Carlos Torres-Verdín

Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear scattering approximation

We introduce a novel approximation to numerically simulate the electromagnetic response of point or line sources in the presence of arbitrarily heterogeneous conductive media. The approximation is nonlinear with respect to the spatial variations of electrical conductivity and is implemented with a source-independent scattering tensor. By projecting the background electric field(i.e., the electric field excited in the absence of conductivity variations) onto the scattering tensor, we obtain an approximation to the electric field internal to the region of anomalous conductivity. It is shown that the scattering tensor adjusts the background electric field by way of amplitude, phase, and cross-polarization corrections that result from frequency-dependent mutual coupling effects among scatterers. In general, these three corrections are not possible with the more popular first-order Born approximation. Numerical simulations and comparisons with a 2.5-dimensional finite difference code show that the new approximation accurately estimates the scattered fields over a wide range of conductivity contrasts and scatterer sizes and within the frequency band of a subsurface electromagnetic experiment. Furthermore, the approximation has the efficiency of a linear scheme such as the Born approximation. For inversion, we employ a Gauss-Newton search technique to minimize a quadratic cost function with penalty on a spatial functional of the sought conductivity model. We derive an approximate form of the Jacobian matrix directly from the nonlinear scattering approximation. A conductivity model is rendered by repeated linear inversion steps within range constraints that help reduce nonuniqueness in the minimization of the cost function. Synthetic examples of inversion demonstrate that the nonlinear approximation reduces considerably the execution time required to invert a large number of unknowns using a large number of electromagnetic data.

Principles of spatial surface electric field filtering in magnetotellurics; electromagnetic array profiling (EMAP)

Electromagnetic Array Profiling (EMAP) is an adaptation of magnetotellurics to overcome spatial aliasing effects associated with the sampling of the surface electric field. Undersampling lateral electric field variations can result in misleading geoelectric interpretations of the subsurface, particularly under the common presence of static distortion. In the EMAP field procedure, electric dipoles are positioned end‐to‐end along a continuous survey path; this configuration, in addition to reducing aliasing effects, lends itself to low‐pass filtering of the lateral electric field variations. We show that lengthening an electric dipole can reduce the static effect due to confined resistivity anomalies smaller than a dipole length. This modification of the sensor characteristics involves a spatial filtering process in which the cutoff wavenumber is inversely proportional to the length of the dipole. However, excessively long dipoles may not prove appropriate at high frequencies where the objective is to sense...

Numerical Simulation of Shale-Gas Production: From Pore-Scale Modeling of Slip-Flow, Knudsen Diffusion, and Langmuir Desorption to Reservoir Modeling of Compressible Fluid

We combine a new pore-scale model with a reservoir simulation algorithm to predict gas production in gas-bearing shales. It includes an iterative verification method of surface mass balance to ensure real-time desorption-adsorption equilibrium with gas production. The pore-scale model quantifies macroscopic petrophysical properties of formations using an algorithm of gas transport in porous media that simultaneously considers the effects of no-slip and slip flow, Knudsen diffusion, and Langmuir desorption. Subsequently, the reservoir model populates petrophysical properties derived from the pore-scale analysis at every numerical grid and at each time-step to calculate the production history and pressure distribution in the reservoir. This approach examines the contribution of different transport processes (i.e. advective flow, Knudsen diffusion, and desorption) to quantify their corresponding contributions to overall flow. Previously, we showed that slip flow and Knudsen diffusion play a significant role in explaining the higher-than-expected permeability observed in shale-gas formations with pore-throat sizes in the range of nanometers. It is shown that Langmuir desorption from organic-matter surfaces is important in the calculation of stored gas in gas-bearing shales. Modeling results show that gas desorption maintains the reservoir pressure via the supply of gas. In comparison to conventional reservoir descriptions, the contributions of slip flow and Knudsen diffusion increase the apparent permeability of the reservoir while gas production takes place. The effects of both mechanisms explain the higher-than-expected gas production rates commonly observed in these formations. Introduction Fossil fuels are perhaps the most significant sources of fossil fuel currently available. Despite increasing environmental consciousness that aims to diversify energy sources to mitigate global climate change, fossil fuels will continue to supply the majority of energy consumption throughout this century. Natural gas is the cleanest fossil fuel, but as a finite source, more challenging reservoirs must be explored to meet the growing world demand (Ground Water Protection Council and ALL Consulting 2009). In this situation, gas-bearing shale strata are important energy resources in North America and they will become increasingly important all over the world. Nevertheless, gas production in these formations has remained mostly unpredictable, which has caused their categorization as unconventional gas reserves (Passey et al. 2010). Determining the petrophysical characteristics of a reservoir (e.g. permeability) and predicting production of gas-bearing shales is essential for economical assessments prior to field development. However, there is no standard model available to predict gas production from shale strata. Existing empirical and simplified models do not predict gas production accurately even though the production is usually higher than predictions made with conventional models (i.e. Darcy’s equation) (Lu et al. 1995; Javadpour et al. 2007; Gault and Stotts 2007; Javadpour 2009; Sondergeld, et al. 2010; Ambrose et al. 2010; Kale et al. 2010; Sondergeld, et al. 2010; Freeman et al. 2010; Shabro et al. 2011). Recently, pore-scale characterization of shale formations using Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) and Atomic Force Microscopy (AFM) methods has advanced our understanding of shale morphologies and physical mechanisms behind gas production in these formations (Ambrose et al. 2010; Sondergeld et al. 2010; Javadpour 2009). At the same time, we have developed a pore-scale method to (1) analyze the imaged pore space; (2) characterize slip and no-slip flows, Knudsen diffusion and Langmuir desorption-adsorption; and (3) calculate apparent petrophysical properties (Shabro et al. 2009; Shabro et al. 2011). Apparent permeability depends on the smoothness of mineral grain surfaces, pressure, temperature, and gas molar mass as well as on pore-scale morphology. Gas and surface types, pressure, and temperature also control Langmuir desorption.

Trace-based and geostatistical inversion of 3-D seismic data for thin-sand delineation; an application in San Jorge Basin, Argentina

Argentina’s San Jorge Basin, which straddles the southern provinces of Chubut and Santa Cruz in the heart of Patagonia, has been producing hydrocarbons since 1907. The region currently accounts for 32% of the country’s production. The existence and early geologic evolution of the basin is due to the same rift process responsible for the opening of the Atlantic Ocean in early Jurassic times. Extensive direct faulting and local erosion accompanied the rift evolution, thereby facilitating the accumulation of chiefly nonmarine terrigenous sediments well into the early Cretaceous. At this point, Andean tectonism became a major source of pyroclastic concentration in the sedimentary column; it was also responsible for pervasive batholitic intrusions. Clastic deposition in the hydrocarbon‐producing zone is characterized by thick shale laminations of lacustrine and floodplain origin, interspersed with much thinner and laterally sparse sand bodies (the hydrocarbon reservoirs).

A two-step linear inversion of two-dimensional electrical conductivity

We introduce a novel approach to the inversion of two-dimensional distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation (see J. Geophys. Res., vol.98, no.B2, p.1759, 1993), which sums in a simple analytical expression an infinitude of terms contained in the Neumann series expansion of the electric field resulting from multiple scattering. Comparisons of numerical performance against a finite-difference code show that the extended Born approximation remains accurate up to conductivity contrasts of 1:1000 with respect to a homogeneous background, even with large-size scatterers and for a wide frequency range. Moreover, the new approximation is nearly as computationally efficient as the first-order Born approximation. Most importantly, we show that the mathematical form of the extended Born approximation allows one to express the nonlinear inversion of electromagnetic fields scattered by a line source as the sequential solution of two Fredholm integral equations. We compare this procedure against a more conventional iterative approach applied to a limited-angle tomography experiment. Our numerical tests show superior CPU time performance of the two-step linear inversion process. >

Two-dimensional high-accuracy simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp finite element method

We simulate electromagnetic (EM) measurements acquired with a logging‐while‐drilling (LWD) instrument in a borehole environment. The measurements are used to assess electrical properties of rock formations. Logging instruments as well as rock formation properties are assumed to exhibit axial symmetry around the axis of a vertical borehole. The simulations are performed with a self‐adaptive goal‐oriented

Efficient Numerical Simulation of Axisymmetric Electromagnetic Induction Measurements Using a High-Order Generalized Extended Born Approximation

hp

A parallel direct solver for the self-adaptive hp Finite Element Method

‐finite element method that delivers exponential convergence rates in terms of the quantity of interest (for example, the difference in the electrical current measured at two receiver antennas) against the CPU time. Goal‐oriented adaptivity allows for accurate approximations of the quantity of interest without the need to obtain an accurate solution in the entire computational domain. In particular, goal‐oriented

Forecasting Gas Production in Organic Shale with the Combined Numerical Simulation of Gas Diffusion in Kerogen, Langmuir Desorption from Kerogen Surfaces, and Advection in Nanopores

hp

Linear iterative refinement method for the rapid simulation of borehole nuclear measurements: Part I — Vertical wells

‐adaptivity becomes essential to simulating LWD instruments, since it reduces the computational cost by several orders of magnitude with respect to the global energy‐norm‐based