Pore-Scale Joint Evaluation of Dielectric Permittivity and Electrical Resistivity for Assessment of Hydrocarbon Saturation Using Numerical Simulations

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 1930-1942 ◽  
Author(s):  
Huangye Chen ◽  
Zoya Heidari

Summary Complex pore geometry and composition, as well as anisotropic behavior and heterogeneity, can affect physical properties of rocks such as electrical resistivity and dielectric permittivity. The aforementioned physical properties are used to estimate in-situ petrophysical properties of the formation such as hydrocarbon saturation. In the application of conventional methods for interpretation of electrical-resistivity (e.g., Archie's equation and the dual-water model) and dielectric-permittivity measurements [e.g., complex refractive index model (CRIM)], the impacts of complex pore structure (e.g., kerogen porosity and intergranular pores), pyrite, and conductive mature kerogen have not been taken into account. These limitations cause significant uncertainty in estimates of water saturation. In this paper, we introduce a new method that combines interpretation of dielectric-permittivity and electrical-resistivity measurements to improve assessment of hydrocarbon saturation. The combined interpretation of dielectric-permittivity and electrical-resistivity measurements enables assimilating spatial distribution of rock components (e.g., pore, kerogen, and pyrite networks) in conventional models. We start with pore-scale numerical simulations of electrical resistivity and dielectric permittivity of fluid-bearing porous media to investigate the structure of pore and matrix constituents in these measurements. The inputs to these simulators are 3D pore-scale images. We then introduce an analytical model that combines resistivity and permittivity measurements to assess water-filled porosity and hydrocarbon saturation. We apply the new method to actual digital sandstones and synthetic digital organic-rich mudrock samples. The relative errors (compared with actual values estimated from image processing) in the estimate of water-filled porosity through our new method are all within the 10% range. In the case of digital sandstone samples, CRIM provided reasonable estimates of water-filled porosity, with only four out of twenty-one estimates beyond 10% relative error, with the maximum error of 30%. However, in the case of synthetic digital organic-rich mudrocks, six out of ten estimates for water-filled porosity were beyond 10% with CRIM, with the maximum error of 40%. Therefore, the improvement was more significant in the case of organic-rich mudrocks with complex pore structure. In the case of synthetic digital organic-rich mudrock samples, our simulation results confirm that not only the pore structure but also spatial distribution and tortuosity of water, kerogen, and pyrite networks affect the measurements of dielectric permittivity and electrical resistivity. Taking into account these parameters through the joint interpretation of dielectric-permittivity and electrical-resistivity measurements significantly improves assessment of hydrocarbon saturation.

2021 ◽  
Author(s):  
Zulkuf Azizoglu ◽  
◽  
Zoya Heidari ◽  

Broadband relative dielectric dispersion measurements are considered interesting options for assessment of water-filled pore volume. Conventional models such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG), often overlook or oversimplify the complexity of pore structure, geometrical distribution of the constituting fluids, and spatial distribution of minerals. This yields to significant errors in assessment of water saturation especially in rocks with complex pore structure. Therefore, it becomes important to quantify the impacts of pore structure and spatial distribution of minerals on broadband relative dielectric dispersion measurements to be able to make decisions about reliability of water saturation estimates from these measurements in a given formation. The objectives of this paper are (a) to quantify the impacts of pore structure and spatial distribution of minerals on relative dielectric permittivity measurements in a wide range of frequencies, (b) to propose a new simple and physically meaningful workflow, which honors pore geometry and spatial distribution of minerals to enhance fluid saturation assessment using relative dielectric permittivity measurements, (c) to verify the reliability of the introduced model in the pore-scale domain. First, we perform numerical simulations of relative dielectric dispersion measurements in the frequency range of 20 MHz to 1 GHz in the pore-scale domain. The input to the numerical simulator includes pore-scale images of actual complex carbonate rock samples. We use a physically meaningful model which honors spatial distribution of the rock constituents for the multi-frequency interpretation of relative dielectric response. To verify the reliability of the model in multiple frequencies, we apply the model to the results of relative dielectric simulations in the pore-scale domain on 3D computed tomography scan (CT-scan) images of carbonate rock samples, which are synthetically saturated to obtain a wide range of water saturation. We successfully verified the reliability of the introduced model in the pore-scale domain using carbonate rock samples with multi-modal pore-size distribution. Estimated water saturations from the results of simulations at 1 GHz resulted in an average relative error of less than 4%. We observed measurable improvements in fluid saturation estimates compared to the cases which CRIM or MG models are used. Results demonstrated that application of conventional models to estimate water saturation from relative dielectric response is not reliable in frequencies below 1 GHz.


Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Artur Posenato Garcia ◽  
Zoya Heidari

The dielectric response of rocks results from electric double layer (EDL), Maxwell-Wagner (MW), and dipolar polarizations. The EDL polarization is a function of solid-fluid interfaces, pore water, and pore geometry. MW and dipolar polarizations are functions of charge accumulation at the interface between materials with contrasting impedances and the volumetric concentration of its constituents, respectively. However, conventional interpretation of dielectric measurements only accounts for volumetric concentrations of rock components and their permittivities, not interfacial properties such as wettability. Numerical simulations of dielectric response of rocks provides an ideal framework to quantify the impact of wettability and water saturation ( Sw) on electric polarization mechanisms. Therefore, in this paper we introduce a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including impacts of pore structure, Sw, and wettability on permittivity measurements. We solve the quasi-electrostatic Maxwell's equations in three-dimensional (3D) pore-scale rock images in the frequency domain using the finite volume method. Then, we verify simulation results for a spherical material by comparing with the corresponding analytical solution. Additionally, we introduce a technique to incorporate α-polarization to the simulation and we verify it by comparing pore-scale simulation results to experimental measurements on a Berea sandstone sample. Finally, we quantify the impact of Sw and wettability on broadband dielectric permittivity measurements through pore-scale numerical simulations. The numerical simulation results show that mixed-wet rocks are more sensitive than water-wet rocks to changes in Sw at sub-MHz frequencies. Furthermore, permittivity and conductivity of mixed-wet rocks have weaker and stronger dispersive behaviors, respectively, when compared to water-wet rocks. Finally, numerical simulations indicate that conductivity of mixed-wet rocks can vary by three orders of magnitude from 100 Hz to 1 GHz. Therefore, Archie’s equation calibrated at the wrong frequency could lead to water saturation errors of 73%.


Author(s):  
Sabyasachi Dash ◽  
◽  
Zoya Heidari ◽  

Conventional resistivity models often overestimate water saturation in organic-rich mudrocks and require extensive calibration efforts. Conventional resistivity-porosity-saturation models assume brine in the formation as the only conductive component contributing to resistivity measurements. They also do not reliably assimilate the spatial distribution of the clay network and pore structure. Moreover, they do not incorporate other conductive minerals and organic matter, impacting the resistivity measurements and leading to uncertainty in water saturation assessment. We recently introduced a resistivity-based model that quantitatively assimilates the type and spatial distribution of all rock constituents to improve reserves evaluation in organic-rich mudrocks using electrical resistivity measurements. This paper aims to expand the application of this model for well-log-based assessment of water/hydrocarbon saturation and to verify the reliability of the introduced method in the Wolfcamp Formation of the Permian Basin. Our recently introduced resistivity model uses pore combination modeling to incorporate conductive (clay, pyrite, kerogen, brine) and nonconductive (grains, hydrocarbon) components in estimating effective resistivity. The inputs to the model are volumetric concentrations of minerals, conductivity of rock components, and porosity obtained from laboratory measurements or interpretation of well logs. Geometric model parameters are also critical inputs to the model. To simultaneously estimate the geometric model parameters and water saturation, we developed an inversion algorithm with two objectives: (a) to estimate the geometric model parameters as inputs to the new resistivity model and (b) to estimate the water saturation. The geometric model parameters are determined for each rock type or formation by minimizing the difference between the measured resistivity and the resistivity estimated from pore combination modeling. We applied the new method to two wells drilled in the Wolfcamp Formation of the Permian Basin. The formation-based inversion showed variation in geometric model parameters, which improved the assessment of water saturation. Results demonstrated that the new method improved water saturation estimates by 24.1% and 32.4% compared to Archie’s and Waxman-Smits models, respectively, in the Wolfcamp Formation. The most considerable improvement was observed in the Middle and the Lower Wolfcamp Formations, where the average clay concentration was relatively higher than the other zones. There was an additional 70,000 bbl/acre of hydrocarbon reserve using the proposed method compared to when water saturation was quantified using Archie’s model in the Permian Basin, which is a 33% relative improvement. It should be highlighted that the new method did not require any calibration effort using core water saturation measurements, which is a unique contribution of this rock-physics-based workflow.


2021 ◽  
Author(s):  
Mehdi Teymouri ◽  
◽  
Zoya Heidari ◽  

Assessment of effective mechanical properties such as elastic properties and brittleness can be challenging in the presence of complex rock composition, pore structure, and spatial distribution of minerals, especially in the absence of acoustic measurements. Conventional methods such as effective medium modeling, are not reliable for assessments of mechanical properties in complex formations such as carbonates, because solid skeleton of carbonates does not consist of granular minerals with ideal shapes. The effective medium models also overlook both the spatial distribution of petrophysical properties, and the coupled hydraulic and mechanical (HM) processes, which causes significant uncertainties in geomechanical evaluations. The objective of this paper is to develop a numerical method to enhance assessment of effective mechanical properties of anisotropic and heterogenous carbonate formations by modeling the variation of effective stress and the evolution of corresponding strain. The developed method takes into account the coupled HM processes, the realistic spatial distribution of rock inclusions (i.e., rock fabrics), dynamic fluid flow, pore pressure, and pore structure. To achieve this objective, we develop a pore-scale numerical simulator by satisfying conservation equations and considering the coupling among relevant HM phenomena. We adopt peridynamic theory to discretize the micro-scale medium. The inputs to our numerical modeling include pore-scale images of rock samples as well as mechanical and hydraulic properties of each rock inclusion. We perform image processing on micro-CT scan images of rock samples to obtain a realistic micro-scale structure of both rock matrix (i.e., concentration, spatial distribution, and shape of rock constituents) and pore space. We then assign realistic mechanical and hydraulic properties to each rock constituent within the pore-scale medium. The outcomes of numerical modeling include the variation of effective stress and the evolution of corresponding strain by honoring the variability in mechanical/hydraulic properties of rock inclusions caused by their spatial distribution, pore pressure, pore structure, natural fractures, and dynamic fluid flow at the micro-scale domain. We then compare the outcomes of numerical models with the mechanical properties estimated based on effective medium models. We performed sensitivity analyses to quantify the effects of concentration and spatial distribution of rock constituents, divergence in spatial distribution of petrophysical, mechanical, and hydraulic properties of inclusions, pore structure and natural micro-fractures, and pore pressure on variations in effective elastic properties of rock samples. We estimated the elastic properties from the stress/strain curves obtained from numerical simulations. We observed significant errors (more than 30.6% relative error depending on the content and distribution of rock constituents) in estimated effective elastic properties by the effective medium models. These errors are due to overlooking the coupled HM analysis, the spatial distribution, actual shape and size of inclusions, pore-structure, and natural micro-fractures by such effective medium models. The presented advanced pore-scale numerical analysis will (a) enhance reliable assessments of effective elastic/mechanical properties of carbonates or any other rock type in the presence of pore pressure and dynamic flow, and (b) assist upscaling techniques for reliable geomechanical evaluation and assessment of fracture propagation in these formations at larger scales.


2021 ◽  
Author(s):  
Zulkuf Azizoglu ◽  
Zoya Heidari ◽  
Leonardo Goncalves ◽  
Lucas Abreu Blanes De Oliveira ◽  
Moacyr Silva Do Nascimento Neto

Abstract Broadband dielectric dispersion measurements are attractive options for assessment of water-filled pore volume, especially when quantifying salt concentration is challenging. However, conventional models for interpretation of dielectric measurements such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG) model require oversimplifying assumptions about pore structure and distribution of constituting fluids/minerals. Therefore, dielectric-based estimates of water saturation are often not reliable in the presence of complex pore structure, rock composition, and rock fabric (i.e., spatial distribution of solid/fluid components). The objectives of this paper are (a) to propose a simple workflow for interpretation of dielectric permittivity measurements in log-scale domain, which takes the impacts of complex pore geometry and distribution of minerals into account, (b) to experimentally verify the reliability of the introduced workflow in the core-scale domain, and (c) to apply the introduced workflow for well-log-based assessment of water saturation. The dielectric permittivity model includes tortuosity-dependent parameters to honor the complexity of the pore structure and rock fabric for interpretation of broadband dielectric dispersion measurements. We estimate tortuosity-dependent parameters for each rock type from dielectric permittivity measurements conducted on core samples. To verify the reliability of dielectric-based water saturation model, we conduct experimental measurements on core plugs taken from a carbonate formation with complex pore structures. We also introduce a workflow for applying the introduced model to dielectric dispersion well logs for depth-by-depth assessment of water saturation. The tortuosity-dependent parameters in log-scale domain can be estimated either via experimental core-scale calibration, well logs in fully water-saturated zones, or pore-scale evaluation in each rock type. The first approach is adopted in this paper. We successfully applied the introduced model on core samples and well logs from a pre-salt formation in Santos Basin. In the core-scale domain, the estimated water saturation using the introduced model resulted in an average relative error of less than 11% (compared to gravimetric measurements). The introduced workflow improved water saturation estimates by 91% compared to CRIM. Results confirmed the reliability of the new dielectric model. In application to well logs, we observed significant improvements in water saturation estimates compared to cases where a conventional effective medium model (i.e., CRIM) was used. The documented results from both core-scale and well-log-scale applications of the introduced method emphasize on the importance of honoring pore structure in the interpretation of dielectric measurements.


SPE Journal ◽  
2011 ◽  
Vol 16 (03) ◽  
pp. 608-624 ◽  
Author(s):  
Jesús M. Salazar ◽  
Carlos Torres-Verdín ◽  
Gong Li Wang

Summary We quantify the influence of oil-based mud (OBM)-filtrate invasion and formation-fluid properties on the spatial distribution of fluid saturation and electrical resistivity in the near-wellbore region. The objective is to appraise the sensitivity of borehole resistivity measurements to the spatial distribution of fluid saturation resulting from the compositional mixing of OBM and in-situ hydrocarbons. First, we consider a simple two-component formulation for the oil phase (OBM and reservoir oil) wherein the components are first-contact miscible. A second approach consists of adding water and surfactant to a multicomponent OBM invading a formation saturated with multiple hydrocarbon components. Simulations also include presence of irreducible, capillary-bound, and movable water. The dynamic process of OBM invasion causes component concentrations to vary with space and time. In addition, the relative mobility of the oil phase varies during the process of invasion because oil viscosity and oil density are both dependent on component concentrations. Presence of surfactants in the OBM is simulated with a commercial adaptive implicit compositional formulation that models the flow of three-phase multicomponent fluids in porous media. Simulations of the process of OBM invasion yield 2D spatial distributions of water and oil saturation that are transformed into spatial distributions of electrical resistivity. Subsequently, we simulate the corresponding array-induction measurements assuming axial-symmetric variations of electrical resistivity. We perform sensitivity analyses on field measurements acquired in a well that penetrates a clastic formation and that includes different values of density and viscosity for mud filtrate and formation hydrocarbon. These analyses provide evidence of the presence of a high-resistivity region near the borehole wall followed by a low-resistivity annulus close to the noninvaded resistivity region. Such an abnormal resistivity annulus is predominantly caused by high viscosity contrasts between mud filtrate and formation oil. The combined simulation of invasion and array-induction logs in the presence of OBM invasion provides a more reliable estimate of water saturation, which improves the assessment of in-place hydrocarbon reserves.


Geophysics ◽  
2021 ◽  
pp. 1-70
Author(s):  
Artur Posenato Garcia ◽  
Zoya Heidari

Interpretation of complex dielectric permittivity measurements is challenging in clay-rich rocks, such as shaly sands and organic-rich mudrocks, due to complex rock fabric and mineralogical composition, which are overlooked by conventional interpretation models. For instance, the impact of fabric features (e.g., laminations, structural/dispersed shale) and diverse constitution (e.g., clay, kerogen, pyrite, brine) to the broadband complex permittivity is not well understood. Therefore, the main objective of this work is to develop a framework capable of reliably quantifying the impact of different minerals and their corresponding spatial distribution on the multi-frequency complex dielectric permittivity measurements in clay-rich rocks.To achieve the aforementioned objective, we introduce a numerical algorithm to compute the dielectric dispersion in 3D pore-scale images of clay-rich rocks. We numerically solve the quasi-electrostatic approximation to Maxwell's equations in the frequency domain through the finite volume method. The clay particles are often sub-resolution in most imaging methods. Therefore, we introduce a workflow to calculate the effective admittance of the clay network. Furthermore, we derive a new equation to incorporate the induced polarization effect into the effective admittance of pyrite particles. Finally, we perform a sensitivity analysis of the complex dielectric permittivity of clay-rich rocks in the frequency range from 100 Hz to 1 GHz to the volumetric concentration and spatial distribution of clays, cation exchange capacity (CEC), volumetric concentration of pyrite, and the orientation of the electric field. Results showed that clays can enhance or diminish electrical conductivity values at different frequencies depending on their intrinsic properties and spatial distribution. Laminations, for instance, significantly enhance dielectric permittivity in the sub-MHz frequency range, but their effect is imperceptible at 1 GHz. Furthermore, the impact of the variation of CEC on permittivity is approximately proportional at 100Hz but negligible at 1 GHz.


2020 ◽  
Author(s):  
Nesrine Chaali ◽  
Daniel Bravo ◽  
Sofiane Ouazaa ◽  
Jose Isidro Beltrán Medina ◽  
Javier Benavides

<p>Increasing consideration is being placed on the environmental impact of soil contamination with heavy metals (HM), especially in productive agricultural areas. So, a key task is to characterize this contamination qualitatively and quantitatively in order to understand the spatial distribution of HM and decide about the adequate management. Traditional sampling to monitor HM distribution is time, cost-consuming and often unrepresentative. Additionally, sparse and punctual data measurements may not allow understanding the real dynamic of HM in the soil profile, and in many cases the collected data fails in providing the needed information. Recently, in-situ geophysical techniques based on electrical resistivity tomography measurements (ERT) were implemented in agriculture as a “proxy” to determine spatial and temporal distribution of HM. The objective of this study was to provide an accurate information for future efficient measures of soil remediation, by understanding the HM distribution, specifically cadmium (Cd) and arsenic (As), using electrical resistivity measurements combined with soil chemical analyses. A UNI-T UT523A devise was used in a “Wenner Alpha” configuration to perform ERT survey at 2 m depth in nine locations of Tolima department-Colombia. 2D-ERT cross sections “Tomograms” were obtained by the Res2Dinv software which allowed characterizing qualitatively the spatial distribution of Cd and As. Chemical concentration values for both Cd (0.36±0.06 mg.kg<sup>-1</sup>) and As (3.00±0.28 mg.kg<sup>-1</sup>) were introduced in the inverse modelling procedure as a solution to provide an easier and reliable alternative to determine the shape, size, and path of the likely electrical resistivity distribution of the studied HM. Tomograms revealed that Cd distribution was mainly observed in deeper soil profile (0.80 m), while As was observed basically in shallower soil layers (0.45 m). Higher electrical resistivity values (330–48000 Ω m) correspond to Cd distribution and lower electrical resistivity values (138-291 Ω m) are related to As distribution. A high positive Pearson correlation (ρ) between electrical resistivity measurements and soil chemical properties (for Cd and As content) was obtained for the nine locations; ρ values of 0.97 and 0.98 were obtained for Cd and As; respectively. A linear regression was performed between ERT measurements and Cd and As contents; (R<sup>2</sup>=0.94, RMSE=0.33) and (R<sup>2</sup>=0.97 RMSE=0.18) for Cd and As; respectively. The results underlie the utility of the combined geophysical techniques, based on electrical resistivity measurements, and soil chemical properties to improve the understanding of HM dynamic.</p><p><strong>Key words</strong>: Geophysical techniques, tomograms, heavy metals, soil chemical properties, spatial distribution, Pearson correlation.</p>


Author(s):  
W. E. King

A side-entry type, helium-temperature specimen stage that has the capability of in-situ electrical-resistivity measurements has been designed and developed for use in the AEI-EM7 1200-kV electron microscope at Argonne National Laboratory. The electrical-resistivity measurements complement the high-voltage electron microscope (HVEM) to yield a unique opportunity to investigate defect production in metals by electron irradiation over a wide range of defect concentrations.A flow cryostat that uses helium gas as a coolant is employed to attain and maintain any specified temperature between 10 and 300 K. The helium gas coolant eliminates the vibrations that arise from boiling liquid helium and the temperature instabilities due to alternating heat-transfer mechanisms in the two-phase temperature regime (4.215 K). Figure 1 shows a schematic view of the liquid/gaseous helium transfer system. A liquid-gas mixture can be used for fast cooldown. The cold tip of the transfer tube is inserted coincident with the tilt axis of the specimen stage, and the end of the coolant flow tube is positioned without contact within the heat exchanger of the copper specimen block (Fig. 2).


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