water saturation correction. Core measurements of tight-gas sandstone samples from the Cotton Valley formation, East Texas, are used to verify the new algorithm.

Extraction of physically realistic pore network properties from three-dimensional synchrotron X-ray microtomography images of unconsolidated porous media systems

This paper presents application of a series of algorithms used to extract pore network structure from high-resolution three-dimensional synchrotron microtomography images of unconsolidated porous media systems. These algorithms are based on the three-dimensional skeletonization that simplifies the pore space to networks in the form of nodes connected to paths. Dilation algorithms were developed to generate inscribed spheres on the nodes and paths of the medial axis to represent pore-bodies and pore-throats of the network, respectively. The end result is a physically representative pore network structure, i.e. three-dimensional spatial distribution (i.e. x-, y-, and z-coordinates) of pore-bodies and pore-throats, pore-body size distribution, pore-throat size distribution, and the connectivity. Systems analyzed in this study include different glass bead systems and natural marine sand. The media ranged in size from 0.123 to 1.0 mm, while the image volumes ranged between 7.7 and 108.9 mm 3. In addition to extracting the pore network structure, the porosity, specific surface area, and representative elementary volume analysis on the porosity were calculated. Spatial correlation between pore-body sizes in the network was investigated using semivariograms and integral scale concepts. The impact of resolution on the calculated property was also investigated. In this work, we show that microtomography is an effective tool to non-destructively extract the structure of many systems. The quality of the datasets depends on photon energy, photon flux, size of the sample, type of the sample, and size of the sample ‘features’. Results show that the developed method of extracting pore network structure is applicable to ideal and natural porous media systems. The impact of resolution on the quantification of the network structure properties varies in its significance based on feature size of the system and the properties being calculated. Therefore, a thorough resolution sensitivity analysis should be carried out to determine the degree of error associated with a system imaged at a given resolution.

Porosity–permeability properties generated with a new 2-parameter 3D hydraulic pore-network model for consolidated and unconsolidated porous media

A new method is presented to construct a simple and general site bond correlated 3D HYdraulic POre Network model (HYPON) of hydraulic behavior of porous media for a wide range of permeability and porosity. Pore scale microstructure in this model is captured through simple power functions of Beti's influence lines that fix both the location and the size of throat (the narrowest section of bond) by relating the important elements of microstructure such as coordination number, porebody sizes and pore wall curvature. The new element in pore-network architecture is thus, the location of throat, which is important for smooth hydraulic transitions during steady state flow conditions. Despite the reduced number of parameters in comparison with other pore-network models, the morphological characteristics of HYPON compare well to those of the process-based predictive models in literature, and these characteristics are sensitive to the variance of porebody sizes rather than to the used type of the porebody size distributions. Processes such as diagenesis and dissolution are captured implicitly through the pore wall curvature parameter. Different combinations of porosity and permeability relations are obtained if the bond curvature and porebody sizes are varied. These relations reveal that effects of diagenesis and dissolution on the permeability may be ignored as they are secondary to effects on porosity.

A Mixed-Percolation Model of Capillary Hysteresis and Entrapment in Mercury Porosimetry

A wealth of information about the structure of porous materials is contained in the experimental data of mercury intrusion and retraction obtained from mercury porosimetry. Proper interpretation of such data requires the use of a model capable of describing the phenomena of capillary pressure hysteresis and mercury entrapment. This work advances the concept of mixed-percolation on cubic lattices representing pore bodies, connected through pore throats, as a general model for the study of hysteresis and entrapment observed in the course of mercury retraction in porosimetry. The dominant phenomena of local capillary instability (snap-off of mercury threads, piston-type intrusion and retraction), affecting the movement of mercury-air interfaces in pore throats and pore bodies, are accounted for and related to the macroscopic capillary pressure-saturation behavior by means of computer simulation. Local correlations among pore throat and pore body sizes, as well as microscopic heterogeneities due to spatial correlations among the pore bodies are also accounted for in the model. The simulator is used to study the dependence of mercury porosimetry curves on pore throat and pore body size distributions and spatial correlations, as well as on contact angle. It is shown that mercury retraction can be successfully modeled as the deterministic outcome of the competition between two simultaneously occurring percolation processes, snap-off in pore throats (bond-percolation) and piston-type retraction from pore bodies (site-percolation).

Network modelling of pore structure and transport properties of porous media

A methodology is presented for the simultaneous prediction of absolute permeabilities, formation resistivity factors and drainage capillary pressure curves of sandstones by employing a network model of pore structure based on bond-correlated site percolation concepts. The model is a regular cubic lattice consisting of pore throats and pore bodies, having respective pore size distributions. Information about the pore structure, obtained from mercury porosimetry and photomicrographic analysis, is utilized to select the pore throat and pore body size distributions in a manner such that the resulting model (i) matches the porosity of the medium and (ii) satisfactorily simulates the drainage capillary pressure curve of the porous medium under consideration. Assumptions made about the cross-sectional shape of the pore throats and their effect on the network model predictions are discussed. Details of the methodology used in the simulation of transport properties with microscopic pore structure parameters are also presented and discussed. The problem of fluid and electric current flow through the simulated porous medium is reduced to an electric analogue-linear network problem and is numerically solved using a conjugate gradients method for computing the absolute permeability and the formation resistivity factor. Good agreement between the predicted and the measured values is observed for a number of sandstone samples having widely different transport properties.

NETWORK SIMULATION OF RELATIVE PERMEABILITY CURVES USING A BOND CORRELATED-SITE PERCOLATION MODEL OF PORE STRUCTURE

This paper deals with the conductivity and relative conductivity properties of irregular 3-D networks of pores that represent the continua of the oil phase and the aqueous phase respectively, during steady slate two phase flow in porous media. The relative conductivity properties presented, correspond to the saturation history defined by the drainage, imbibition and secondary drainage capillary pressure curves respectively. Use has been made of the pore accessibility history of a 20 × 20 × 20 network and a 10 × 10 × 10 nodes core portion of the network is used to write the flow equations. A set of 1001 linear equations is solved using the Preconditioned Conjugate Gradients Method for the conductivities of the wetting phase and the non-wetting phase respectively, as a function of network saturation and saturation history. The effects of pore throat size distribution and pore body size distribution on relative permeability behaviour has been investigated. Furthermore, the effect of conductivity function q(D...

Mercury porosimetry of ordered sphere compacts: Investigation of intrusion and extrusion pore size distributions

Intrusion—extrusion hysteresis in mercury porosimetry is thought to be caused either by mercury contact angle hysteresis or by the domination of extrusion by pore bodies and intrusion by throats to the pore network. Mostly, only the information obtained during the intrusion of mercury has been used in the pore structure characterization of materials via mercury porosimetry. The use of the data obtained during extrusion has been the subject of several recent studies in an attempt to reach a more complete picture of pore structure. In this work, the possible use of both intrusion and extrusion for pore structure characterization have been investigated. Submicron monosize spherical particles of silica and yttrium hydroxycarbonate were synthesized and ordered compacts of these powders have been prepared. Mercury porosimetry tests on these high-density compacts (typically 68 – 70% of sphere density) have shown the presence of two pore peaks for intrusion and extrusion with the exception of one compact. Comparisons of intrusion pore sizes with the theoretical sizes of the constrictions for ordered sphere packings have shown reasonable agreements. Similar comparisons between the sizes of cavities in sphere packings and the extrusion pore sizes did not show the same agreement. Results for one sample did not show a distinct extrusion pore size even at very large pore sizes, most probably due to the domination of mercury extrusion by very few large pores present in the sample. For all other samples, the extrusion pore sizes were close to the actual sphere size and the extrusion was most probably dominated by a few vacant sphere sites in the ] ordered structures. The results of this work have shown that the possibility of using extrusion data for pore body size distribution determination is in serious doubt. The presence of very few larger pores in the porous body may dominate the whole extrusion process and can cause the extraction of inaccurate pore size information from the extrusion data.