Pore Connectivity Factor Research Articles

Bayesian linearized inversion for petrophysical and pore-connectivity parameters with seismic elastic data of carbonate reservoirs

Abstract Carbonate reservoirs are important targets for promoting the oil and gas reserve exploration and production in China. However, such reservoirs usually contain the developed complex pore structures, which heavily affect the precision in seismic prediction of petrophysical parameters. As one of the most important parameters to characterize reservoir rock, pore-related parameters can not only describe the pore structure, but also be used to evaluate the oil/gas bearing capabilities of potential reservoirs. The conventional rock-physics models (e.g. Gassmann's model) are formulated assuming fully-connected pores, which is unable to accurately capture the geometrical complexity in real rocks. In order to characterize the influences of multiple pores on the elastic properties, this work presents a rock-physics modelling method for carbonates, wherein the percentage composition of connected pores is equivalently quantified as the pore-connectivity factor. The method treats the pore-connectivity factor as an objective variable to characterize the spatial variations of pore structure. Specifically, the method combines the differential equivalent medium theory and Gassmann's model, and derives a linearized forward operator to quantitatively link porosity, water saturation, and pore-connectivity factor to seismic elastic parameters. According to the Bayesian linear inverse theory, the simultaneous estimation of petrophysical and pore-connectivity parameters is achieved. To characterize the statistical variations with multiple lithofacies, the Gaussian mixture model is employed to quantify the prior distribution of the objective variables. The posterior distribution of the objective variables is analytically expressed with the linearized forward operator. Numerical experiments show that the accuracy of the proposed method in predicting elastic parameters is improved. Compared with the conventional Xu-White model and the varying pore aspect ratio method, the accuracy of predicted P-wave velocity increases by 10.29% and 1.33%, respectively, and the predicted S-wave velocity increases by 6.44% and 0.03%, in terms of correlation coefficient. The application to the field data validates the effectiveness of the method, wherein the porosity and water saturation results help indicating the spatial distribution of potential reservoirs.

GAS TRANSPORT PARAMETERS OF RECYCLED CONCRETE AND CLAY BRICK AGGREGATE BLENDED WITH AUTOCLAVED AERATED CONCRETE GRAINS

Gas diffusivity (Dp/D0: the ratio of gas diffusion coefficient, Dp, to gas diffusion in free air, D0) and air permeability (ka), and their variations with air-filled porosity (e) play key roles in surface gas exchange and vapor transport in permeable pavement and water-retentive pavement systems. This study carried out a series of laboratory measurements of Dp/D0 and ka for graded recycled concrete (RC) and clay brick (RCB) aggregates, and RC and RCB blended with autoclaved aerated concrete (AAC) grains at proportions of 20% and 40%. The tested samples were saturated after compaction, and the Dp/D0 and ka were measured during the drying process from saturation to air-dry. Results showed that Dp/D0 and ka of graded RC and RCB decreased most with increased proportions of AAC grains; in particular, the effect of AAC blending on Dp/D0(e) relationships decreased. For most tested samples, pore-connectivity factor and diffusion-based tortuosity (T) gradually increased with drying, and T values were decreased slightly by blending with AAC grains. Equivalent pore diameter for gas flow values of graded RC and RCB showed a clear decrease with drying; on the other hand, those of AAC blended RC and RCB did not depend on e. Combining previous models and fitted T(e) relations for tested samples, the Dp/D0(e) relations and MLWs for ka(e) captured well the values of graded RC and RCB blended with AAC grains, implying that the previous gas transport parameter models would be useful for quick assessment of roadbed materials.

An alternative admixture to reduce sorptivity of alkali-activated slag cement by optimising pore structure and introducing hydrophobic film

The high water absorption rate of alkali-activated slag (AAS) cement, which causes concerns to designers and constructors as “long-term” durability, was addressed using an alternative admixture, calcium stearate (CaSt). The macro- and micro-performance of AAS cement with two levels of CaSt dosage (4 wt%, 8 wt% of slag) were characterised under the water to binder ratio (W/B) ranging from 0.35 to 0.45 and benchmarked against corresponding Portland cement (PC) samples by sorptivity along with compressive strength, porosity, electrical resistivity, pore connectivity, pore size distribution and pore geometries. The interpretation of results showed that CaSt played an instrumental role in pore structure features of AAS and the use of CaSt could significantly reduce its sorptivity, even lower than that of the corresponding PC samples. It is also found that the recommended usage of CaSt is 4% of slag, beyond which no significant variation in sorptivity can be detected. The performance improvement was caused by two main mechanisms, optimising the pore structure (more entrained pores, less pore connectivity factor and less microcracks) and introduce of the hydrophobic film on the pore surface. One limitation of using CaSt was noted as well. That is, the strength development of AAS can be affected and it can be avoided through modifying mix proportions according to practical requirements. Therefore, CaSt can be used as a chemical admixture for AAS to solve the concern on its high sorptivity behaviour.

Directional-Permeability Assessment in Formations With Complex Pore Geometry With a New Nuclear-Magnetic-Resonance-Based Permeability Model

Summary This paper proposes a new method for directional-permeability assessment with nuclear-magnetic-resonance (NMR) measurements. Conventional techniques for permeability assessment from NMR measurements include empirical correlations such as SDR (Schlumberger-Doll-Research) and Coates models. However, carbonate rocks are known for lack of good correlations between pore-body-size and pore-throat-size, which makes it challenging and often unreliable to estimate permeability from NMR T2 (spin-spin relaxation time) distribution in carbonate formations with complex pore structure. It also was proposed that conventional permeability models can be improved by incorporating an estimated pore-connectivity factor. However, none of the previously introduced techniques reflects the anisotropic characteristics of rock permeability. The new NMR-based directional-permeability model, introduced in this paper, incorporates a directional pore-connectivity factor into a conventional NMR-based permeability model. We introduce two approaches to quantify the directional pore-network connectivity of rock samples with pore-scale images. The first approach calculates directional pore connectivity in 3D pore-scale images with a topological technique. The second approach combines image analysis and electrical formation factor. The new NMR-based permeability model enables assessment of rock permeability in any desired direction. We successfully calibrated and tested the introduced NMR-based permeability model on carbonate, sandstone, and sandpack samples with complex pore geometry or anisotropic permeability. The anisotropic permeability used for calibration and test purposes was obtained by the lattice Boltzmann method (LBM) simulations on microcomputed tomography (CT) images of rock samples. The comparison between the permeability estimates with our new NMR model and conventional NMR models (e.g., SDR and Coates models) demonstrated that the NMR-based directional-permeability model significantly improves assessment of rock permeability, by reflecting rock's anisotropic characteristics and minimizing calibration efforts. The outcomes of this research can significantly improve permeability assessment in complex carbonate reservoirs and anisotropic sandstone reservoirs, and can be extended further to organic-rich mudrock formations.

Study of the pore structure of the lightweight concrete block with lapilli as an aggregate to predict the liquid permeability by dielectric spectroscopy

Lightweight concrete with basaltic lapilli as an aggregate is commonly employed in the Canary Islands to manufacture prefabricated blocks. The high porosity of this aggregate provides blocks with low density and good acoustic and thermal insulating properties. However, these properties are the source of moisture condensation inside the block, compromising the building comfort. For these reasons, the pore network by means of dielectric spectroscopy, mercury intrusion porosimetry and hydraulic conductivity is analyzed. The electrical conductivity of the concrete block is measured and used to describe the porosity and pore connectivity factor using a modified form of Bergman equation that considers two conducting phases. Besides, hydraulic conductivity is also measured by a falling head permeability cell, finding a correlation between the liquid permeability and its predicted value by the Katz–Thompson equation. From these studies the measured parameters (porosity, tortuosity, hydraulic and electrical conductivity) are related to the pore network parameters (connectivity and permeability).

Variable Pore Connectivity Model Linking Gas Diffusivity and Air‐Phase Tortuosity to Soil Matric Potential

Soil‐gas diffusivity (Dp/Do) and its dependency on soil matric potential (ψ) is important when taking regulative measures (based on accurate predictions) for climate gas emissions and also risk‐mitigating measures (based on upper‐limit predictions) of gaseous‐phase contaminant emissions. Useful information on soil functional pore structure, e.g., pore network tortuosity and connectivity, can also be revealed from Dp/Do–ψ relations. Based on Dp/Do measurements in a wide range of soil types across geographically remote vadose zone profiles, this study analyzed pore connectivity for the development of a variable pore connectivity factor, X, as a function of soil matric potential, expressed as pF (=log |−ψ|), for pF values ranging from 1.0 to 3.5. The new model takes the form of X = X* (F/F*)A with F = 1 + pF−1, where X* is the pore network tortuosity at reference F (F*) and A is a model parameter that accounts for water blockage. The X–pF relation can be linked to drained pore size to explain the lower probability of the larger but far fewer air‐filled pores at lower pF effectively interconnecting and promoting gas diffusion. The model with X* = 2 and A = 0.5 proved promising for generalizing Dp/Do predictions across soils of wide geographic contrast and yielded results comparable to those from widely used predictive models. The X–pF model additionally proved valuable for differentiating between soils (providing a unique soil structural fingerprint for each soil layer) and also between the inter‐ and intraaggregate pore regions of aggregated soils. We further suggest that the new model with parameter values of X* = 1.7 and A = 0 may be used for upper limit Dp/Do predictions in risk assessments of, e.g., fluxes of toxic volatile organics from soil to indoor air at polluted soil sites.

Characterizing pore volume, sizes, and connectivity in pervious concretes for permeability prediction

Methods of characterizing the pore structure features in a cement-based material with open pore structure, called pervious concrete, and the use of these pore structure features in permeability prediction is the focus of this paper. Porosity of several pervious concrete mixtures is determined using volumetric and area fraction methods whereas stereology and mathematical morphology based methods are used to extract the characteristic pore sizes. The characteristic pore sizes determined using several methods relate well to each other. A Weibull probability distribution function is found to adequately model the pore size distribution in pervious concretes. The values of porosity and the morphologically determined pore sizes, along with the pore phase connectivity represented using an electrical conductivity ratio, are used in a Katz–Thompson type relationship to predict the permeability of pervious concretes. It is shown in this paper that maximization of water transport behavior of pervious concretes is best achieved by increasing the pore connectivity factor.

Hierarchical, Bimodal Model for Gas Diffusivity in Aggregated, Unsaturated Soils

The soil gas diffusion coefficient (Dp) and its dependency on soil air content, ε, and tortuosity–connectivity of the air‐filled pore networks control the transport and fate of gaseous‐phase contaminants in variably saturated soil. The bimodality in pore size distribution of structured soil often yields a variation of Dp with ε in the intraaggregate pore region that is distinctly different from that in the interaggregate region. Data imply a highly nonlinear behavior of soil gas diffusivity, Dp(ε)/Do (where Do is the gas diffusion coefficient in free air), in the interaggregate region of aggregated soils similar to that of structureless soils with a unimodal pore size distribution, probably due to diffusion‐limiting effects by connected water films at low ε. In contrast, for the intraaggregate region, we show that the impedance factor F* (= Dp/εDo) and tortuosity factor T [= (1/F*)1/2] are approximately constant for most soil media. We suggest a typically well‐defined separation between the two pore regions at the minimum for the pore connectivity factor X* [= log(Dp/Do)/log(ε)], at which point the interaggregate pores are devoid of water while the intraaggregate pore region is water saturated. Based on this, a hierarchical two independent region (TIR) Dp/Do model was developed by applying a cumulative series of Buckingham–Currie power‐law functions, FεX A nonlinear, water‐content‐dependent expression for F best described the measured Dp/Do in the interaggregate region, while constant F (around 0.5) and X (around 1) generally sufficed for the intraaggregate region. The TIR model better predicted gas diffusivities for both aggregate fractions and highly structured soils across the entire range of moisture conditions with RMSE reduced by two to five times compared with traditional predictive Dp(ε)/Do models.

Interfacial area based variable tortuosity‐connectivity for unsaturated media: A comparison using Miller–Miller scaling and Arya–Paris model

The tortuosity and/or pore connectivity factor, τ, in unsaturated media is typically represented by Seɛ, where Se = effective saturation. The exponent ɛ is treated as an optimized parameter with typical values of 0.5 and 2, respectively, for Mualem and Burdine‐type models. In this study, the tortuosity and/or connectivity term in Mualem and Burdine models is replaced by a normalized ratio, τ(Se = 1) / τ(Se); τ(Se) is the ratio of air–water interfacial area for a soil sample to the interfacial area for the corresponding idealized capillary bundle. The interfacial area for a soil sample is based on Leverett's (1941) thermodynamic considerations and is obtained by integrating the area under the laboratory‐measured moisture retention curve. In addition to Miller–Miller scaling used in an earlier work, the idealized medium retention curve in this study is based on translation via the Arya–Paris (AP) model of the particle size distribution data for a soil sample into its pore size distribution. The saturation‐dependent, variable tortuosity concept is tested for 24 fine‐textured samples in addition to 22 coarse‐textured samples considered in the earlier study. For both fine‐ and coarse‐textured samples, the interfacial area based variable τ(Se) formulation provides at least as good a fit of the measured and predicted unsaturated hydraulic conductivities, K, as a function of moisture content, θ, as the standard Brooks–Corey–Burdine and van Genuchten–Mualem models. Specifically, for the fine‐textured samples, Brooks–Corey–Burdine K(θ) predictions based on the variable τ(Se) model compare well with K(θ) measurements, with an r2 of 0.86, a regression slope of 1.02, and a relatively low residual mean squared deviation of 1.13. Unlike the Burdine (Se2) and Mualem (Se0.5) empirical models, the τ(Se)‐based model parameters have explicit physical significance because the interfacial area in unsaturated media can be measured using interfacial tracers. The use of the AP model to represent the idealized medium retention data suggests its broader applicability for both fine‐ and coarse‐textured media.

Variable Pore Connectivity Factor Model for Gas Diffusivity in Unsaturated, Aggregated Soil

The soil gas diffusion coefficient (Dp) and its variations with soil air content (ε) and soil water matric potential (ψ) control vadose zone transport and emissions of volatile organic chemicals and greenhouse gases. This study revisits the 1904 Buckingham power‐law model where Dp is proportional to εX, with X characterizing the tortuosity and connectivity of air‐filled pore space. One hundred years later, most models linking Dp(ε) to soil water retention and pore size distribution still assume that the pore connectivity factor, X, is a constant for a given soil. We show that X varies strongly with both ε and matric potential [given as pF = log(−ψ, cm H2O)] for individual soils ranging from undisturbed sand to aggregated volcanic ash soils (Andisols). For Andisols with bimodal pore size distribution, the X–pF function appears symmetrical. The minimum X value is typically around 2 and was observed close to ψ of −1000 cm H2O (pF 3) when interaggregate voids are drained. To link Dp with bimodal pore size distribution, we coupled a two‐region van Genuchten soil water retention model with the Buckingham Dp(ε) model, assuming X to vary symmetrically around a given pF. The coupled model well described Dp as a function of both ε and ψ for both repacked and undisturbed Andisols and for other soil types. By merely using average values of the three constants in the proposed symmetrical X–pF expression, predictions of Dp were better than with traditional models.

Electrical conductivity based characterization of plain and coarse glass powder modified cement pastes

This paper describes the use of electrical conductivity to characterize plain and coarse glass powder modified cement pastes. It is observed that the glass powder addition facilitates improved hydration of the cement grains. For the proportions investigated in this study, and the particle size of glass powder, this advantage is negated by the reduced amount of hydration products, i.e., the dilution effect. The variation of electrical conductivity and its derivative with time can be related to the various phases in the microstructural development of the paste. It is observed from the time derivative of conductivity plots that the addition of glass powder results only in minor changes in the setting time of the pastes. Higher the glass powder content, higher the normalized conductivity (ratio of conductivity at a certain glass powder content to that of plain paste) at very early times, and then it falls to a value closer to or less than 1.0 at later times. A parallel model is used to represent effective conductivity as a function of the pore solution conductivity, porosity, and pore connectivity factor. The pore solution conductivity increases with increase in glass powder content. The porosity of the pastes reduces with increase in glass powder content at early ages and increases at later ages. A reduced pore connectivity factor is observed for pastes with higher glass powder content at later times. However, this does not imply increased volume of hydration products as is commonly interpreted for normal pastes, but the electrical conduction pathways are made more tortuous by the relatively large volume of un-reacted filler material in the pore structure.

Characterizing Enhanced Porosity Concrete using electrical impedance to predict acoustic and hydraulic performance

Enhanced Porosity Concrete (EPC) is manufactured by gap grading coarse aggregates to create interconnected porosity in the system. The porosity and physical features of the pore network are characterized in this paper using Electrical Impedance Spectroscopy (EIS). Porosity alone was found to be an inaccurate indicator of the electrical conductivity of the sample. While several studies have shown that a conventional form of Archie's law can describe porous systems, it was observed that Archie's law did not completely describe the electrical conductivity of the EPC system. Therefore, a modified version of Archie's law was used that incorporated the matrix conductivity, which described the system more accurately than the conventional form. The pore connectivity factor determined using EIS is found to be linearly related to the acoustic absorption of the material. Similarly, conductivity results determined from EIS were used with total porosity to compute the hydraulic connectivity factor. This factor was related to intrinsic permeability calculated from hydraulic conductivity (measured using a falling head permeameter). Based on these studies, it appears that a single electrical impedance test could provide information for the design, quality control/quality assurance, and utilization of EPC.

Development of thermal energy storage concrete

In this paper, a two-step procedure to produce thermal energy storage concrete (TESC) is described. At the first step, thermal energy storage aggregates (TESAs) were made from porous aggregates absorbing phase changing materials (PCMs). At the second step, TESC was produced with a normal mixing method and using TESAs. An adequate amount of PCM can be incorporated into concrete by the two-step procedure. It can be seen experimentally that the energy storage capacity of the TESC was comparable with that of a commercially available PCM. The experimental results showed that the geometrical features of the porous structure of the aggregates had significant effect on their absorbing ability of the PCM. Aggregates with large pore connectivity factor and transport tunnel in boundary part can absorb more PCM. It was also found that the phase changing behavior was affected by the volume fraction of PCM in concrete.

Evaluation of Microporosity, Pore Tortuosity, and Connectivity of Montmorillonite Solids Pillared with LaNiOx Binary Oxide. A Combined Application of the CPSM Model, the αs-Plot Method and a Pore Percolation−Connectivity Model

The present work deals with the comparative application of the CPSM (corrugated pore structure model), the αs plot and the pore connectivity methods for pore structure analysis and especially the detection of microporosity of a category of montmorillonite clays pillared with LaNiOx binary oxide. A quite good agreement between the corresponding results deduced from the three methods was confirmed. The raising of the LaNiOx content caused a change of pore volume, surface area, and microporosity whereas the relevant curves pass through a maximum. The CPSM model, through the simulation of gas sorption hysteresis, enables the evaluation of unified mesomicropore size distributions, pore surface areas, tortuosity factors, τCPSM, and relative microporosities. It is also concluded that pore tortuosity, (τCPSM), is inversely proportional to the pore connectivity factor (c), and the nominal pore length (Ns) (i.e., a CPSM parameter) is proportional to the number of pore lengths (L) (i.e., a parameter of the pore conn...

Analysing problems in describing field and laboratory measured soil hydraulic properties

Accurate in situ determination of unsaturated soil hydraulic properties is often not feasible because of natural variability of most field soils, and because of instrumental limitations. Therefore the soil hydraulic properties are often measured in the laboratory, or derived by computer models using simple standard laboratory methods. This paper analyses problems in describing field hydraulic properties of a Ap horizon of a silty loam, basing on data from different laboratory methods: (i) A standard pressure plate apparatus and (ii) a constant-head permeameter were used to measure the static retention characteristics and the saturated hydraulic conductivity independently. (iii) An instantaneous profile method was applied to measure water retention and conductivity simultanously. Relatively new technics involving “undisturbed” soil samples instrumented with mini tensiometers and Time Domain Reflectometry (TDR) mini probes characterise the experiment. The models by Mualem and van Genuchten (MvG) were used to describe the soil hydraulic functions. The different laboratory results were then compared with the hydraulic field properties measured in instantaneous profile manner. The laboratory method allows a high spatial and temporal resolution; this facilitates an investigation of some of the assumptions made, when fitting the MvG models to hydraulic data. A reasonably good description of the hydraulic data was obtained when setting the residual water content, θ r, to 0 and the pore connectivity factor, l, to 0.5 because θ r and l were not sensitive. However, a poor fit resulted when the saturated water content, θ s, was equated to the porosity, and the saturated hydraulic conductivity, k s to its independently measured value. Values for θ s and k s derived from field measurements were somewhat higher than those obtained from laboratory samples. To demonstrate the influence of the different input data on a water balance, the cumulative drainage from an initially saturated soil column was simulated with different sets of hydraulic parameters estimated from field and laboratory data. Parameters derived from the laboratory results consistently yielded lower predictions of cumulative drainage compared to hydraulic parameters derived from field measurements. The differences were relatively small when an initial water content corresponding to 60 cm suction (field capacity) was used.