Depth Of Investigation Research Articles

Applications of Asymptotic Solutions of the Diffusivity Equation to Infinite Acting Pressure Transient Analysis

Summary Understanding how pressure propagates in a reservoir is fundamental to the interpretation of pressure and rate transient measurements at a well. Unconventional reservoirs provide unique technical challenges as the simple geometries and flow regimes [wellbore storage (WBS) and radial, linear, spherical, and boundary-dominated flow] applied in well test analysis are now replaced by nonideal flow patterns due to complex multistage fracture completions, nonplanar fractures, and the interaction of flow with the reservoir heterogeneity. In this paper, we introduce an asymptotic solution technique for the diffusivity equation applied to pressure transient analysis (PTA), in which the 3D depletion geometry is mapped to an equivalent 1D streamtube. This allows the potentially complex pressure depletion geometry within the reservoir to be treated as the primary unknown in an interpretation, compared with the usual method of interpretation in which the depletion geometry is assumed and parameters of the formation and well are the unknown properties. The construction is based upon the solution to the Eikonal equation, derived from the diffusivity equation in heterogeneous reservoirs. We develop a Green’s function that provides analytic solutions to the pressure transient equations for which the geometry of the flow pattern is abstracted from the transient solution. The analytic formulation provides an explicit solution for many well test pressure transient characteristics such as the well test semi-log pressure derivative (WTD), the depth of investigation (DOI), and the stabilized zone (SZ) (or dynamic drainage area), with new definitions for the limit of detectability (LOD), the transient drainage volume, and the pseudosteady-state (PSS) limit. Generalizations of the Green’s function approach to bounded reservoirs are possible (Wang et al. 2017) but are beyond the scope of the current study. We validate our approach against well-known PTA solutions solved using the Laplace transform, including pressure transients with WBS and skin. Our study concludes with a discussion of applications to unconventional reservoir performance analysis for which reference solutions do not otherwise exist.

Sensitivity analysis of inverted model parameters from transient electromagnetic measurements affected by induced polarization effects

We investigate the application of the distance-based global sensitivity analysis (DGSA) to evaluate the sensitivity of electrical model parameters obtained from transient electromagnetic (TEM) data including induced polarization (IP) effects. We propose novel open-source forward modeling and inversion routines for single-loop TEM data including IP effects with the maximum phase angle model to model the frequency dependence of the complex resistivity. In a first step, we evaluate the accuracy of our forward modeling and inversion routines using numerical studies, where the actual variations of layer thicknesses and resistivities, as well as the frequency dependence of the complex resistivity is known. In a second step, we extend our investigation to field data and apply our approach to three distinct case studies in layered media: 1) a confined aquifer corresponding to conductive non-polarizable media, 2) a graphite deposit corresponding to highly conductive and polarizable anomalies in a resistive host rock and 3) an ice glacier corresponding to highly resistive polarizable media. Our DGSA results reveal that standard depth of investigation (DOI) approaches may overestimate the true sensitivity of the model obtained from the inversion. TEM data collected in conductive layered media without IP effects show reduced sensitivity above the predicted DOI. The case studies in polarizable media demonstrate that the maximum phase angle is more influential on the TEM model response than the relaxation time and dispersion coefficient. Our DGSA results for polarizable media reveal that TEM field data collected at the graphite deposit and at the ice glacier are sensitive to the geometry of the polarizable layer.

Deep-learning-based airborne transient electromagnetic inversion providing the depth of investigation

We develop an integrated workflow that uses deep-learning (DL)-based approaches for processing and inverting airborne transient electromagnetic (ATEM) data. Our novel workflow automates these preprocessing steps and enables real-time inversion in the field. Thus, we develop an entire inversion workflow using three DL networks that cover all steps from preprocessing to imaging. The preprocessing DL network performs interpolation to discard data that are severely noise contaminated and suppress the effects of noise in a late-time channel. We use an inversion DL network and a depth of investigation (DOI) network to generate images of subsurface resistivities exclusively within the DOI range where reliable predictions can be made. To optimize the inversion process, our approach focuses on designing the inversion DL network to simultaneously minimize data misfit and model misfit. By addressing these two aspects, we ensure a more robust outcome in the final resistivity images. The practical applicability of the workflow is verified by comparing the imaging results of the field data with those of conventional inversion and geologic interpretation. Each workflow is nearly automatic and very fast; we expect that our workflow will contribute to the development of real-time imaging software for the ATEM survey, which expands the applications of the ATEM survey in various fields.

Electrical Resistivity Tomography Investigation of Permafrost Conditions in a Thermokarst Site in Fairbanks, Alaska

<abstract> <p>The degradation of permafrost poses severe environmental threats to communities in cold regions. As near-surface permafrost warms, extensive topographic variability is prevalent in the Arctic and Sub-Arctic communities. Geologic hazards such as thermokarst are formed due to varying rates of permafrost degradation, resulting in ground subsidence. This gradual subsidence or abrupt collapse of the earth causes a danger to existing infrastructure and the economic activities of communities in cold regions. Understanding the causes of thermokarst development and its dynamics requires imaging its underground morpho-structures and characterizing the surface and subsurface controls. In this study, we conducted a two-dimensional (2D) electrical resistivity tomography (ERT) survey to characterize the permafrost conditions in a thermokarst prone site located in Fairbanks, Alaska. To increase the reliability in the interpretability of the ERT data, borehole data and the depth-of-investigation (DOI) methods were applied. By using the 2D and three-dimensional (3D) ERT methods, we gained valuable information on the spatial variability of transient processes, such as the movement of freezing and thawing fronts. Resistivity imaging across the site exhibited distinct variations in permafrost conditions, with both low and high resistive anomalies observed along the transects. These anomalies, representing taliks and ice wedges, were characterized by resistivity values ranging from 50 Ωm and above 700 Ωm, respectively. The results from this study showed the effectiveness of ERT to characterize permafrost conditions and thermokarst subsurface morpho-structures. The insights gained from this research contribute to a better understanding of the causes and dynamics of thermokarst, which can be instrumental for engineers in developing feasible remedial measures.</p> </abstract>

Processing of electrical resistivity tomography data using convolutional neural network in ERT-NET architectures

Electrical resistivity tomography (ERT) inversion has emerged as an effective method for predicting resistivity in complex geological structures. In most cases, traditional ERT inversion problems are posed as nonlinear optimization problems. Solving distribution resistivity inversion can be computationally challenging for two reasons: one is the significant cost of software and the other is the issue of local minima. The ERT-NET architecture was developed in this study to learn the parameter regression relationship between geophysical ERT datasets and subsurface models. We developed a novel convolutional neural network (CNN) technique that comprised of a fully connected network (ERT-INET) and a fully convolutional network (ERT-UNET); both train ambiguity information of the inverted resistivity based on processing ERT datasets. We also output our network segmentation of pixel-wise prediction for ERT-INET and structured prediction segmentation. The noise assessments of our network inversion were managed by employing depth of investigation (DOI) and statistical analysis for evaluation performance. The DOI appeared to be effective in conveying the breadth of possibility within our networks. Moreover, the performances are either the synthetic resistivity model or the field resistivity data, both of which have an average of greater than 95%. The inversion results of both architectures are precisely and accurately expressed, containing approximately the ground truth models and thereby also the field observation models. We conclude that these ERT-NET architectures could be one approach to ERT interpretation handling, and we strongly suggest alternatives that promote the geoelectrical method of interpretation.

Detection Performance Analysis of Array Dielectric Dispersion Logging Based on Sensitivity Function

Dielectric logging is a critical method for exploring and developing complex oil and gas reservoirs, such as tight reservoirs, low-resistivity contrast reservoirs, and shale oil and gas reservoirs. The sensitivity function is extended to high-frequency dielectric logging in this paper. The detection characteristics of attenuation and phase shift of an array dielectric logging tool in different modes are investigated, along with the influencing factors such as resistivity and dielectric constant. The results show the following: (1) The symmetrical coil system structure makes the sensitivity distribution symmetrically distributed, and the detection range is more focused. In the same measurement mode, the depth of investigation (DOI) becomes deeper under high resistivity formation, and the sensitivity range oscillates outward when the dielectric constant becomes greater. (2) The DOIs of different frequencies and source spacings cover the radial zone between 1 cm and 15 cm. The detection range has been enlarged to include part of the invasion zones, improving the measurement data’s dependability. (3) With the increase in the dielectric constant, the curve tends to oscillate, and this behavior makes the DOI slightly shallower. Additionally, this oscillation phenomenon is obvious when the frequency, resistivity, and dielectric constant increase, particularly in high-frequency detection mode (F2, F3).

Integrated Approach Determines Formation-Water Salinity

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 22548, “Integrated Approach for Formation-Water-Salinity Determination,” by Tariq Alshaikhmubarak, SPE, and Laila Mira, SPE, Saudi Aramco, and Sherif Ghadiry, Schlumberger, et al. The paper has not been peer reviewed. Copyright 2022 International Petroleum Technology Conference. Reproduced by permission. _ In the complete paper, two methodologies are tested to achieve measurement of formation-water salinity. First, a novel dry-weight chlorine (DWCL) measurement from an advanced spectroscopy tool is used to estimate the formation salinity at the depth of investigation of the device. The second methodology uses a new downhole induction resistivity cell in the formation-tester tool. The chlorine measurement, along with the flowline-induction-resistivity measurement, helps enhance the quality of saturation evaluation for quick decision making during logging operations and acceleration of evaluation studies instead of waiting on laboratory results. Chlorine Work Flow The ability to quantify chlorine concentration can help derive formation salinity as a continuous curve. Because chlorine has a large capture cross section, it is possible to extract it from capture gamma ray spectra with acceptable uncertainty, but the real challenge is to split the total chlorine signal seen by the tool into formation chlorine signal and borehole contribution. The chlorine signal split is a fundamental step in this work flow, outlined in Fig. 1. Once the chlorine concentration in the formation is obtained—expressed as DWCL—several petrophysical applications are enabled. The first is computation of water volume assuming a known formation-water salinity. The second is computation of the sodium chloride (NaCl) equivalent salinity from an independent volume of water and DWCL. Finally, one can solve for the NaCl equivalent water salinity. Equations to achieve these steps are provided in the complete paper. Interpretation Considerations Capture spectroscopy measurements have a shallow depth of investigation (DOI) in the range of 8–10 in., which means sensitivity to mud-filtrate invasion in the volume of rock probed by the tool. The mud-filtrate invasion is controlled by several factors, including mud overbalance, formation exposure time to mud, formation porosity and permeability, and mudcake-formation process and efficiency. These factors must be considered when using the chlorine work flow to assess the effect of the invading water-based-mud (WBM) filtrate, which normally has a different salinity than the formation water. The main effect of oil-based-mud (OBM) filtrate invasion, assuming that only the oil phase is invading the formation, is a reduction of water volume at the measurement DOI, degrading the statistical precision of the DWCL and increasing the uncertainty in the computed salinity.

Fluid Identification Derived from Formation Chlorine Measurements and Reservoir Characterization of Tight Carbonate in Sichuan Basin, China

Summary Natural gas production in the Sichuan Basin reached 30×109 m3 in 2020, but the shortfall between this and the production goal of 50×109 m3 in 2025 requires further exploration. The complex mineralogy and low porosity in tight carbonate reservoirs reduce the accuracy of formation water saturation calculations from Archie’s equation, which brings uncertainties to the reservoir characterization. Therefore, it is necessary to incorporate other methods as supplements to methods based on resistivities. In this paper, we outline a method that incorporates wireline-induced gamma spectroscopy, nuclear magnetic resonance (NMR), array dielectric, and borehole images. Spectroscopy is not only used to estimate the mineralogy of the reservoir, but it also provides measurements, such as chlorine concentration and thermal neutron capture cross section (sigma). The amount of chlorine in the formation is proportional to the water volume in the reservoir, hence formation water saturation. Sigma is also an indicator of the formation water saturation. It enables formation water saturation calculation without resistivity measurements. Case studies are presented from carbonate reservoirs in the Sichuan Basin, China. A robust and comprehensive petrophysical description of mineralogy, porosity, pore geometry, free fluid volume, rock type, and formation water saturation is presented. Calculation of formation water saturation from chlorine and sigma proves to be successful in both water-based mud and oil-based mud (OBM) environments. The depth of investigation (DOI) of chlorine from spectroscopy is about 8 to 10 in. for 90% of the signal. The various DOIs of different measurements must be considered when performing the fluid identification. Bound fluid saturation can reach more than 50% in tight carbonate reservoirs. Formation water saturation is not the only factor that determines the fluid type. Free fluid saturation from NMR must also be incorporated. Finally, a robust methodology integrating formation water saturation derived from dielectric and spectroscopy, and free fluid saturation derived from NMR shows great advantage in fluid identification in tight carbonate reservoirs. In this paper, we discuss a novel combination of wireline logging tools for fluid identification in a tight carbonate reservoir in the Sichuan Basin. It reduces the uncertainty when estimating formation water saturation and when resistivity measurements are suppressed in OBM environments. The gas zones identified by the new method have promising predictions of gas production. This workflow can also be applied to other tight carbonate plays in China.

Exploration of a Copper Ore Deposit in Elbistan/Turkey Using 2D Inversion of the Time-Domain Induced Polarization Data by Using Unstructured Mesh

We present the results of a direct current (DC) resistivity and time-domain induced polarization (TDIP) survey exploring a copper ore deposit in Elbistan/Turkey. The ore deposit is elongated below a valley and is of disseminated form with sulfide content. DC and IP data were acquired using the pole-dipole array on eight parallel profiles crossing the valley perpendicularly. The length of each profile was 300 m with an inter-profile distance of about 50 m. The data were interpreted by a newly developed 2D DC/TDIP inversion algorithm. The finite element algorithm uses a local smoothness constrained regularization on unstructured meshes. The finite element forward solution, as well as the inverse problem, is solved by an iterative preconditioned conjugate solver. The depth of investigation (DOI) was determined from cumulative sensitivities of the 2D inversion algorithm results. Because of the dissemination of the ore, the 2D inversion of the DC data was ambiguous: However, due to the sulfide content, a strong chargeability anomaly associated with the ore body was detected. We show that chargeability anomalies can generally be detected in the absence or presence of corresponding resistivity anomalies. This highly chargeable structure was confined in lateral direction. Although the lower boundary of the structure could not be resolved by the applied field set-up, a rough estimation of it could be derived at a depth of 90 m using synthetic modeling analyses. The 2D chargeability models are consistent with existing borehole information.

Technical note: Efficient imaging of hydrological units below lakes and fjords with a floating, transient electromagnetic (FloaTEM) system

Abstract. Imaging geological layers beneath lakes, rivers, and shallow seawater provides detailed information critical for hydrological modeling, geologic studies, contaminant mapping, and more. However, significant engineering and interpretation challenges have limited the applications, preventing widespread adoption in aquatic environments. We have developed a towed transient electromagnetic (tTEM) system for a new, easily configurable floating, transient electromagnetic instrument (FloaTEM) capable of imaging the subsurface beneath both freshwater and saltwater. Based on the terrestrial tTEM instrument, the FloaTEM system utilizes a similar philosophy of a lightweight towed transmitter with a trailing offset receiver pulled by a small boat. The FloaTEM system is tailored to the specific freshwater or saltwater application as necessary, allowing investigations down to 100 m in freshwater environments and up to 20 m on saline waters. Through synthetic analysis, we show how the depth of investigation of the FloaTEM system greatly depends on the resistivity and thickness of the water column. The system has been successfully deployed in Denmark for a variety of hydrologic investigations, improving the ability to understand and model processes beneath water bodies. We present two freshwater applications and a saltwater application. Imaging results reveal significant heterogeneities in the sediment types below the freshwater lakes. The saline water example demonstrates that the system is capable of identifying and distinguishing clay and sand layers below the saline water column.

A Flexible Single Loop Setup for Water-Borne Transient Electromagnetic Sounding Applications.

Water-borne transient electromagnetic (TEM) soundings provide the means necessary to investigate the geometry and electrical properties of rocks and sediments below continental water bodies, such as rivers and lakes. Most water-borne TEM systems deploy separated magnetic transmitter and receiver loop antennas—typically in a central or offset configuration. These systems mostly require separated floating devices with rigid structures for both loop antennas. Here, we present a flexible single-loop TEM system, the light-weight design of which simplifies field procedures. Our system also facilitates the use of different geometries of the loop antenna permitting to adjust the depth of investigation (DOI) and the minimum sounding depth in the field. We measure the turn-off ramp with an oscilloscope and use the DOI to assess the minimum and maximum exploration depth of our single-loop TEM system, respectively. A reduction of the loop-antenna size improves early-time TEM data due to a reduced length of the turn-off ramp, whereas an increase of the loop-antenna size enhances the signal strength at late times, which allows to investigate deeper structures below the lake bed. We illustrate the capabilities of our system with a case study carried out at Lake Langau in Austria. Our results show that our system is capable of reaching a DOI of up to 50 (with a maximum radius of the circular loop of ), while it also resolves the water layer down to a minimum thickness of (when the radius is reduced to ).

A Decomposed Fracture Network Model for Characterizing Well Performance of Fracture Networks on the Basis of an Approximated Flow Equation

Abstract The gridless analytical and semianalytical methodologies can provide credible solutions for describing the well performance of the fracture networks in a homogeneous reservoir. Reservoir heterogeneity, however, is common in unconventional reservoirs, and the productivity can vary significantly along the horizontal wells drilled for producing such reservoirs. It is oversimplified to treat the entire reservoir matrix as homogeneous if there are regions with extremely nonuniform properties in the reservoir. However, the existing analytical and semianalytical methods can only model simple cases involving matrix heterogeneity, such as composite, layered, or compartmentalized reservoirs. A semianalytical methodology, which can model fracture networks in heterogeneous reservoirs, is still absent; in this study, we propose a decomposed fracture network model to fill this gap. We discretize a fractured reservoir into matrix blocks that are bounded by the fractures and/or the reservoir boundary and upscale the local properties to these blocks; therefore, a heterogeneous reservoir can be represented with these blocks that have nonuniform properties. To obtain a general flow equation to characterize the transient flow in the blocks that may exhibit different geometries, we approximate the contours of pressure with the contours of the depth of investigation (DOI) in each block. Additionally, the borders of each matrix block represent the fractures in the reservoir; thus, we can characterize the configurations of complex fracture networks by assembling all the borders of the matrix blocks. This proposed model is validated against a commercial software (Eclipse) on a multistage hydraulic fracture model and a fracture network model; both a homogeneous case and a heterogeneous case are examined in each of these two models. For the heterogeneous case, we assign different permeabilities to the matrix blocks in an attempt to characterize the reservoir heterogeneity. The calculation results demonstrate that our new model can accurately simulate the well performance even when there is a high degree of permeability heterogeneity in the reservoir. Besides, if there are high-permeability regions existing in the fractured reservoir, a BDF may be observed in the early production period, and formation linear flow may be indistinguishable in the early production period because of the influence of reservoir heterogeneity.

Localization of deep voids through geophysical signatures of secondary dewatering features

Discrete deep targets are a significant challenge for most surface-based geophysical techniques, even when considering high property contrasts. In general, surface-based geophysical methods lose lateral and vertical resolution with depth as a result of the limited acquisition geometry and increased signal attenuation. The former can be overcome through use of cross-borehole methods, but lateral localization is still needed for optimal borehole placement. As such, a relatively small, deep void located near the maximum depth of investigation (DOI) is very unlikely to be detected. Yet, secondary features associated with these voids can be exploited for enhanced detection performance. When voids are located below the groundwater table, a significant amount of dewatering and pumping is required to make them a functional passageway. This dewatering not only removes water from the void space but also the surrounding formation, resulting in a much larger, if more diffuse, secondary target: an induced groundwater table gradient. Many geophysical sensing methods are sensitive to subsurface moisture content. We have implemented a 2D joint-petrophysical mixing model (JPM), using inverted electrical resistivity tomography (ERT) and inverted seismic refraction models to sense changes in the groundwater table gradient. Our results are validated using the depth to bedrock, groundwater-surface water information, ground-penetrating radar, and time-domain reflectometry methods. Our initial proof of concept is applied to a shallow area with a significant soil moisture gradient, through different surface soil types and bedrock. The 2D JPM results are used to generate an estimate of air, moisture, and matrix percent fractions in the investigation area, providing a clear delineation of the groundwater surface and associated gradient. This refined hydraulic gradient estimate can then be used to laterally locate a void at or below the DOI of ERT and seismic refraction.

Multiwindow weighted stacking of surface-wave dispersion

Surface-wave methods are classically used to characterize shear (S-) wave velocities ([Formula: see text]) of the shallow subsurface through the inversion of dispersion curves. When targeting 2D shallow structures with sharp lateral heterogeneity, windowing and stacking techniques can be implemented to provide a better description of [Formula: see text] lateral variations. These techniques, however, suffer from the trade-off between lateral resolution and depth of investigation (DOI), which is well-known when using the multichannel analysis of surface waves (MASW) method. We have adopted a novel methodology aimed at enhancing lateral resolution and DOI of MASW results through the use of multiwindow weighted stacking of surface waves (MW-WSSW). MW-WSSW consists of stacking dispersion images obtained from data segments of different sizes, with a wavelength-based weight that depends on the aperture of the data selection window. In that sense, MW-WSSW provides additional weight to short wavelengths in smaller windows so as to better inform shallow parts of the subsurface, and vice versa for deeper velocities. Using multiple windows improves the DOI, whereas applying wavelength-based weights enhances the shallow lateral resolution. MW-WSSW was implemented within the open-source package SWIP and applied to the processing of synthetic and real data sets. In both cases, we compared it with standard windowing and stacking procedures that are already implemented in SWIP. MW-WSSW provided convincing results with optimized lateral extent, improved shallow resolution, and increased DOI.

Mapping Complex Injectite Bodies With Multiwell Electromagnetic 3D Inversion Data

Electromagnetic (EM) inversion processing of ultradeep resistivity data has advanced from one dimensional (1D) to three dimensional (3D). These advances have helped improve the geological complexity that can be imaged and provide additional reservoir information. The large depth of investigation (DOI) of ultradeep LWD EM tools means that distant boundaries might not be detected by any other sensor in the tool string, making it difficult to verify the results. As inversion results represent a model of the subsurface resistivity distribution and not a direct measurement, it is important to have high confidence in the results. Directly comparing the component data measured by the tool to the modeled component data from the inversion across multiple frequencies provides confidence in the resultant model where the data have a close fit. However, as measurement sensitivities decrease with distance, there is potential for non-uniqueness, generating a model that is geologically unrealistic. Increased confidence can be achieved with independent verification of the model. This paper details results from a trilateral well in an injectite reservoir wherein the sand distribution was expected to be complex. The 1D inversions showed the vertical distribution of the sand, but the results were sometimes distorted by lateral resistivity variations. The 3D inversion of the data allowed the lateral resistivity variations to be resolved. These results can be corroborated by direct comparison with azimuthal resistivity images. Additionally, the laterals all diverged from the same main bore and remained close together initially in an area containing major sand injectites. The 3D inversions from two of the wells overlap and define similarly shaped structures, providing confidence in the 3D inversion model. In complex geobodies, such as the injectites described, significant lateral variation in the reservoir distribution is expected, which is not captured by 1D inversion. Understanding the shape of these structures and their potential connectivity using 3D inversion provides a major increase in reservoir understanding that is critical to completion design.

Application of geoelectrical resistivity for delineating crystalline basement aquifers in Basiri, Ado-Ekiti, Southwestern Nigeria

Delineating crystalline basement aquifers with adequate capacity to store and transmit sufficient groundwater is quite challenging as substantial spatial variability predominantly marked the basement aquifers. Electrical resistivity is a non-invasive geophysical technique for delineating weathered and fractured zones that permit groundwater accumulation in the basement rocks. This study uses two-dimensional (2D) electrical resistivity imaging (ERI) to delineate the weathering profile developed above the crystalline basement rocks and thus assesses the groundwater potential of the aquifer systems in Basiri, Ado-Ekiti, southwestern Nigeria. The study evaluated the reliability of the 2D ERI images by computing the depth of investigation (DOI) index to predict the depth extent at which the 2D resistivity models are no longer reliable. This approach can be used to minimise the mismatch between the resistivity models and subsurface targets, particularly in complex and subtle hydrogeological conditions as in the crystalline basement complex. This study indicates that the weathering profile developed into a two-layered aquifer system—a low yield shallow saprolite aquifer overlying a deeper fractured bedrock (saprock) aquifer with greater capacity to support adequate drawdown for high yield.

The impact of conductive layers on depth of investigation estimation in 2D geoelectrical imaging: A case study of West Bani Mazar, El Minia, Egypt

The appearing of clay (conductive) layer(s) at different depths of the lithological succession has been widely observed in the Upper Egypt district. This phenomenon has dramatic effects on the resultant depth of investigation of any geoelectrical survey of such environment. Study the effect of such layers on estimating Depth of Investigation (DOI) is the main goal of this article. Because the reliability of the Two Dimensional Electrical Resistivity Imaging (2DERI) models alters rapidly with changing conductive layers depths as well as noisy data ratios, an accurate estimation of DOI is critical to help geophysists determining the optimum hydrogeophysical survey design in clayey environments. The modified depth of investigation method which mainly depends on the statistical method is applied to estimate the DOI. In this article, the study is based on synthetic and field data sets. Wenner (W), Wenner Schlumberger (WSC) and Dipole-Dipole (DD) electrode arrays were chosen to clarify which electrode gives larger DOI in the conceptual models (presence conductive layer at 0, 50 and 100 m depths) from the ground surface. Moreover, the study will include a test for the effect of adding 10% noise to synthetic data sets on DOI estimation.It is well known that Wenner array better matches with layer-like targets, DD with 3D horizontally limited ones. Based on these results, there is a relationship between DOI and depth of the conductive layer [larger DOI is recorded when conductive layer exists at deeper depths and vice versa].This could be related to the existence of a conductive layer in the lithology succession that can limit the current to flow vertically and subsequently, affects DOI estimation. 2D ERI field data from West Bani Mazar, El Minia is used to support the supposed first conceptual model on DOI estimation.

A calibration method for estimating mudcake thickness and porosity using NMR data

Mudcake thickness affects wellbore operations such as differential sticking, well completion, and wellbore clean-up operations. One of the properties for which a drilling fluid is screened during laboratory tests is the thickness of the mudcake it produces. Such laboratory tests are routinely conducted on ceramic discs or rock samples, at a specified temperature and pressure. Mathematical models have also been reported for predicting cake thickness and mud induced formation damage. The problem here is that the conditions upon which both laboratory tests and mathematical models are run do not match all conditions in the wellbore during drilling. Calliper tools can be used to directly quantify mudcake thickness in wellbore, however, they cannot differentiate between a sloughing hole and a mudcake. This study therefore explores the potentiality of nuclear magnetic resonance (NMR) logging tools to measure the thickness and porosity of mudcake, and mud induced formation damage in wellbores. This proposed approach utilizes measurements routinely taken from a multi-frequency NMR logging tool, namely T2 relaxation times at three depth of investigations (DOI). For this specific application, the first DOI captures the mudcake and the near wellbore region, the second DOI captures an inner radius (invaded zone), while the third DOI measures the virgin zone. NMR measurements in these three DOIs were simulated in our laboratory experiments. From the acquired NMR measurements, we identified characteristic T2 – curves for mudcakes and solid infiltration and then defined a workflow to obtain them. The areas under these characteristic T2-curves showed good correlations with the mudcake porosity and thickness. Based on these, several calibration curves were developed for mudcake thicknesses, porosity and formation damage. The calibration curves appear to be robust since they were obtained from a variety of rock types with a wide range of porosity and permeability.

Integration of Pressure Transient Data into Reservoir Models Using the Fast Marching Method

SummaryCalibration of reservoir model properties by integration of well-test data remains an important research topic. Well-test data have been recognized as an effective tool to describe transient flow behavior in petroleum reservoirs. It is also closely related to the drainage volume of the well and the pressure-front propagation in the subsurface. Traditional analytic means of estimating reservoir permeability relies on an interpretation of the diagnostic plot of the well pressure and production data, which usually leads to a bulk average estimation of the reservoir permeability. When more detailed characterization is needed, a forward model that is sensitive to the reservoir heterogeneity needs to be established, and a numerical inversion technique is required.We use the concept of the diffusive time of flight (DTOF) to formulate an asymptotic solution of the diffusivity equation that describes transient flow behavior in heterogeneous petroleum reservoirs. The DTOF is obtained from the solution of the Eikonal equation using the fast marching method (FMM). It can be used as a spatial coordinate that reduces the 3D diffusivity equation to an equivalent 1D formulation. We investigate the drainage-volume evolution as a function of time in terms of the DTOF. The drainage volume might be directly related to the well-test derivative, which can be used in an inversion calculation to calibrate reservoir model parameters.The analytic sensitivity coefficients of the well-test derivative with respect to reservoir permeability are derived and incorporated into an objective function to perform model calibration. The key to formulating the sensitivity coefficients is to use the functional derivative of the Eikonal equation to derive the analytic sensitivity of the DTOF to reservoir permeability. Its solution is implemented by tracking the characteristic trajectory of the local Eikonal solver within the FMM. The major advantage of calculating the sensitivity coefficients using the FMM is its significant computational efficiency during the iterative inversion process.This inverse-modeling approach is tested on a 2D synthetic heterogeneous reservoir model and then applied to the 3D Brugge Field, where a single well with constant flow rate is simulated. The well-test derivative is shown to be inversely proportional to the drainage volume and is treated as the objective function for inversion. With an additional constraint to honor the prior model, our inverse-modeling approach will adjust the reservoir model to obtain permeability as a function of distance from the well within the drainage volume. It provides a modification of reservoir permeability both within and beyond the depth of investigation (DOI).

Parallel tempered trans-dimensional Bayesian inference for the inversion of ultra-deep directional logging-while-drilling resistivity measurements

As one of the most important downhole technology, directional electromagnetic (EM) logging-while-drilling (LWD) has been developing over the decades. The new generation of resistivity logging service expands the depth of investigation (DoI) to over 100 ft from the wellbore. As a result, more geological features are within the scope of the logging tool, which increases the complexity of logging measurements dramatically. Reservoir imaging relies on the inversion of the logging measurements, whereas most conventional inversion approaches depend on the deterministic optimization which oftentimes suffers from local minima. Many efforts were focused on the improvement of data processing workflow by using prior knowledge of the formation structure to constrain the optimizer from stepping into local minima although the prior can be inaccurate. To reduce the negative impact of inaccurate prior assumptions, we propose to infer the model parameters via the trans-dimensional Markov chain Monte Carlo (tMCMC) method. Governed by the Bayesian theorem, the trans-dimensional inference addresses the complexity of the model by allowing the number of layers of the target model to be a free parameter. Driven by the measurements, the joint posterior distribution of model parameters is sampled accordingly, which provides a probability solution of a potential answer. Bayesian sampling is computationally expensive with a slow convergence rate. In this paper, we propose a meta-technique called parallel tempering (PT) combining with tMCMC to improve the sampling performance. PT is also known as replica Bayesian sampling where multiple Markov chains are constructed to explore the posterior distribution simultaneously with periodic information exchange between chains. Verified by our experiments, combining tMCMC and PT builds an efficient and reliable framework for interpreting ultra-deep LWD resistivity measurements. The inversion results from a series of benchmark models demonstrate that the proposed data-driven framework is robust and can be used to infer a reservoir-scale earth model.