Saturation Exponent Research Articles

Effects of Foam Microbubbles on Electrical Resistivity and Capillary Pressure of Partially Saturated Porous Media.

Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas–water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.

Petrophysical evaluation using the geometric factor theory and comparison with archie model

The Archie model is empirical because it is based on curve-fitting methods, while the Geometric Factor Theory (GFT) is a physics-based porosity-conductivity model. Both these are used to compute water saturation (Sw) in simple Archie rocks (clean sandstones). Studies considering Archie's work demonstrated that Archie equation was not applicable to carbonates and shaly sands, and all the scientifically incorrect shaly sand equations were counterproductive modifications of the Archie equation. Nevertheless, instead of replacing Archie equation with some more meaningful equation, researchers tried to improve and modify Archie equation so that it can work in other reservoirs (carbonates and shaly sands) where it was not even applicable. In this paper, the Archie's and Geometric Factor Theory (GFT) equations were applied to the same data sets (well log and core), and the results were compared qualitatively and quantitatively. Outcomes from these approaches are closely similar in some wells; however, they differ in others by 2–3 porosity units. The wells where results differ from the core-derived results, n (saturation exponent) is modified to account for the differences. The log-based Sw values of 0.27 (Well-A), 0.24 (Well-B), 0.38 (Well-F) and 0.45 (Well-G) against core driven 0.27 (Well-A), 0.24 (Well-B), 0.36 (Well-F) and 0.46 (Well-G) show that the GFT driven estimates provide a good match with the core data than the Archie. Additionally, the cross-plots of GFT provide peculiar information about the pore geometry and diagenesis of rocks. It is, therefore, recommended to supplant Archie model with the Geometric Factor Theory model because the latter gives better results and is a physics-based porosity-conductivity model that also has a physical interpretation.

Permeability measurement and discovery of dissociation process of hydrate sediments

The study on the permeability of methane hydrates in fine quartz sands contributes to the accurate prediction of gas/water production and can effectively express the characteristics of fluid migration. In this study, the water effective permeability (kw) of methane hydrates in three fine quartz sands containing various hydrate saturation (SH) were carried out under steady water injection and production. Experimental results indicated that the effect of particle sizes on kw was significant even though the difference in the average particle size of three fine quartz sands was relatively limited. The differential pressure of the hydrate sediments was completely recorded during permeability measurement, and the stabilization and decomposition process of hydrate could be clearly represented by differential pressure. The kw increased rapidly with the decomposition of hydrate and the appearance of flow channel in the hydrate sediments. Hydrate dissociation process was recorded in situ by Cold Field Emission Scanning Electron Microscopy (CFE–SEM), the dissociation of hydrates in pore space was clearly visible, and the hydrates in pore space were first dissociated into many small regions. A new reduction model between water relative permeability (krw) and SH was proposed on the basis of experimental results, and the experimental data fitted well with hydrates occupying pore centers. The effect of particle sizes on krw was eliminated, the Archie saturation exponent n tended to increase with the increase of SH, and n was recommended between 20 and 30.

Storing CO2as solid hydrate in shallow aquifers: Electrical resistivity measurements in hydrate-bearing sandstone

A recent proposed carbon dioxide (CO2) storage scheme suggests solid CO2hydrate formation at the base of the hydrate stability zone to facilitate safe, long-term storage of anthropogenic CO2. These high-density hydrate structures consist of individual CO2molecules confined in cages of hydrogen-bonded water molecules. Solid-state storage of CO2in shallow aquifers can improve the storage capacity greatly compared to supercritical CO2stored at greater depths. Moreover, impermeable hydrate layers directly above a liquid CO2plume will significantly retain unwanted migration of CO2toward the seabed. Thus, a structural trap accompanied by hydrate layers in a zone of favorable kinetics are likely to mitigate the overall risk of CO2leakage from the storage site. Geophysical monitoring of the CO2storage site includes electrical resistivity measurements that relies on empirical data to obtain saturation values. We have estimated the saturation exponent in Archie’s equation,n≈ 2.1 (harmonic mean) for CO2and brine saturated pore network, and for hydrate-bearing seal (SH < 0.4), during the process of storing liquid CO2in Bentheimer sandstone core samples. Our findings support efficient trapping of CO2by sedimentary hydrate formation and show a robust agreement between saturation values derived from PVT data and from modifying Archie’s equation.

Hydrate growth in quartzitic sands and implication of pore fractal characteristics to hydraulic, mechanical, and electrical properties of hydrate-bearing sediments

Gas hydrate pore habits significantly impact the pore-scale structure within hydrate-bearing sediments, and thus, play a central role in the physical property evolution. Characterization and quantification of the effective pore space within hydrate-bearing sediments at different hydrate saturations have not been well offered. This study performs random simulations of hydrate nucleation and growth in quartzitic sands to understand effects of hydrate saturation and hydrate pore habits on fractal characteristics of the effective pore space. Normalized pore-size fractal dimension and normalized maximal pore diameter are characterized and found to decrease with increasing hydrate saturation. In order to predict hydrate saturation dependent pore fractal characteristics, theoretical and empirical models are proposed and further extended to give implications to hydraulic, mechanical, and electrical properties of hydrate-bearing sediments during hydrate dissociation. Implications include that hydrate dissociation facilitates the absolute permeability and the electrical conductivity, and enhances first and then reduces the saturation exponent of Archie's law; hydrate dissociation also lowers the capillary pressure, and this promotes relative permeability to gas but inhibits relative permeability to water even the water saturation remains as a constant; shear strength of unsaturated hydrate-bearing sediments drops down due to the decreasing capillary pressure as hydrate dissociation. These implications all meet with conclusions in previous literatures.

Hydraulic - Electrical Flow Units and Water Saturation Calculation: Dam Formation, South Western Qatar, Arabian Gulf

Hydraulic-electric flow units represent two different concepts with different measuring units. They are frequently used to confirm each other’s for distinguishing the different reservoir flow zones but sometimes give undesirable results. 60 limestone samples were collected from the upper part of the Dam Formation exposed in the Al-Nakhsh area, Southwestern Qatar Peninsula. These samples represent the Upper Dam sediments which are considered as an important aquifer for underground water in its subsurface occurrences in Qatar and nearby areas. Porosity, gas permeability and electrical resistivity were laboratory measured for the collected samples. Saturation exponent (n), cementation exponent(m) and pore throat radius (r35) were calculated for each sample. The vertical profile of gas permeability and pore throat radius (R35) is accomplished. Also, gas-permeability versus porosity is performed. Numerous useful and applicable relationships have been found. The obtained reservoir flow units which are distinguished according to hydraulic flow indicators (RQI and Øz) are only three units. However, the hydraulic-electric cross-plots (i.e. n-R35 and n-FZI) indicate three and four reservoir flow units respectively. In conclusion, the obtained number of reservoir flow units in the study area ranges from 3-4. It means that the hybrid hydraulic-electric combination sometimes shows flow units in concordance with the single type parameter, but occasionally give dissimilar results. An innovative nomograph is constructed according to an empirical equation related to the Dam Formation [1] to estimate the water saturation (SW) in oolitic carbonate facies. The present nomograph is verified by carbonate facies, deltaic distributary channel and barrier bar sandstone. The obtained values of water saturation from the proposed model are acceptable in case of both resistivity ratio ( Rt/Rw) and porosity (Ø) are available.

Work Flow Determines Petrophysical Properties From As-Received Core Samples

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 191476, “As-Received Core Electrical-Properties Tests for Determining Formation Factor (FF) and Resistivity Index (RI),” by Kent Newsham, SPE, and Roland Chemali, SPE, Occidental Oil and Gas, and Ray Hanna, SPE, Robert Lee, and Craig Whitney, Core Laboratories, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed. This paper introduces a new core-analysis work flow for determining resistivity index (RI), formation factor (FF), and other petrophysical properties directly from an as-received (AR) set of core samples. Unlike common practices that require lengthy core cleaning and wettability restoration, the new work flow does not introduce external liquids or alter the wettability of the matrix. It starts with AR cores in the laboratory. With the new work flow, cleaning, drying, and resaturating the sample are no longer required. The risk of altering the initial wetting state of the sample is minimal. Additionally, laboratory-analysis time is cut from weeks to days. This is particularly valuable because FF and RI play an essential role in estimating hydrocarbon in place using Archie’s equation, and in providing insight into partial oil-wetting conditions. Samples used in the method are from the Avalon and Wolfcamp formations; however, it is also applicable to permeable, conventional rocks. Introduction The estimation of volume of hydro-carbon in place (HIP) is a key formation-evaluation objective. In 1942, Gus Archie established the algorithm relating bulk resistivity (Rt), porosity , formation water resistivity (Rw), and water saturation (Sw). The Archie equation, and modified Archie methods, are the most-common petrophysics application for estimating HIP, and remain at the center of log-based formation evaluation. The Archie equation provides the method to estimate the volume of HIP in terms of Sw and phi. To solve Archie’s equation in terms of Sw, the petrophysicist starts by deriving Rt and phi directly from well logs. The remaining parameters must be determined independently, using cores and fluid samples brought back to the surface. In some situations, some of these parameters can be determined purely from logs, but in low-permeability formations, one must make assumptions that cause an increase in the uncertainty of Sw and HIP. Conventional electrical properties-based core analysis requires lengthy core cleaning and wettability restoration. However, in low-permeability formations, it is difficult to extract all hydrocarbon from samples without rigorous solvent cleaning, which potentially could alter the original fluid distribution and wetting state of the sample. Furthermore, with ultralow- permeability formations, complete de-saturation is nearly impossible without crushing the rock. Small errors in the cementation exponent (m) or the saturation exponent (n) can cause large errors in the Sw. In organic mudstones, with the presence of kerogen, the matrix becomes partially oil-wet, resulting in increasing n values significantly greater than 2.0. Under estimating the value of n will result in errors in Sw and may mischaracterize an oil-wet formation.

Carbonate rocks resistivity determination using dual and triple porosity conductivity models

Abstract The rocks may be classified as Archie rocks or Non-Archie rocks, depending on the link between pore structure and resistivity of the rock. For carbonate rocks, keeping this factor in view, the applicability of Archie's law tends to be unreasonable and employing Archie's equation will ultimately lead to inaccurate estimates of the water saturation. Numerous investigators have reported models that forms a link between laboratory results and field well logs to determine water saturation in intricate pore systems. In case of complex systems, Archie's law fails to correctly define the resistivity-index curves. In addition, it is imperative to carry out investigations at lower saturation values in order to elaborate the non-Archie characteristics. This brings the dual and triple porosity conductivity models into the equation. As these models are essential in defining the considerable changes of the resistivity-index curves, both qualitatively and quantitatively. The linkage between the two models is depicted electrically in series or in parallel. Moreover, it is possible to have a combination of the two configurations. As a result, the experimental results can be modeled accurately using least parameters. This work presents two models to determine water saturation in carbonate rocks, containing dual and triple porosity systems. This study also investigates the impact of different influential parameters such as saturation exponents, conductivity ratios, and pore volume fraction of each network systems, on the new models. Finally, the effect of each parameter is individually studied and the sensitivity analysis on the RI curves is produced. A new approach to apply these models is also explained which requires the use of NMR log, mercury injection capillary pressure (MICP) measurement, and simple plotting techniques to determine the water saturation. The proposed new models help petrophysicists to estimate water saturation in Non-Archie rocks, containing double and triple porosity network systems.

Developing a new hydrate saturation calculation model for hydrate-bearing sediments

This study incorporates X-ray computed tomography (CT) technology into the in-situ observation of the xenon hydrate formation process in sand sediments under excess gas conditions. While the scanning images were used to obtain microscopic distribution information of the hydrate, we implemented the finite element method (FEM) to calculate the resistivity of the hydrate-bearing samples obtained from scanning images. Consequently, it was observed that the resistivity index (RI) versus hydrate saturation (Sh) data matched better with our new calculation model rather than the simple Archie formula fitting model (i.e. experimental fitting model). Besides, we calculated the resistivity versus the hydrate saturation curves based on digital rock models with idealized hydrate distributions. These distributions included adhesive type, cemented type and scattered type. Observation of microscopic distribution and simulation results indicated that the resistivity versus hydrate saturation exhibited certain differences for the three types of hydrate distributions. We also found that saturation exponent (n) is a function of the hydrate saturation (Sh), which can be applied in the proposed new calculation model in order to calculate the resistivity versus hydrate saturation data. This suggests that the established model is a useful methodology for the purpose of saturation calculations and reservoir identification in hydrate-bearing sediments.

Correlations for effect of temperature on oil/water relative permeability in clastic reservoirs

For more than half a century, a large number of scholars have endeavored to delineate the effects of temperature on two-phase relative permeability curves using different oils and porous media. However, we still cannot predict how the relative permeability will change with temperature in a specific rock-fluid system. In fact, even a cursory review of the literature on the effect of temperature on oil/water relative permeability will show that a bewildering array of conflicting results have been reported. These inconsistent results are partly due to the likelihood that the effect of temperature is different in different rock-fluid systems and partly due to differences in the measurements techniques that can introduce varying experimental artifacts. The main objective of this study was to see whether some of the contradictions in the reported results would be resolved by examining the effects of temperature on relative permeability separately in different classes of rock-fluid systems. Another objective was to develop empirical correlations for estimating the value of oil/water relative permeability in different systems at higher temperatures.Reported results from a large number of experimental studies of the effect of temperature on relative permeability were collected to generate a large dataset of oil/water relative permeability curves. This dataset was partitioned into four parts representing four different classes of rock-fluid systems, namely: 1) light oil in unconsolidated sand, 2) heavy oil in unconsolidated sand, 3) light oil in consolidated sandstone and 4) heavy oil in consolidated sandstone. The effect of temperature on irreducible water saturation, residual oil saturation, the endpoint relative permeability to oil and water and the generalized Corey saturation exponents of oil and water were analyzed separately for each rock-fluid system. It was found that, although the scatter in reported data is large, some discernable differences are present in the effect of temperature in different rock fluid types. Separate correlations, in the form of generalized Corey saturation exponent model with temperature dependent parameters, were developed for oil/water relative permeability in different rock-fluid systems.

Effect of evaporative drying on complex conductivity spectra of sandstones

Dehydration is a common process occurring in natural environments, rocks, and building materials. Suitable methods for monitoring the changing moisture content should be identified. We have investigated the impact of dehydration of sandstones on complex conductivity spectra. Spectral induced polarization measurements were performed on five sandstone samples during evaporative drying. The complex conductivity spectra indicate considerable changes with decreasing saturation. The relationship between conductivity and saturation can be described by a power law known as the second empirical Archie equation. Separate saturation exponents have been determined for the real and imaginary parts of conductivity. The imaginary part of conductivity indicates higher saturation exponents for the investigated sandstones compared to the real part. Obviously, the saturation exponents depend on the method used for changing water saturation. Evaporative drying, which is used in our experiments, causes an increase of pore-water salinity and results in lower saturation exponents for the real part of conductivity but higher exponents for the imaginary part in comparison with the classical imbibition/drainage technique. We evaluate a theoretical approach that considers the influence of pore water salinity on the saturation exponents of the real and imaginary parts of conductivity. The complex conductivity spectra are processed by a Debye decomposition procedure. The resulting integrating parameters such as direct current resistivity, total chargeability, normalized chargeability, and mean relaxation time indicate a power law dependence on saturation. Our experiments indicate that the imaginary part of conductivity and normalized chargeability have a high sensitivity related to the drying process of rocks and might be suitable indicators to monitor the changes of moisture content in sandstones.

Measurement of Spontaneous Imbibition Capillary Pressure, Saturation and Resistivity Index by Counter Current Technique at Net Reservoir Stress and Elevated Temperature

Capillary pressure and resistivity index spontaneous imbibition experiments by the porous plate method, in a core holder at elevated temperature and net reservoir stress, are both difficult and time consuming special core analysis measurements to perform. In this type of experiment, low capillary forces act against a low permeable porous plate and only one face of the cylindrical core sample is in capillary contact with the fluid saturated porous plate. In this paper, core samples having different lithology, petrophysical properties and wettability are analysed by counter current spontaneous imbibition, starting at initial water saturation (Swi), at net confining pressure and elevated temperature. Synthetic brine is used as the wetting phase and Isopar L mineral oil as the non-wetting phase. This methodology is applied to investigate and evaluate how to obtain more reliable, more efficient and faster saturation imbibition data combined with electrical measurements, during spontaneous imbibition measurements. Resistivity index (RI), saturation exponent (n) (by single saturation equilibrium point using Archie’s second law RI= Sw-n) and wettability information using representative fluids, confining pressure and temperature are also obtained by applying this specific counter current imbibition technique and improved procedural approach.

Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence.

The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 4096^{3} grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.

K-Mean Cluster Analysis for Better Determining the Sweet Spot Intervals of the Unconventional Organic-Rich Shale: A Case Study

Abstract The petrophysical analysis is the crucial task for evaluating the quality of unconventional organic-rich shale and tight gas reservoirs. The presence of organic matter and the ultra-tight with over complex pore system have remained a lack of understanding of how to evaluate the extensive parameters of porosity considering organic content, gas saturation, organic richness, brittleness index, and sweet spot interval by only using conventional log. Therefore, this study offers effectively applied techniques and better analysis for interpreting these parameters by maximizing and integrating geological, geochemical, rock mechanical and engineering data. In general, the field data used in this study are from the first dedicated well for source rock exploration in the North Sumatra Basin, Indonesia. The developed method was derived by using conventional log. All interpretation results were validated by laboratory data measurements of routine and special core analysis, petrography, total organic carbon (TOC) and organic maturation, and brittleness index (BI) calculation. Moreover, the high quality of NMR log data was used as well to ensure our developed techniques present good estimations. Briefly about the methods, we started to determine the total and effective porosity based on the density log by including the presence of organic matter and multi-mineral analysis in these estimations. Then, we used the revised water saturation-TOC of water saturation while the TOC was predicted in advance by averaging three results from the correlation of TOC-Density, modified CARBOLOG and Passey’s ΔlogR methods. Equally important, in order to obtain the reliable gas saturation prediction, we used saturation exponent (n), cementation factor (m), and the tortuosity factor (a) parameters which obtained from laboratory measurement of formation resistivity factor and resistivity index (FFRI). In addition, the brittleness index was predicted based on sonic log data. Finally, all parameters needed for determining gas shale sweet spot have been made. Then, we developed a way to evaluate the sweet spot interval by using K-mean clustering. In conclusion, this clustering result properly follows the shale quality index parameters which consist of organic richness and maturation, brittleness index, the storage capacity of porosity and gas saturation. This study shows that these petrophysical applied techniques leads us to interpret the best position of shale interval to be developed with a simple, fast, and accurate prediction way. Furthermore, as a novelty, this method can be used as rock typing method and obviously can reduce uncertainty and risks in organic-rich shale exploration.

Hydrocarbon viability prediction of some selected reservoirs in Osland Oil and gas field, Offshore Niger Delta, Nigeria

Abstract An alternative approach involving the use of modified expressions for the free fluid index (FFI) permeability (K), reservoir quality index (RQI) and flow zone indicator (FZI), was used to predict the viability of hydrocarbon in some selected reservoirs. The aim of this work is to predict flow units, transmissibility and primary recovery through porosity (Ф) derived from wire-line logs. In the absence of core data, Ф values derived from the density log (RHOB) were optimised herein. Alternative expressions for the FFI, K, RQI, and FZI were suggested. A simplified approach with the use of only porosity dependent expressions for these parameters (FFI, K RQI, and FZI) that lies within the scope of the study was used for the evaluation of the reservoirs. Quick-look models for the prediction of RQI an FZI based on these the redefined equations were presented. Drudgery and computational errors that may come with the use of a range of other dependent parameters [irreducible water saturation (Swirr), formation factor (F), tortuosity factor (a) and cementation exponent (m)] were avoided. The reservoir, in well D1, is about 90 ft (27 m) thick, with the upper 30 ft (9 m) occupied by gas, the next 28 ft (8.5 m) is filled with oil and the remaining 32 ft (9.8 m) is water filled. The reservoir, in well D2, is about 110 ft (33.5 m) thick and it is oil saturated. Within D1 reservoir, average Ф, FFI, K, RQI, and FFI are 0.2, 0.18, 1256mD, 2.5 μm and 10.1 μm respectively. Within D2 reservoir, average Ф, FFI, K, RQI, and FFI are 0.25, 0.23, 5166mD, 4.5 μm and 13.5 μm respectively. Significant transmissibility and good rates of hydrocarbons recoveries are anticipated within the evaluated reservoirs.

Comparison of different dielectric models to calculate water saturation and estimate textural parameters in partially saturated cores

Accurate estimation of water saturation is central in predicting capillary pressure and relative permeability, under special core analysis in the laboratory. We have explored the use of dielectric measurements at different frequencies to estimate water saturation. In addition to water saturation, dielectric measurements are sensitive to the distribution of water and oil in a porous system, reflected by the apparent cementation factor [Formula: see text], which describes the water phase tortuosity. We have performed an experimental study to benchmark water saturation from dielectric measurements on eight carbonate cores and estimated their cementation exponent [Formula: see text] and saturation exponent [Formula: see text] in Archie’s equation from dielectric data. All cores went through a series of drainage/imbibition steps, creating varying saturations of brine/fluorocarbon. Fluorocarbon was chosen because it is invisible to proton nuclear magnetic resonance (NMR). Therefore,NMR porosity represents only the water-filled porosity and can be used to benchmark dielectric water-filled porosity. Three dielectric models were used for the comparison of the dielectric water-filled porosity with the one from NMR, i.e., the complex refractive index model (CRIM), bimodal model, and Stroud-Milton-De (SMD) model, and very good agreement of 1.5 porosity units on average is found. Despite its simplicity, CRIM predicted well the water-filled porosity in this experiment. However, it cannot provide information about the texture, which is captured by bimodal and SMD models. We also estimated [Formula: see text] and [Formula: see text] based on [Formula: see text] found from bimodal and SMD models, and good agreement with [Formula: see text] from resistivity data was shown. This is the first time to our knowledge that such a rich set of dielectric and NMR measurements was acquired at different saturation stages in a surface laboratory. This study is useful in benchmarking the water saturation from dielectrics, comparing different dielectric models, and demonstrating feasibility of estimating textural parameters.

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Abstract. Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg–Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly nonlinear hydrogeophysical problem investigated. GSA results show that in short time periods, the saturated hydraulic conductivity (Ks) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas in long time periods, the residual water content (θs), the Mualem–van Genuchten parameter (n) and the Archie saturation exponent (na) become influential, with strong interactions between them. The Mualem–van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (Ks,θs,α,n) and geophysical parameters (na,Csat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

Fully coupled inversion on a multi-physical reservoir model – Part I: Theory and concept

State of the art reservoir monitoring delivers numerous property data with high resolution. Especially the consistent interpretation of pressure data with different geophysical methods requires multi-physical modelling and inversion workflows. Such a workflow is developed based on the reservoir monitoring concept of the Ketzin pilot site for CO2 storage, Germany. The workflow consists of three physical models, (i) a single phase hydraulic model, (ii) a multiphase CO2 migration model and (iii) a geoelectrical model. Calibration is carried out to match observation data groups hydraulic pressure, CO2 pressure, CO2 arrival time and geoelectrical cross-hole observations. Calibration parameters are spatially distributed hydraulic permeability and porosity, compressibility, the relative permeability function and the geoelectrical saturation exponent. Geoelectrical measurements with low coverage that cannot be inverted with traditional methods could be included, since the multiphysical reservoir model acts as physical regularisation. The indirect nature of geophysical data is overcome by implementation of petrophysical relations between permeability and porosity and between CO2 saturation and electrical resistivity. Stability against field data is increased by reducing the impact of structural noise through preprocessing the observation data. Stability against the overparameterisation is added by Tikhonov regularisation and singular value decomposition, the latter combined with super parameter definition reducing the problem dimensions and simulation time by three quarters. A synthetic case study demonstrates that the model resolves the spatial permeability and identifies the petrophysical relation between CO2 saturation and electrical resistivity. The weighting scheme balances different observation data groups and measurement intervals. The model to measurement misfit is reduced proprotionally for all observation data groups, while the geoelectrical data are most difficult to match.

Hydrocarbon saturation in Bakken Petroleum System based on joint inversion of resistivity and dielectric dispersion logs

Bakken Petroleum System (BPS) is composed of both conventional and unconventional units, which exhibits significant variations in lithology, rock texture, clay content, total organic carbon, accompanied by high connate water salinity, presence of disseminated pyrite grains, and low values of porosity. These petrophysical attributes of the BPS lead to inconsistency in the oil-in-place estimates for those obtained from Electromagnetic (EM) induction log, Nuclear Magnetic Resonance (NMR) log, dielectric dispersion log measured by Array Dielectric Tool (ADT), and Dean-Stark core measurements. For purposes of improved hydrocarbon saturation estimation and petrophysical characterization in the BPS, a joint-inversion-based interpretation was performed on dispersive electrical conductivity and dielectric permittivity measurements at 4 dielectric-log-acquisition frequencies and 1 induction resistivity acquired at 20 kHz. This analysis was performed across a 350-ft depth interval in one of the science wells intersecting the BPS. Three geo-electromagnetic mixing models, namely Complex Refractive Index model, Stroud-Milton-De model, and Waxman Smits model are integrated and coupled to the inversion scheme to simultaneously estimate water saturation, formation brine conductivity, cementation exponent and saturation exponent in BPS.Water saturation estimates obtained using the proposed interpretation method were compared against those obtained from NMR log, Dean-Stark core measurements and service company’s dielectric inversion. In Middle Bakken from depth XX720 to XX750 ft, our estimates of water saturation are in better agreement with those estimated by service company’s mineral inversion method and service company’s dielectric interpretation as compared to those obtained from NMR interpretation and Dean Stark core measurement. Water saturation and formation brine conductivity estimates in Middle Bakken are in the ranges of 0.5–1 and 25–45 S/m, respectively. Inversion-derived brine conductivity and saturation exponent estimates are most uncertain in Lodgepole and Three Forks 2 formations, which exhibit a wide range of pore size distribution. Average relative errors in matching the 1 induction resistivity and 8 dielectric dispersion logs using the inversion-derived estimates are 33% and 20%, respectively, in the 350-ft depth interval of BPS. The proposed inversion achieves high certainty for the estimates when the formation has low clay content, low electrical anisotropy, and high porosity.

Complex conductivity of oil-contaminated clayey soils

Spectral induced polarization (SIP) is considered as a promising tool in environmental investigations. However, few works have done regarding the electrical signature of oil contamination of clayey soils upon induced polarization. Laboratory column experiments plus one sandbox experiment are conducted in this study to investigate the performances of the SIP method in oil-contaminated soils. First, a total of 12 soils are investigated to reveal the influences of water and soil properties on the saturation dependence of the complex conductivity below 100 Hz. Results show that the magnitude of the complex conductivity consistently decreases with decreasing water saturation for all soils samples. The saturation n and quadrature conductivity p exponents tend to increase slightly with increasing water salinity when using a linear conductivity model. The saturation exponent increases marginally with the cation exchange capacity (CEC) and the specific surface area (Ssp) while the quadrature conductivity exponent exhibits a relatively stronger dependence on both CEC and Ssp. For the low CEC soil samples (normally ≤10 meq/100 g), the quadrature conductivity exponent p correlates well with the saturation exponent n using the relationship p = n−1. SIP method is further applied in a sandbox experiment to estimate the saturation distribution and total volume of the oil. Results demonstrate that the SIP method has a great potential for mapping the organic contaminant plume and quantifying the oil volume.