Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.     

The 3D shear experiment over the Natih field in Oman: the effect of fracture-filling fluids on shear propagation

This is the final paper in a series on the 3D multicomponent seismic experiment in Oman. In this experiment a 3D data set was acquired using three-component geophones and with three source orientations. The data set will subsequently be referred to as the Natih 9C3D data set. We present, for the first time, evidence demonstrating that shear waves are sensitive to fluid type in fractured media. Two observations are examined from the Natih 9C3D data where regions of gas are characterized by slow shear-wave velocities. One is that the shear-wave splitting map of the Natih reservoir exhibits much larger splitting values over the gas cap on the reservoir. This increase in splitting results from a decrease in the slow shear-wave velocity which senses both the fractures and the fracture-filling fluid. Using a new effective-medium model, it was possible to generate a splitting map for the reservoir that is corrected for this fluid effect. Secondly, an anomaly was encountered on the shear-wave data directly above the reservoir. The thick Fiqa shale overburden exhibits a low shear-wave velocity anomaly that is accompanied by higher shear reflectivity and lower frequency content. No such effects are evident in the conventional P-wave data. This feature is interpreted as a gas chimney above the reservoir, a conclusion supported by both effective-medium modelling and the geology.
With this new effective-medium model, we show that introduction of gas into vertically fractured rock appears to decrease the velocity of shear waves (S2), polarized perpendicular to the fracture orientation, whilst leaving the vertical compressional-wave velocity largely unaffected. This conclusion has direct implications for seismic methods in exploration, appraisal and development of fractured reservoirs and suggests that here we should be utilizing S-wave data, as well as the conventional P-wave data, as a direct hydrocarbon indicator.     

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled‐source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled‐source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two‐dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three‐dimensional modelling results suggest that controlled‐source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole‐to‐surface controlled‐source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.     

Electromagnetic fields in a steel-cased borehole

The development of an electromagnetic numerical modelling scheme for a magnetic dipole in an arbitrary casing segment in an inhomogeneous conductivity background has been difficult, due to the very high electrical conductivity and magnetic permeability contrasts between the steel casing and the background medium. To investigate the effect of steel casing efficiently, we have developed an accurate but simple finite‐element modelling scheme to simulate electromagnetic fields in a medium of cylindrically symmetric conductivity structures. In order to preserve the cylindrical symmetry in the resulting electromagnetic fields, a horizontal loop current source is used throughout. One of the main advantages of the approach is that the problem is scalar when formulated using the azimuthal electric field, even if the casing is both electrically conductive and magnetically permeable. Field calculations have been made inside the cased borehole as well as in another borehole which is not cased. Careful analyses of the numerical modelling results indicate that the anomaly observed in a cross‐borehole configuration is sensitive enough to be used for tomographic imaging.     

The Role of Electrical Anisotropy in Magnetotelluric Responses: From Modelling and Dimensionality Analysis to Inversion and Interpretation

The study of electrical anisotropy in the Earth, defined as the electrical conductivity varying with orientation, has experienced important advances in the last years regarding the investigation of its origins, how to identify and model it, and how it can be related to other parameters, such as seismic and mechanical anisotropy. This paper provides a theoretical background and a review of the current state of the art of electrical anisotropy using electromagnetic methods in the frequency domain, focusing mainly on magnetotellurics. The aspects that will be considered are the modelling of the electromagnetic fields with anisotropic structures, the analysis of their responses to identify these structures, and how to properly use these responses in inversion and interpretation. Also, an update on the most recent case studies involving anisotropy is provided.     

Influence of frequency-dependent anisotropy on seismic amplitude-versus-offset signatures for fractured poroelastic rocks

Frequency-dependent amplitude variation with offset offers an effective method for hydrocarbon detections and analysis of fluid flow during production of oil and natural gas within a fractured reservoir. An appropriate representation for the frequency dependency of seismic amplitude variation with offset signatures should incorporate influences of dispersive and attenuating properties of a reservoir and the layered structure for either isotropic or anisotropic dispersion analysis. In this study, we use an equivalent medium permeated with aligned fractures that simulates frequency-dependent anisotropy, which is sensitive to the filled fluid of fractures. The model, where pores and fractures are filled with two different fluids, considers velocity dispersion and attenuation due to mesoscopic wave-induced fluid flow. We have introduced an improved scheme seamlessly linking rock physics modelling and calculations for frequency-dependent reflection coefficients based on the propagator matrix technique. The modelling scheme is performed in the frequency-slowness domain and can properly incorporate effects of both bedded structure of the reservoir and velocity dispersion quantified with frequency-dependent stiffness. Therefore, for a dispersive and attenuated layered model, seismic signatures represent a combined contribution of impedance contrast, layer thickness, anisotropic dispersion of the fractured media and tuning and interference of thin layers, which has been avoided by current conventional methods. Frequency-dependent amplitude variation with offset responses was studied via considering the influences of fracture fills, layer thicknesses and fracture weaknesses for three classes amplitude variation with offset reservoirs. Modelling results show the applicability of the introduced procedure for interpretations of frequency-dependent seismic anomalies associated with both layered structure and velocity dispersion of an equivalent anisotropic medium. The implications indicate that anisotropic velocity dispersion should be incorporated accurately to obtain enhanced amplitude variation with offset interpretations. The presented frequency-dependent amplitude variation with offset modelling procedure offers a useful tool for fracture fluid detections in an anisotropic dispersive reservoir with layered structures.     

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions. We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.     

Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered

Starting from an analytical reservoir model that incorporates full interaction with an elastic overburden, a new hybrid mathematical approach is developed by combining two numerical discretization methods. A tabular reservoir (petroleum reservoir or an aquifer) in an infinite or semi-infinite domain is viewed as a macroscopic displacement discontinuity, allowing use of the efficient displacement discontinuity mathematical method to calculate stresses and displacements that arise because of pressure changes. A 3-D finite element method using a poroelastic formulation is used to discretize the reservoir itself. By coupling the displacement discontinuity and finite element methods, a 3-D large-scale poroelastic reservoir can be simulated within an infinite or semi-infinite domain. The numerical model has been verified through comparison to known solutions, and some time-dependent pressure drawdown problems are analyzed. Results indicate that including the complete overburden (reservoir surroundings) response has a significant effect on pressure drawdown in a poroelastic reservoir during pumping, and should be incorporated in appropriate applications such as well test equations and subsidence analyses.     

Emulation of a process-based estuarine hydrodynamic model

Emulation modelling can be an effective alternative to traditional mechanistic approaches for complex environmental systems and, if carefully conceived, can offer significantly reduced run times and user expertise requirements. We present a case study of dynamic emulation for the domain of estuarine water quality modelling, by reporting the development and evaluation of a one-dimensional hydrodynamic model emulator. The proposed “neuroemulator” retains the dynamic nature of the process-based model utilizing a set of artificial neural networks. The underlying hydrodynamic model is routinely used for analysis and management of the northern reach of the San Francisco Bay-Delta estuary, a large complex region of strategic importance for water supply and ecosystem services on the Pacific coast of California, USA. The reduced computational expense of the emulator affords opportunities for direct use, as well as embedded use within other modelling frameworks such as those developed for reservoir operations and socio-hydrology.     

Modelling and inversion of electromagnetic data using an approximate plate model

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates . The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.     

Simultaneous core sample measurements of elastic properties and resistivity at reservoir conditions employing a modified triaxial cell – a feasibility study

Adaptations of existing triaxial cells for ultrasonic P- and S-wave measurements are well documented. This paper proposes further modification of such a cell so that also resistivity measurements can be carried out simultaneously at reservoir conditions. By employing the top cap and the pedestal of the cell as electrodes, axial resistivity measurements are now feasible. In order to minimize the polarization effect of this two-electrode arrangement, careful analyses have been carried out to optimize the choice of electrode coating and measurement frequency band. Radial resistivity measurements are also included in the system by introducing a strap-electrode system.
In a reservoir under production changes in both saturations, temperature (if steam injection) and stresses can take place. Therefore the modified triaxial system should be able to measure the integrated effects on the acoustic parameters and electric responses caused by variations in each of these parameters. The feasibility of the system to obtain such reliable information is demonstrated, employing a small selection of core samples. In the future such combined measurements on reservoir core samples can be used to link both seismic and electromagnetic observations to the actual earth model and constrain both modelling and inversion.     

一维垂直各向异性介质频率域海洋可控源电磁资料反演方法

本文提出了一维垂直各向异性(VTI)介质倾斜偶极源频率域海洋可控源电磁(CSEM)资料高斯-牛顿反演方法.在电阻率各向异性介质水平偶极源和垂直偶极源海洋CSEM正演算法的基础上,利用欧拉旋转方法,实现了各向异性介质倾斜偶极源海洋CSEM正演算法.海洋可控源电磁场关于地下介质横向电阻率(ρ_h)和垂向电阻率(ρ_v)的偏导数(即灵敏度矩阵)是解析计算的,结合垂直各向异性介质横向电阻率与垂向电阻率的关系,将各向异性率融入到正则化因子选择中,实现了正则化因子的自适应选择.理论模型合成数据和实测资料反演算例表明,我们提出的反演方法能够较准确的重构海底围岩和基岩的各向异性电阻率以及高阻薄层的埋藏深度、厚度和垂向电阻率.     

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

Rock-physics forward modelling to predict seismic behaviour: A case study for exploration target in Mahanadi basin,East Coast of India

One of the major aspects of rock-physics forward modelling is to predict seismic behaviour at an undrilled location using drilled well data. It is important to model the rock and fluid properties away from drilled wells to characterize the reservoir and investigate the root causes of different seismic responses. Using the forward modelling technique, it is possible to explain the amplitude responses of present seismic data in terms of probable rock and reservoir properties. In this context, rock-physics modelling adds significant values in the prospect maturation process by reducing the risk of reservoir presence in exploration and appraisal phases. The synthetic amplitude variation with offset gathers from the forward model is compared with real seismic gathers to ensure the fidelity of the existing geological model. ‘Prospect A’ in the study area has been identified from seismic interpretation, which was deposited as slope fan sediments in Mahanadi basin, East Coast of India. The mapped prospect has shown class-I amplitude variation with offset response in seismic without any direct hydrocarbon indicator support. The existing geological model suggests the presence of an excellent gas reservoir with proven charge access from the fetch area, moderate porosity and type of lithology within this fan prospect. But, whether the seismic response from this geological model will exhibit a class-I amplitude variation with offset behaviour or ‘dim spot’ will be visible; the objective of the present study is to investigate these queries. A rock-physics depth trend analysis has been done to envisage the possibilities of class-I reservoir in ‘Prospect A’. Forward modelling, using a combination of mechanical and chemical compaction, shows the synthetic gas gathers at ‘Prospect A’, which are class I in nature. The study has also depicted 2D forward modelling using lithology and fluid properties of discovery well within similar stratigraphy to predict whether ‘dim spot’ will be seen in seismic. The estimated change in synthetic amplitude response has been observed as ∼5% at contact, which suggests that the changes will not be visible in seismic. The study connects the existing geological model with a top-down seismic interpretation using rock-physics forward modelling technique to mature a deep-water exploratory prospect.     

Fast and accurate three‐dimensional controlled source electromagnetic modelling†

We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation.     

GPR modelling by the Fourier method: improvement of the algorithm

We improve two aspects of the modelling scheme for the simulation of electromagnetic radio waves, based on the Fourier pseudospectral method.
When there are large contrasts in the material properties, use of the standard algorithm (regular grid) causes a series of artefacts, as, for instance, ringing and acausal events. These problems, due to the non-locality of the differential operator, are solved by using the staggered Fourier method (staggered grid).
Realistic radiation patterns can be obtained from simple combinations of magnetic and electric sources. If the directivity pattern of the antenna is known, from either a finite-difference simulation or an analytic evaluation or an experimental characterization, it can then be simulated by a composite-source concept. This effective source is implemented in the modelling algorithm by means of a perturbation technique, which first computes the intensity and directional spectra of the single electromagnetic sources. Their location is optimized to obtain the best fit with a minimum number of sources. The approach is, in principle, valid for the far-field radiation pattern of the antenna.     

Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial‐stacked seismic data are available. The multi‐property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log‐facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock‐physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.     

Seismoelectric and electroseismic responses to a point source in a marine stratified model

We investigate the seismoelectric/electroseismic wavefields excited by a point source in an air/seawater/three-layered porous medium configuration containing a hydrocarbon layer. The results show that if an explosive source for excitation is used, receivers at seafloor can record the coseismic electromagnetic fields accompanying the P, S, fluid acoustic waves and the interface responses converted from the acoustic waves at seafloor interface and from the seismic waves at the interfaces beneath the seafloor. Employing a vertical electric dipole source shows that, with the exception of the interface responses converted from electromagnetic waves at seafloor, the interface responses converted from transmitted electromagnetic waves at the interfaces beneath the seafloor can also be identified. Given that the strength of the explosive source is within excitation capability of industry air guns, the generated interface responses from the hydrocarbon layer can be detected by current electromagnetic sensors considering the low ambient noise at the seafloor. Our results demonstrate the feasibility of the seismoelectric method applied to marine hydrocarbon exploration. Electroseismic modelling results suggest that it is not practical to employ this method to prospect marine hydrocarbon layer due to the weak interface response signal, unless a much larger current is injected into seafloor.