Myung Jin Nam

Simulation of triaxial induction measurements in dipping, invaded, and anisotropic formations using a Fourier series expansion in a nonorthogonal system of coordinates and a self-adaptive hp finite-element method

Borehole triaxial induction instruments were designed to diagnose and measure rock electrical conductivity parallel and perpendicular to the bedding plane. Experience has shown that the interpretation of triaxial induction measurements often requires numerical modeling for a proper diagnosis of rock electrical conductivity anisotropy in the presence of geometric effects such as dipping wells, layer boundaries, and invasion. We introduce a new algorithm to simulate triaxial induction measurements that combines a Fourier series expansion in a nonorthogonal system of coordinates with a 2D goal-oriented, self-adaptive, high-order hp finite-element method. This procedure enables the accurate and reliable simulation of triaxial induction measurements across reservoir rock formations with extreme contrasts of electrical conductivity while reducing the 3D computational complexity associated with deviated wells. Numerical results indicate that borehole dip effects on triaxial induction measurements are larger than...

Simulation of DC dual-laterolog measurements in complex formations: A Fourier-series approach with nonorthogonal coordinates and self-adapting finite elements

Dual laterolog DLL makes use of a galvanic conduction principle to focus electrical currents into rock formations, therebyminimizingshoulderandboreholeeffectsinthemeasurement of formation resistivity. The tool includes two separate focusing systems: deep-sensing LLd and shallow-sensing modes LLs. Laterolog current-focusing systems were designed for operation primarily in vertical boreholes penetrating horizontal layers; only recently their design has been revised for operation in deviated wells in the presence of electrical anisotropy. We simulated three-dimensional3DDLLmeasurementsindipping,invaded, and electrically anisotropic formations and appraised the corresponding effects on apparent resistivity logs. Simulations were performedbycombiningtheuseofaFourier-seriesexpansionin anonorthogonalsystemofcoordinateswithanexisting2Dgoaloriented, higher-order, and self-adaptive finite-element method. This numerical algorithm yields accurate solutions in limited CPUtimebecauseonlyafewFouriermodesareneededtosimulate practical applications. For the calculation of focused currents, we introduced an embedded postprocessing method that incorporates a synthetic focusing principle to compute current intensitiesateachiterativestepofoptimalmeshrefinements.Our numerical method accurately simulates 3D DLL measurements in rock formations that exhibit extreme contrasts of electrical resistivity. Simulations indicate that LLs resistivity logs are more sensitive to both invaded and anisotropic layers than LLd resistivity logs. In deviated wells, shoulder-bed effects on apparent resistivitylogsincreasewithanincreaseofdipangle,andareemphasized across thin conductive layers. Electrical anisotropy effects on apparent resistivity logs increase substantially with dip angle.

Assessment of Delaware and Groningen effects on dual-laterolog measurements with a self-adaptive hp finite-element method

Wedescribenumericalsimulationsofanomalousdual-laterolog DLL borehole measurements, including Delaware and Groningen effects. Both effects give rise to abnormally high readings of DLL measurements under extreme logging conditions. Specifically, a low resistive bed below a highly resistivelayercauseselectricalcurrentstoconcentratewithin the borehole, which generates a negative potential at the referenceelectrodeand,consequently,anabnormallyhighreading in DLL measurements. These effects are exacerbated by thepresenceofcasingand/oratnonzerofrequencies.Simulationsareperformedwitha2Dgoal-oriented,high-order,selfadaptive hp finite-element method together with an embedded postprocessing method. Results indicate that the presence of electrodesB andN is critical for proper simulation of Delaware effects on DLL measurements. Delaware effects onDLLlogsdecreaseasthecurrentreturnelectrodeismoved farther away from either the logging point or the borehole. The frequency of operation also affects deep laterolog measurements,generatingtheso-calledGroningeneffect.

Simulation of eccentricity effects on short- and long-normal logging measurements using a Fourier-hp-finite-element method*

Resistivity logging instruments are designed to measure the electrical resistivity of a formation, and this can be directly interpreted to provide a water-saturation profile. However, resistivity logs are sensitive to borehole and shoulder-bed effects, which often result in misinterpretation of the results. These effects are emphasised more in the presence of tool eccentricity. For precise interpretation of short- and long-normal logging measurements in the presence of tool eccentricity, we simulate and analyse eccentricity effects by combining the use of a Fourier series expansion in a new system of coordinates with a 2D goal-oriented high-order self-adaptive hp finite-element refinement strategy, where h denotes the element size and p the polynomial order of approximation within each element. The algorithm automatically performs local mesh refinement to construct an optimal grid for the problem under consideration. In addition, the proper combination of h and p refinements produces highly accurate simulations even in the presence of high electrical resistivity contrasts. Numerical results demonstrate that our algorithm provides highly accurate and reliable simulation results. Eccentricity effects are more noticeable when the borehole is large or resistive, or when the formation is highly conductive.

A Review on Methods for Constructing Rock Physics Model of Saturated Reservoir Rock for Time-Lapse Seismic

ABSTRACT Rock physics analysis bridges variations in reservoir parameters (such as fluid saturation, temperature, pressure, and so on) to the changes in seismic properties of reservoir rock. By constructing a rock physics model (RPM) of saturated reservoir rock, we can make a feasibility study for time-lapse seismic surveys and an interpretation of time-lapse seismic data. However, due to the complexity of subsurface structures and reservoir conditions at each stage of oil production, no single relation can explain relationship between variations in reservoir parameters and changes in seismic properties, and thus constructing proper RPM for a given reservoir is a difficult task. This study makes an analysis on previous researches that studied the relationship to review methods of constructing RPMs. In order to suggest a proper way of making a proper model for a given situation, the review analyzes and explains four different approaches of constructing RPMs, i.e., Gassmanns model, Kriefs relation, Duffy-Mindlins model and Wyllies time average equation. Further the review explains how we can obtain input data to the four models, which are moduli and densities of grain, fluid and dry rock. The assumptions and applications of the four RPM-constructing approaches are also discussed in detail to give an insight for a proper construction of RPMs.

A comparison of accuracy and computation time of three-dimensional magnetotelluric modelling algorithms

This paper presents a comparison of four different three-dimensional (3D) magnetotelluric (MT) modelling algorithms in terms of accuracy and computation time. Three of them use the finite difference method while the last one uses the edge finite-element method. The modelling algorithms are analysed with respect to governing equations, boundary conditions, solvers, preconditioners and static divergence correction. The accuracy of the algorithms is examined by simulating MT responses for two different models, both of which have anomalous bodies in simple background media. Although the simulated responses generally show good agreement, small discrepancies are observed over the anomalous bodies. These discrepancies are caused by the difference between the electric- and magnetic-field formulations used by the algorithms. The three algorithms using the finite difference method are adequate for 3D inversion of MT data since they produce solutions in a short computation time. Although the algorithm using the edge finite-element method requires longer computation time than the others, it can provide more accurate solutions and model surface topography.

A review on time-lapse seismic data processing and interpretation

Time-lapse (TL) seismic or 4D seismic has great potential in monitoring and interpreting time-varying variations in reservoir fluid properties during hydrocarbon production. The TL surveys interpret dynamic changes in reservoir parameters by detecting differences in seismic responses from different vintages, which are obtained by repeated seismic surveys over the same area. For a proper and more precise quantitative interpretation of the TL seismic responses, TL seismic processing enhances repeatability of the TL-data sets, and thus reduces artificial differences that come from unavoidable differences in repeated-seismic-survey environments. This study aims to bring an insight to the state of the art in both TL seismic data processing and interpretation by reviewing previously-published researches. TL data processing is a sequential process conducting 4D binning and simultaneous 4D pre-stack processing; 4D binning improves spatial repeatability while “simultaneous 4D pre-stack processing” derives common processing operators employing cross-equalization (XEQ) as a core technique. TL seismic interpretation is categorized by the characteristics of data being interpreted into two strategies: interpretation of data sets from all TL vintages and interpretation of differences in seismic data between vintages.

In-Loop Transient Electromagnetic Responses With Induced Polarization Effects of Deep-Sea Hydrothermal Deposits

A transient electromagnetic (TEM) system using a small loop source is advantageous to the development of compact autonomous instruments, which are well suited to a submersible-based survey. Since the electrical conductivity of subseafloor materials can be frequency dependent, these induced polarization (IP) effects may affect the reliability of TEM data interpretation. In this paper, we investigate the IP effects on the TEM responses of deep-sea hydrothermal mineral deposits with a thin sediment cover. Time-domain target signals are larger and appear earlier in horizontal magnetic fields than in vertical magnetic fields. The IP effects cause transient magnetic fields to enhance initially, to decay rapidly, and then to reverse the polarity. The dc conductivity and chargeability in Cole-Cole parameters influence the time of sign reversals and the enhancement of target responses, simultaneously. A damped least squares inversion scheme is applied to reconstruct a polarizable hydrothermal deposit model using synthetic TEM sounding data sampled from a time interval before the sign reversal. The test example demonstrates that the Cole-Cole parameters of a highly conductive layer can be resolved more effectively from vertical magnetic fields than from horizontal magnetic fields.

A preliminary study on sensitivity of seismic responses to changes in reservoir parameters using various RPM-constructing strategies

Rock physics model (RPM) transforms reservoir characteristics into elastic seismic properties which control generation of seismic responses through synthetic seismic simulation. The changes in fluid saturation or pressure lead to corresponding changes in seismic responses based on constructed RPM. The different RPMs are first constructed based on four different strategies of Gassmanns equation, Kriefs formulation, Duffy–Mindlins method, and Wyllies equation. Differences among these RPMs are analyzed before performing sensitivity analysis of changes in seismic responses with respect to changes in reservoir parameters. The synthetic seismic responses used for the analysis are generated from the seismic simulation, which algorithm is developed by using a finite difference method based on staggered grid with convolutional perfect match layer and free surface.

A Parallel, Fourier Finite-Element Formulation with an Iterative Solver for the Simulation of 3D LWD Measurements Acquired in Deviated Wells

We describe a new method to simulate resistivity measurements acquired with induction logging instruments in deviated wells. The method combines: (1) a highly e-cient iterative solver, (2) a parallel implementation, (3) a Fourier Finite-Element (FFE) formulation in a non-orthogonal system of coordinates, and (4) a 2D hp-Finite Element (FE) goal-oriented self-adaptive grid-reflnement strategy. We apply the new method to simulate measurements acquired with a logging-while-drilling (LWD) instrument operating at 1.75MHz in a 55-degree deviated well. Numerical results conflrm the high-accuracy and e-ciency of the method. An error level below 1% is achieved in reservoirs with high-contrast in electrical resistivity using an average CPU time of 1{3 minutes per logging position.