# Poster Session and Reception

Tuesday, May 12, 2015 - 4:00pm - 6:00pm

Lind 400

**Inverse Acoustic Scattering with Reduced Data**

Jacob Rezac (University of Delaware)

We consider the problem of detecting three-dimensional inclusions from quasi-backscattering far field data generated by an incident field of time-harmonic fixed frequency plane waves modeled with the Born approximation. We assume only partial far field data is known and use a sampling-type method to reconstruct small obstacles. In particular, at the location of a device transmitting an incident wave, we assume far field data is collected only along a line extending a short distance from the transmitting device.**3D Fracture Propagation Modeling Using Phase Field**

Sanghyun Lee (The University of Texas at Austin)

This work presents recent progress in phase-field-based fracture modeling in heterogeneous porous media. We develop robust numerical algorithms that can be used for three-dimensional applications. Specially, we present a Newton loop that combines a primal-dual active set method (required for treating the crack irreversibility)for pressurized fractures and couple this loop with a pressure-diffraction equation in order to solve for fluid flow in the porous media and the fracture.

The resulting algorithm splits geomechanics and flow computations in terms of a fixed-stress approach. Several numerical examples considering pressurized fractures in heterogeneous media and fluid-filled fracture propagation in porous media substantiate our developments.

This is a joint work with A. Mikelic, M.F. Wheeler, and T. Wick.**Modeling Material Failure and Rock Joint Using the Material-Point Method**

Ling Xu (University of Notre Dame)

Rock fractures upon a large explosive loading. Joints are often seen in rock. Thus there is an inherent need to include these features when performing analyses on the safety of underground structures such as tunnels. In this work, we studied the damage near an tunnel subjected to an explosion at some distance. A numerical model is developed, based on an elastic-decohesive constitutive equation. The Material-Point method is applied to simulate such a process.

Co-authors: Howard Schreyer, Deborah Sulsky**Numerical Methods for Time Domain Two-dimensional Wave-structure Interaction**

Tonatiuh Sanchez-Vizuet (University of Delaware)

The interaction between an acoustic wave on an unbuounded domain and a linearly elastic bounded solid is studied with boundary integral equation methods. In the Laplace domain the system is modeled as an exterior problem for the Laplace resolvent equation and an interior problem for the Navier-Lam\'{e} resolvent equation communicating through coupling conditions at the boundary of the solid. Well posendess is shown via an equivalent non standard transmission problem. For problems with constant elastic coefficients, third order space discretization is achieved on a staggered grid in both elastic and acoustic domains by the deltaBEM method. For problems with variable elastic coefficients a Boundary Element-Finite Element symmetric coupling scheme is applied. In both cases, time marching is done via Convolution Quadrature.**Towards Non-destructive Testing of Delamination**

Irene de Teresa Trueba (University of Delaware)

I will present some results on the scattering of linear acoustic waves in the presence of a small delamination (opening) in the interface between two different materials. The concept of approximated transmission conditions is used to treat the problem in a way that avoids meshing thin flaws, so the numerical implementation becomes much less expensive.

In particular, in the first approximation, the opening is represented by the portion of the interface where the fields satisfy appropriate jump conditions.

These results are done for the case of the direct scattering problem, and the obtained approximated model will be used to develop the Linear Sampling Method to solve the inverse problem of reconstructing the location of the delamination.**Hybrid Pore-scale Modeling with Three Scales**

Malgorzata Peszynska (Oregon State University)

We combine two methodologies of pore-scale modeling of flow and transport: continuum models and network models. We have shown that the first can work with real porescale data, and can quite accurately predict the Darcy scale conductivities, and their change due, e.g., to reactive transport, phase transitions, bioclogging, and/or coal matrix swelling, but requires substantial computational effort which is prohibitive for transient simulations. The second has much smaller complexity, but can only represent the pore-scale geometry in a very coarse way, with large uncertainties. We set up a hierarchy of continuum to network to Darcy scales for efficient three-scale dynamically correcting models of coupled flow and transport, and show examples of bioclogging, sandstone, and proppant geometries.**Finite Element Formulation of Mode-III Brittle Fracture with Surface Tension Excess Property**

Mallikarjunaiah Muddamallappa (Texas A & M University)

In this work, we study a finite element formulation of mode-III brittle fracture in a linear, homogeneous, elastic body. The modified continuum-mechanics model incorporates a curvature dependent surface tension on the crack-surface that give rise to a linearized jump momentum balance (JMB) crack-face boundary condition containing higher order tangential derivatives. For a numerically stable finite element implementation, we propose a reformulation of the JMB using a boundary Green’s function and Hilbert’s transform resulting in a Fredholm second kind integral equation for the crack-edge Neumann data. The obtained numerical results indicate bounded crack-tip stresses and a cusp-shaped crack-surface opening profile with a sharp crack-tip.

*This is a joint work with Lauren Ferguson (AFRL) and Jay Walton (Texas A&M University).**3D Simulator of Elasticity Equation for Non-planar Hydraulic Fractures**

Sonia Mogilevskaya (University of Minnesota, Twin Cities)

Realistic modeling of hydraulic fracturing processes requires an advanced computational tool that is capable of accurately predicting the trajectories of non-planar hydraulic fractures near the wellbore Such tool must be based on a fully three-dimensional (3D) solid-fluid coupled model in which elasticity equation is an integral part. This work presents the Boundary Element-based algorithm for the analysis of multiple non-planar 3D cracks.**Viscoplastic Flow in a Hele-Shaw Cell**

Duncan Hewitt (University of British Columbia)

Viscoplastic fluids are characterized by a yield stress below which they do not deform. The flow of viscoplastic fluid down slender conduits or through porous media has application in a range of industrial and geophysical settings, from the plumbing of mud volcanoes to the transport of proppant slurries in hydraulic fracturing. A theoretical and numerical study of viscoplastic flow in a Hele-Shaw cell in the presence of various kinds of obstructions is presented. Flow around isolated blockages in the cell is investigated, together with flow past step-wise contractions or expansions in the width of the cell, all within the simplifying Hele-Shaw approximation of a narrow gap. It is shown that the yield stress of the fluid leads to stagnant regions in the vicinity of the obstruction, while the length scale over which the flow is affected by the obstruction increases as the yield stress is increased. This work is extended to consider flow in cells with randomly roughened walls, and it is shown that constructive interference of local contractions and expansions in this case leads to a pronounced channellization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the paths of the channels in the limit of large yield stress, or, equivalently, weak flow.**Why Fracking Works? And Why Not Well Enough?**

Zdenek Bazant (Northwestern University)Marco Salviato (Northwestern University)

The advances in hydraulic fracturing technology have been astonishing. Although many aspects of the technology are well understood, the topology, geometry, and evolution of the crack system remain an enigma. These aspects have to be clarified if the current rate gas recovery from the shale strata, which is only about 5% to 15%, is ever to be exceeded.**CaMI Monitoring Field Research Station**

Amin Saeedfar (CMC Research Institutes)

The Containment and Monitoring Institute (CaMI) of CMC Research Institutes, Inc and the University of Calgary are developing a joint project to build a Field Research Station for research into monitoring technologies for containment and conformance of subsurface fluids, particularly CO2. The field research station is a platform for development and performance validation of technologies intended for measurement, monitoring and verification of CO2 storage. Outcomes of the research will also have adjacent applications such as assessing and monitoring cap rock integrity in oil sands during production and assessing fugitive emissions in shale gas production. CaMI is investing $10 million in capital funding into this project. We are inviting industry to join in this collaborative development with participation offered via sponsorship, contract research and development projects, facility rental and through technology company creation and support. The facility will be used for education, graduate student and industry professional training, as well as public outreach and engagement activities.**Modeling Flow and Fracture Propagation in Porous Fractured Media by Finite Element Method**

Ahmad Pouya (École Nationale des Ponts-et-Chaussées)

Mathematical and numerical developments are presented for modeling flow and fracture propagation in fractured porous media by Finite Element Method. Weak formulation for flow in a fractured porous matrix, integrating the discontinuity of fluid velocity across the fracture, is established. The fracture propagation is modeled by an interface damage processes using the cohesive zone model extended to mode I and II loadings. The hydromechanical coupling is modeled by an iterative process between mechanical and hydraulic modules of the numerical code*Porofis*. The numerical method obtained in this way allows simulating fracture propagation with specific instability phenomena like steak-slip or crack kinking, and also hydraulic fracture process with residual fracture aperture and well production enhancement.**Inverse Source Problems for Enhanced Oil Recovery by Maximization of Wave Motion in Reservoirs**

Loukas Kallivokas (The University of Texas at Austin)

We discuss a methodology for computing the optimal spatio-temporal characteristics of surface wave sources used for focusing the emitted wave energy to a targeted subsurface formation. The wave energy is delivered to the formation to enhance the mobility of oil particles trapped in its pore space. We formulate the associated wave propagation problem for heterogeneous, semi-infinite media. We report the results of our numerical experiments attesting to the methodology's ability to specify the spatio-temporal description of sources that maximize the wave energy delivery. We also perform reliability analysis to assess the effect the imperfect knowledge of formation properties has on the energy focusing.**On the Elastic-wave Imaging and Interfacial Characterization of Heterogeneous Fractures**

Bojan Guzina (University of Minnesota, Twin Cities)Fatemeh Pourahmadian (University of Minnesota, Twin Cities)Roman Tokmashev (University of Minnesota, Twin Cities)

Identification of the spatial distribution and temporal variation of k s and k n has recently come under the spotlight [2] owing to: i) its potential role as an early indicator of interfacial instability and failure, and ii) its relevance to deciphering the mechanism of shallow earthquakes. In hydraulic fracturing, imaging k s/k n in the fracking process is the subject of mounting attention [1,4] due to its potential application in: i) imaging the proppant injection process, ii) discriminating between newly created, old, and proppant-filled fractures, and iii) monitoring the evolution of hydraulic conductivity of an induced fracture network and thus assessing the success of stimulation strategies.