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Behzad Ghanbarian - One of the best experts on this subject based on the ideXlab platform.
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Theoretical power-law relationship between permeability and Formation Factor
Journal of Petroleum Science and Engineering, 2021Co-Authors: Behzad Ghanbarian, Frank MaleAbstract:Abstract Permeability k and Formation Factor F are important petrophysical properties that have broad applications to reservoir engineering. Although well-log analysis has advanced reservoir characterizations, direct measurement of k is still not available. Accordingly, resistivity logs and more particularly Formation Factor have been frequently used to estimate k. In this study, we present a theoretical framework to relate k to F. We use power-law scaling from continuum percolation theory to develop a theoretic relationship between k and F, which is similar in form to a published power-law equation with empirical coefficients. Our result gives a physical interpretation to this empirical relationship. We also compare power-law scaling laws from percolation theory with data derived from experimental measurements and numerical simulations in the literature. Using the Curve Fitting toolbox of MATLAB, the parameters of the power-law equations are determined, and the significance of the non-universal power laws are discussed.
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Formation Factor in Bentheimer and Fontainebleau sandstones: Theory compared with pore-scale numerical simulations
Advances in Water Resources, 2017Co-Authors: Behzad Ghanbarian, Carl Fredrik BergAbstract:Abstract Accurate quantification of Formation resistivity Factor F (also called Formation Factor) provides useful insight into connectivity and pore space topology in fully saturated porous media. In particular the Formation Factor has been extensively used to estimate permeability in reservoir rocks. One of the widely applied models to estimate F is Archie's law ( F = ϕ − m in which ϕ is total porosity and m is cementation exponent) that is known to be valid in rocks with negligible clay content, such as clean sandstones. In this study we compare Formation Factors determined by percolation and effective-medium theories as well as Archie's law with numerical simulations of electrical resistivity on digital rock models. These digital models represent Bentheimer and Fontainebleau sandstones and are derived either by reconstruction or directly from micro-tomographic images. Results show that the universal quadratic power law from percolation theory accurately estimates the calculated Formation Factor values in network models over the entire range of porosity. However, it crosses over to the linear scaling from the effective-medium approximation at the porosity of 0.75 in grid models. We also show that the effect of critical porosity, disregarded in Archie's law, is nontrivial, and the Archie model inaccurately estimates the Formation Factor in low-porosity homogeneous sandstones.
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universal scaling of the Formation Factor in clays example from the nankai trough
Journal of Geophysical Research, 2015Co-Authors: Hugh Daigle, Behzad Ghanbarian, Pierre Henry, Marianne ConinAbstract:Electrical conductivity is a fundamental characteristic describing how strongly a network opposes flow of electrical current. In fully water-saturated porous media the conductivity, represented by the Formation Factor, is mainly controlled by porosity, connectivity of the conducting phases, and the tortuosity of electrical current paths. Previous work has shown that universal scaling derived from percolation and effective medium theories accurately describes the relationship between Formation Factor and porosity when the percolation threshold is taken account, as well as the porosity value at which the scaling switches from percolation theory to effective medium theory. We determined the Formation Factor in clay-rich sediments based on cation exchange capacity measurements on samples from five scientific ocean drilling sites in the Nankai Trough. We then compared the results to predictions from universal scaling after determining the volume of clay-bound water and the percolation threshold. We found that the previously reported universal scaling relations hold in these clay-rich sediments once the corrections are made for the clay-bound water, and that percolation scaling appears to be valid over the entire range of observed porosities, probably due to relatively broad pore size distributions or low pore system connectivity. Our results show that universal scaling can be applied to describe the porosity dependence of the Formation Factor in clay-rich sediments when appropriate corrections are made for the presence of clay-bound water.
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universal scaling of the Formation Factor in porous media derived by combining percolation and effective medium theories
Geophysical Research Letters, 2014Co-Authors: Behzad Ghanbarian, A G Hunt, Robert P Ewing, Thomas E SkinnerAbstract:The porosity dependence of the Formation Factor for geologic media is examined from the perspective of universal scaling laws from percolation and effective medium theories. Over much of the range of observed porosity, the expected percolation scaling is observed, but the values of the numerical preFactor do not conform to the simple predictions from percolation theory. Combining effective medium and percolation theories produces a numerical preFactor whose value depends on both the threshold porosity and the porosity above which the Formation Factor crosses from percolation to effective medium scaling. This change allows extraction of a numerical value of the preFactor, which is reasonably close to experimental values. Subsequent evaluation of the porosity dependence of the Formation Factor shows that difficulties in prior comparisons of theory and experiment are largely removed when percolation scaling is allowed to transition to effective medium scaling far above the percolation threshold.
A. Revil - One of the best experts on this subject based on the ideXlab platform.
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Diffusion of ionic tracers in the Callovo-Oxfordian clay-rock using the Donnan equilibrium model and the Formation Factor.
Geochimica et Cosmochimica Acta, 2009Co-Authors: D. Jougnot, A. Revil, Philippe LeroyAbstract:Abstract The transient diffusion of cationic and anionic tracers through clay-rocks is usually modeled with parameters like porosity, tortuosity (and/or constrictivity), sorption coefficients, and anionic exclusion. Recently, a new pore scale model has been developed by Revil and Linde [Revil A. and Linde N. (2006) Chemico-electromechanical coupling in microporous media. J. Colloid Interface Sci. 302, 682–694]. This model is based on a volume-averaging approach of the Nernst–Planck equation. The influence of the electrical diffuse layer is accounted for by a generalized Donnan equilibrium model through the whole connected pore space that is valid for a multicomponent electrolyte. This new model can be used to determine the composition of the pore water of the Callovo-Oxfordian clay-rock, the osmotic efficiency of bentonite as a function of salinity, the osmotic pressure, and the streaming potential coupling coefficient of clay-rocks. This pore scale model is used here to model the transient diffusion of ionic tracers (22Na+, 36Cl−, and 35 SO 4 2 - ) through the Callovo-Oxfordian clay-rock. Speciation of SO 4 2 - shows that ∼1/3 of the SO4 is tied-up in different complexes. Some of these complexes are neutral and are therefore only influence by the tortuosity of the pore space. Using experimental data from the literature, we show that all the parameters required to model the flux of ionic tracers (especially the mean electrical potential of the pore space and the Formation Factor) are in agreement with independent evaluations of these parameters using the osmotic pressure determined from in situ pressure measurements and HTO diffusion experiments.
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Thermal conductivity of unsaturated clay-rocks
Hydrology and Earth System Sciences Discussions, 2008Co-Authors: D. Jougnot, A. RevilAbstract:Abstract. The thermal conductivity of porous materials can be related to the electrical conductivity and therefore electrical resistivity tomography can be used to map the thermal conductivity of porous rocks. In this paper, a relationship is developed to connect the thermal conductivity of unsaturated clay-rocks to the thermal conductivity of the different phases of the porous composite, a textural parameter called the thermal Formation Factor, and the tortuosity of the water phase. The thermal Formation Factor is related to the electrical Formation Factor and to the first Archie's first exponent m. The tortuosity of the water phase is related to the second Archie's exponent n and to the relative saturation of the water phase. A very good agreement is obtained between the new model and thermal conductivity measurements of packs of glass beads and cores of the Callovo-Oxfordian argillite at different saturations of the water phase. Anisotropy of the effective thermal conductivity is mainly due to the anisotropy of the thermal conductivity of the solid phase.
Richard D. Jarrard - One of the best experts on this subject based on the ideXlab platform.
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Porosity‐Formation Factor and porosity‐velocity relationships in Barbados prism
Journal of Geophysical Research, 1999Co-Authors: Stephanie N. Erickson, Richard D. JarrardAbstract:Ocean Drilling Program Leg 171A collected logging while drilling (LWD) data to investigate the porosity and velocity structure of Barbados accretionary complex. Porosity and velocity measurements were needed for interpretation of prism dynamics. However, the LWD tool string did not measure velocity, and previous velocity data from Barbados prism are scarce and generally of low quality. Furthermore, most density-based porosities are subject to errors associated with variations in smectite content. To determine porosities more accurately, we use smectite-corrected, density-based porosities to calibrate a porosity-Formation Factor (FF) transform, then calculate porosities from resistivity logs. We used cation exchange capacity (CEC) measurements and LWD logs to evaluate the possibility that resistivity is affected by clay conduction. The CEC data warn of potential clay conduction, especially in smectite-rich zones, but LWD data indicate that clay conduction is minor in these high-porosity sediments. Instead, tortuosity is the secondary control of FF, after porosity. By comparing resistivity-based porosities to velocities from vertical seismic profiles, we determine a porosity-velocity transform applicable to Barbados. We then use this transform to calculate velocity logs from resistivity-based porosity logs.
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Porosity/Formation‐Factor relationships for high‐porosity siliciclastic sediments from Amazon Fan
Geophysical Research Letters, 1998Co-Authors: Stephanie N. Erickson, Richard D. JarrardAbstract:The electrical resistivity of siliciclastic rocks is a function both of pore-fluid resistivity and of Formation Factor (FF), an intrinsic rock property. For low-porosity rocks, FF depends on clay conduction and porosity. In contrast, we find that FF of high-porosity sediments (fractional porosities of 0.3–0.6) from Amazon Fan is controlled primarily by porosity and pore geometry; clay conduction is a minor effect. Porosity vs. Formation Factor (FF) plots for Amazon Fan well logs demonstrate two distinct trends which are dependent on the amount of shale present. Muds, with more than about 0.4 shale fraction, follow a trend that increases to much higher FF as porosity decreases, compared to sands and slightly muddy sands. This separation is of opposite sign to the separation between low-porosity sandstones and shales attributable to clay conduction. We conclude that in high-porosity muds, presence of clays reduces Formation conductivity by increasing the tortuosity of pores.
Ivars Neretnieks - One of the best experts on this subject based on the ideXlab platform.
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Formation Factor logging by electrical methods. Comparison of Formation Factor logs obtained in situ and in the laboratory.
Journal of contaminant hydrology, 2003Co-Authors: Martin Löfgren, Ivars NeretnieksAbstract:In this paper, a new in situ method for obtaining the Formation Factor, which is essential for the matrix diffusion, is described and tested in intrusive igneous rock. The method is based on electrical resistivity measurements in rock where the pore water and rock resistivities are essential parameters. The method is based on electromigration instead of diffusion as in traditional diffusion experiments. In previous works, quantitative Formation Factors of rock have been obtained by electrical methods in the laboratory. Here, a similar approach is used in situ. An in situ logging campaign was performed by SKB during 2000 in the 1700-m-deep borehole KLX02 in Laxemar, Sweden. The rock resistivity was measured with the slimhole Dual Laterolog from Antares. The groundwater resistivity was measured with the Difference Flow Meter from Posiva. A Formation Factor log was obtained with the maximum vertical resolution of 10 cm. In order to validate the log, 100 rock samples were taken from the bore core, and a Formation Factor log was obtained by using electrical methods in the laboratory. Both direct current (DC) and alternating current (AC) were used. The measurements on the core confirmed that the in situ log was quantitative, but with a possible systematic error. The in situ Formation Factors were on average about 1/3 to 1/5 of the laboratory Formation Factors, depending on depth.
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Formation Factor measurements in granite in the laboratory – Comparison of through diffusion and electromigration techniques.
MRS Proceedings, 2002Co-Authors: Martin Löfgren, Ivars NeretnieksAbstract:Traditionally the effective diffusivity in and the Formation Factor of intrusive igneous rock have been measured in the laboratory by through diffusion (TD) experiments, which are very time consuming in larger samples with low porosity. In previous work alternating current (AC) has been used to measure the Formation Factor directly in large samples. In this paper direct current is used to actually transport the tracers through the rock sample in so called through electromigration (TEM) experiments. In these experiments electoosmosis has to be corrected for. The experimental time is reduced substantially when adding an electromigratory flux to the diffusive flux. TD, TEM and AC experiments were performed on a 15 mm thick unweathered granite sample from Laxemar, Sweden. The tracers uranin and iodide were used. The Formation Factor measured with the three methods varied between 1.2·10 -4 - 2.87·10 -4 .
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Formation Factor determinations by in situ resistivity logging
MRS Proceedings, 2000Co-Authors: Martin Löfgren, Y Ohlsson, Ivars NeretnieksAbstract:Matrix diffusion in bedrock is traditionally studied by laboratory liquid diffusion experiments, which are time consuming and expensive. A new way of studying matrix diffusion is to measure the electrical resistivity of the rock. This could be done either in laboratories or in-situ . A fast method of obtaining a Formation Factor log, later used in matrix diffusion calculations, for an entire borehole is proposed. It is a standard procedure in geophysical well logging to measure rock resistivity and there are well-developed tools for this in the oil industry. The SKB, Sweden, uses boreholes with a small diameter (56 mm) and this reduces the options in choosing resistivity tools. Therefore they have so far relied on the Normal log that only gives quantitative measurements in special cases, after corrections are made. Modern tools, such as the slimhole Dual-Laterolog, are accurate with a high vertical resolution. The pore fluid resistivity is required when obtaining a Formation Factor log. In previous work the borehole fluid resistivity has been used. A new method measures the resistivity in groundwater from local fractures. These values seem more appropriate to use as new in-situ measurements show that there may be local groundwater resistivity differences. A preliminary study shows that the conductivity could be obtained in saline Swedish groundwater by measuring the chloride concentration only. Anomalies in the Formation Factor log have to be sorted out by using supporting core logging and non-electrical in-situ methods.
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A study of rock matrix diffusion properties by electrical conductivity measurements
MRS Proceedings, 1999Co-Authors: Y Ohlsson, Ivars NeretnieksAbstract:Traditional rock matrix diffusion experiments on crystalline rock are very time consuming due to the low porosity and extensive analysis requirements. Electrical conductivity measurements are, on the other hand, very fast and larger samples can be used than are practical in ordinary diffusion experiments. The effective diffusivity of a non-charged molecule is readily evaluated from the measurements, and influences from surface conductivity on diffusion of cations can be studied. A large number of samples of varying thickness can be measured within a short period, and the changes in transport properties with position in a rock core can be examined. In this study the Formation Factor of a large number of Aespoe diorite samples is determined by electrical conductivity measurements. The Formation Factor is a geometric Factor defined as the ratio between the effective diffusivity of a non-charged molecule, to that of the same molecule in free liquid. The variation of this Factor with position among a borecore and with sample length, and its coupling to the porosity of the sample is studied. Also the surface conductivity is studied. This was determined as the residual conductivity after leaching of the pore solution ions. The Formation Factor of most of the samplesmore » is in the range 1E-5 to 1E-4, with a mean value of about 5E-5. Even large samples (4--13 cm) give such values. The Formation Factor increases with increasing porosity and the change in both Formation Factor and porosity with position in the borecore can be large, even for samples close to each other. The surface conductivity increases with increasing Formation Factor for the various samples but the influence on the pore diffusion seems to be higher for samples of lower Formation Factor. This suggests that the relation between the pore surface area and the pore volume is larger for samples of low Formation Factor.« less
Willem Van Tilburg - One of the best experts on this subject based on the ideXlab platform.
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Religious denomination as a symptom-Formation Factor of depression in older Dutch citizens.
International journal of geriatric psychiatry, 2000Co-Authors: Arjan W. Braam, Caroline M. Sonnenberg, Aartjan T.f. Beekman, Dorly J. H. Deeg, Willem Van TilburgAbstract:Objectives. The type of symptoms in depression is likely to be influenced by cultural environment. As religion represents an important cultural resource for older adults, it is hypothesised that religious denomination represents a symptom-Formation Factor of depression in the older generation. Focusing on older Dutch citizens, it is expected that depressed Calvinists report: (1) less depressed affect, (2) more vegetative symptoms, and (3) more guilt feelings, than Roman Catholics and non-church members. Methods and procedures. The Center for Epidemiologic Studies Depression Scale (CES-D) was used to distinguish depressed (N = 395) and non-depressed (N = 2333) older adults, and to assess depressive symptom-profiles. The Diagnostic Interview Schedule (DIS) was used to assess major depressive episodes and criterion-symptoms of depression. Results. Depressed Calvinists, especially males, had higher scores on the vegetative CES-D subscale. The same was found for non-church members with Calvinist parents. Among those who have a major depressive episode in later life (N = 84), support was found for all hypotheses. Feelings of guilt were also more prevalent among Roman Catholics. Conclusions. Religious denomination modified the type of symptoms in late-life depression. As a Calvinist background was associated with less depressive affect and more inhibition, there is a risk of underdiagnosis of major depression in older Calvinists in the Netherlands. Copyright (C) 2000 John Wiley and Sons, Ltd.