C. Jeong

Optimization of sources for focusing wave energy in targeted formations

We discuss a numerical approach for identifying the surface excitation that is necessary to maximize the response of a targeted subsurface formation. The motivation stems from observations in the aftermath of earthquakes, and from limited field experiments, whereby increased oil production rates were recorded and were solely attributable to the induced reservoir shaking. The observations suggest that focusing wave energy to the reservoir could serve as an effective low-cost enhanced oil recovery method. In this paper, we report on a general method that allows the determination of the source excitation, when provided with a desired maximization outcome at the targeted formation. We discuss, for example, how to construct the excitation that will maximize the kinetic energy in the target zone, while keeping silent the neighbouring zones. To this end, we cast the problem as an inverse-source problem, and use a partial-differential-equation-constrained optimization approach to arrive at an optimized source signal. We seek to satisfy stationarity of an augmented functional, which formally leads to a triplet of state, adjoint and control problems. We use finite elements to resolve the state and adjoint problems, and an iterative scheme to satisfy the control problem to converge to the sought source signal. We report on one-dimensional numerical experiments in the time domain involving a layered medium of semi-infinite extent. The numerical results show that the targeted formations kinetic energy resulting from an optimized wave source could be several times greater than the one resulting from a blind source choice, and could overcome the mobility threshold of entrapped reservoir oil.

Estimation of oil production rates in reservoirs exposed to focused vibrational energy

This work was partially supported by an Academic Excellence Alliance grant between King Abdullah University of Science andTechnology (KAUST) and the University of Texas at Austin and by the Society of Petroleum Engineers STAR Fellowship and theWilliam S. Livingston Fellowship at the University of Texas at Austin awarded to the first author. The travel of the first author to the19th SPE Improved Oil Recovery Symposium is supported by the Society of Petroleum Engineers Faculty Enhancement Travel Grant.This support is gratefully acknowledged.

NEAR-SURFACE LOCALIZATION AND SHAPE IDENTIFICATION OF A SCATTERER EMBEDDED IN A HALFPLANE USING SCALAR WAVES

We discuss the inverse problem associated with the identification of the location and shape of a scatterer fully embedded in a homogeneous halfplane, using scant surficial measurements of its response to probing scalar waves. The typical applications arise in soils under shear (SH) waves (antiplane motion), or in acoustic fluids under pressure waves. Accordingly, we use measurements of either the Dirichlet-type (displacements), or of the Neumann-type (fluid velocities), to steer the localization and detection processes, targeting rigid and sound-hard objects, respectively. The computational approach for localizing single targets is based on partial-differential-equation-constrained optimization ideas, extending our recent work from the full-1 to the half-plane case. To improve on the ability of the optimizer to converge to the true shape and location we employ an amplitude-based misfit functional, and embed the inversion process within a frequency- and directionality-continuation scheme, which seem to alleviate solution multiplicity. We use the apparatus of total differentiation to resolve the targets evolving shape during inversion iterations over the shape parameters, a la.2,3 We report numerical results betraying algorithmic robustness for both the SH and acoustic cases, and for a variety of targets, ranging from circular and elliptical, to potato-, and kite-shaped scatterers.

An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.

A Time-Domain Substructuring Method for Dynamic Soil Structure Interaction Analysis of Arbitrarily Shaped Foundation Systems on Heterogeneous Media

Soil-structure-interaction (SSI) effects are typically non-negligible for structures that possess one or more of the following attributes: a massive super-structure and/or foundation elements, a large uninterrupted footprint or interface with the soil domain, and a soft, supporting soil medium. The SSI effects comprise the dynamic interaction between: (1) the far-field soil domain; (2) the (potentially inelastically behaving) near-field soil domain; and (3) the structure. The far-field domain is semi-infinite unless the bedrock or a rock outcrop is very near and, thus, it can be represented with a reduced-order model in the form of impedance functions. The use of impedance functions in SSI analyses allows the computational cost to be reduced by several orders of magnitude without compromising the solution accuracy. Moreover, it is now possible to obtain time-domain representations of the inherently frequency-dependent impedance functions. As such, accurate nonlinear time-history analyses of problems that involve SSI effects can be now carried out in a computationally efficient manner. However, the current catalogue of impedance functions is limited to simple foundation shapes and soil profiles. In the present study, we provide a systematic approach with which impedance functions for arbitrarily shaped foundations resting on (or embedded in) heterogeneous soil domains can be obtained. In order to obtain the impedance functions, forward wave propagation analyses are carried out on a high-performance computing platform. The finite element method is employed to account for the arbitrary heterogeneity of soil and for different foundation types and geometries. In the forward analyses, the semi infinite remote boundaries are treated with Perfectly Matched Layers (PML) which, to date, are considered to offer the best Wave-Absorbing Boundary Condition (WABC) representation. Practical examples are provided that display pronounced variations in impedance functions with respect to frequency, which illustrate and quantify the importance of using frequency-dependent impedance functions in SSI analyses.

Computation of acoustic wave responses due to moving underwater acoustic sources in complex underwater environments using a spectral element method

This work presents a new numerical approach for computing underwater acoustic wave responses due to moving underwater acoustic sources in complex underwater environments using a Spectral Element Method (SEM). The SEM is similar to the Finite Element Method (FEM), but uses a higher-order shape function with Gauss-Lobatto-Legendre quadrature, naturally creating a diagonal mass matrix. Thus, we can use fast explicit time integration, taking advantage of a diagonal mass matrix, without compromising accuracy. Therefore, the SEM is much more suitable for large-scale parallel 3D time domain wave analyses than the conventional FEM. In our numerical experiments, we used a large-scale parallel SEM wave simulator, SPECFEM3D. We verified the SEM solution of acoustic (fluid pressure) waves in a 3D acoustic fluid setting of an infinite extent, induced by a moving point source, by using its analytical counterpart. Numerical experiments showed that our tool accurately accommodates wave behavior at fluid-solid interfaces ...

High-resolution spectral-element computation of underwater noises due to offshore piling

Offshore piling has been effective in building foundations of offshore structures, such as wind turbines, bridges, and oil rigs. Despite such merits, underwater noise due to offshore piling is considered to be its critical setback. Pile driving creates a high-level underwater sound that harms marine ecosystems. There have been studies that successfully predicted these noises by using numerical methods, for example, Finite Element Method (FEM). However, there has been no FEM study that considers anti-symmetric irregular domains and complex bathymetry to compute underwater noises in the high-frequency range (>1000 Hz) due to expensive computational costs of FEM. To bridge the gap, this work attempts to explore a novel, powerful simulation tool to efficiently obtain offshore piling noises in complex settings and in the high-frequency range. We adopted and modified an open-source large-scale parallel Spectral Element Method (SEM) wave simulator, SPECFEM3D. SEM is known to be much more efficient than FEM for w...

Reconstruction of moving acoustic sources in heterogeneous elastic solid

A novel computational framework for reconstructing spatial and temporal profiles of moving acoustic sources from wave responses measured at sparsely distributes sensors is introduced in this paper. This method can be applied to a broad range of acoustic-source inversion (ASI) problems for heterogeneous, complex-shaped coupled dynamic systems. The finite element method (FEM) is used to obtain wave response solutions due guessed moving sources. An adjoint-gradient based optimization technique iteratively improves the guesses so that the guessed moving sources converge on the actual moving sources. To reconstruct acoustic source profiles without a-priori knowledge of sources, we will employ high-resolution discretization of source functions in space and time. Because of such dense discretization, the order of magnitude of number of inversion parameters could range from millions to billions. Numerical experiments prove the robustness of this method by reconstructing spatial and temporal profiles of multiple dynamic moving body forces in a one-dimensional heterogeneous solid bar. The sources create stress waves propagating through the bar. The guessed source functions are spatially discretized by using linear shape functions with an element size of 1m at discrete times with a time step of 0.001s. Thus, the total number of control parameters in this example is 100,000 (i.e., 100 (in space) by 1000 (in time)). The convergence toward the target in the numerical examples is excellent, reconstructing the spatial and temporal footprints of the sources.