Drosos Kourounis

Shape-from-Operator: Recovering Shapes from Intrinsic Operators

We formulate the problem of shape‐from‐operator (SfO), recovering an embedding of a mesh from intrinsic operators defined through the discrete metric (edge lengths). Particularly interesting instances of our SfO problem include: shape‐from‐Laplacian, allowing to transfer style between shapes; shape‐from‐difference operator, used to synthesize shape analogies; and shape‐from‐eigenvectors, allowing to generate ‘intrinsic averages’ of shape collections. Numerically, we approach the SfO problem by splitting it into two optimization sub‐problems: metric‐from‐operator (reconstruction of the discrete metric from the intrinsic operator) and embedding‐from‐metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem). We study numerical properties of our problem, exemplify it on several applications, and discuss its imitations.

On the solution of boundary value problems using spheroidal eigenvectors

In the present work an attempt is made to construct the Navier vector functions in spheroidal geometry in a form convenient for the solution of boundary value problems. The complexity of the problem is moderated by exploiting general properties of the vector operators, the underlying Helmholtz equation kernel functions as well as the symmetries of the problem. Finally, the proposed analysis is illustrated in the case of electromagnetic and elastic fields.

Needles: toward large-scale genomic prediction with marker-by-environment interaction

Genomic prediction relies on genotypic marker information to predict the agronomic performance of future hybrid breeds based on trial records. Because the effect of markers may vary substantially under the influence of different environmental conditions, marker-by-environment interaction effects have to be taken into account. However, this may lead to a dramatic increase in the computational resources needed for analyzing large-scale trial data. A high-performance computing solution, called Needles, is presented for handling such data sets. Needles is tailored to the particular properties of the underlying algebraic framework by exploiting a sparse matrix formalism where suited and by utilizing distributed computing techniques to enable the use of a dedicated computing cluster. It is demonstrated that large-scale analyses can be performed within reasonable time frames with this framework. Moreover, by analyzing simulated trial data, it is shown that the effects of markers with a high environmental interaction can be predicted more accurately when more records per environment are available in the training data. The availability of such data and their analysis with Needles also may lead to the discovery of highly contributing QTL in specific environmental conditions. Such a framework thus opens the path for plant breeders to select crops based on these QTL, resulting in hybrid lines with optimized agronomic performance in specific environmental conditions.

Results of the First Norne Field Case on History Matching and Recovery Optimization Using Production and 4D Seismic Data

In preparation for the SPE Applied Technology Workshop, ``Use of 4D seismic and production data for history matching and optimization – application to Norne (Norway)’’ held in Trondheim 14-16 June 2011, a unique test case (Norne E-segment) study based on real field data of a brown field offshore Norway was organized to evaluate and compare mathematical methods for history matching as well as methods on optimal production strategy and/or enhanced oil recovery. The integrated data set provided an opportunity to discuss emerging and classical history matching and optimization methods after being tested using real field data. The participants of this comparative case study were expected to come up with a history matched model preferably using an integration of production and time-lapse seismic data and with an optimal production strategy for the remaining recoverable resources for the future period. Participants were allowed to suggest techniques to enhance recovery. Taking into account that the Norne benchmark case is a case study based on real data and no one exactly knows the true answer, participants and delegates were encouraged to discuss the methods, results and challenges during the course of the workshop, and thus in this case there are no winners or losers. Everyone who participated gained experience during the course of the exercise. Participants were asked to history match the model until the end of 2004 and optimally predict the production (oil, water and gas rates) performance until the end of 2008. Participants were from different universities in collaboration with other research organizations namely Stanford University in collaboration with IBM and Chevron, TU Delft in collaboration with TNO, Texas A&M University, and NTNU in collaboration with Sintef. This paper summarizes the presented results from these groups and the outcome of the discussion of the workshop delegates. Introduction The Center of Integrated Operation in petroleum industry at NTNU (IO Center) in conjunction with the Society of Petroleum Engineers (SPE) organized an applied technology workshop about the use of real data from the Norne Field. The workshop attracted 80 delegates and international speakers from more than ten countries all over the world, namely the United States of America, Saudi Arabia, the Netherlands, Brazil, Denmark, Angola, Nigeria, the United Kingdom, Russia, India, and Norway. The uniqueness of this workshop was that it addressed for the first time a comparative case study that uses real field data that includes time lapse seismic data. The purpose of reservoir management is to control operations to maximize both shortand long-term production. This consists of life-cycle optimization based on reservoir model uncertainties together with model updating by production measurements, timelapse seismic data and other available data. Time-lapse seismic data helps to determine reservoir changes that occur with time and can be used as a new dimension in history matching since they contain information about fluid movement and pressure changes between and beyond the wells. The well production schedule and history are provided for the period from Dec. 1997 to Dec. 2004 and comprise the observation data for the history match. A previous full field calibration was performed by the operator to match the history up until 2003. The reservoir attributes previously calibrated include fault transmissibility multipliers, regional relative permeability parameters, and large-scale (absolute) permeability and porosity heterogeneity using regional and constant multipliers, in total defining a global history match for a single (structural) reservoir description. The exercise was to improve the match and then perform a recovery optimization. In total five groups participated in this exercise and four presented their results during the workshop (see Table 1). The limited number of participants was due to the inaccesability of the Norne database (license limitation) to commercial companies. Table 1: Participants to the case study. University/Company Main Contributors Stanford University, Chevron & IBM Amit Suman, Drosos Kourounis, Tapan Mukerji and Khalid Aziz Delft / TNO Slawomir Szklarz, Lies Peters and Remus Hanea Texas A&M Eric Bhark, Rey Alvaro, Mohan Sharma, Akhil DattaGupta NTNU Ola T. Miljeteig, Richard Rwechungura, Anass Ammar and Jon Kleppe University of Texas Austin Reza Tavakoli and Mary Wheeler** **Did not present the results in the workshop Description of the Norne Field The Norne Field is located in the blocks 6608/10 and 6508/10 on a horst block in the southern part of the Nordland II area in the Norwegian Sea. The rocks within the Norne reservoir are of Late Triassic to Middle Jurassic age. The present geological model consists of five reservoir zones. They are the Garn, Not, Ile, Tofte and Tilje. Oil is mainly found in the Ile and Tofte Formations, and gas in the Garn formation. The sandstones are buried at a depth of 2500-2700 m. The porosity is in the range of 25-30% while permeability varies from 20 to 2500 mD (Steffensen and Karstad, 1995; Osdal et al., 2006). The data consist of near, mid and far stack 3D seismic data acquired in 2001, 2003 and 2004. More information about the Norne field, provided data and first case release are given in Chapter 5 (Rwechungura et al., 2010). The first package includes the E-segment of the Norne field; other benchmarks will include larger parts of the field. Further, the seismic data were also separated to suit the requirement of coverage of the Esegment only. Accordingly, the E-segment was chosen because it has the highest quality seismic data of the entire field. The E-segment of the Norne Field consists of 8733 active grids and 5 wells as of the end of 2004, i.e., 2 injectors and 3 producers. Participants were given a password to access the Norne database through the website www.ipt.ntnu.no/~norne. Description of the Exercise The exercise was defined six months prior to the workshop on History Matching and EOR optimization using both production and time lapse seismic data. This benchmark case considers the time frame from 1997 to 2004 for history matching and 2005 to 2008 for recovery optimization. The actual 2004 simulation model containing all information and properties was given. In addition, production and injection data from 1997 to the end of 2004, and 4D-seismic data for the same period (2003-2001 and 2004-2001) were provided. These data are the basis for the history match performed by participants. The following was the defined workflow:  Download the Eclipse Norne model and import it into their reservoir simulator. The production history for 1997-2004, reports and all required data are given in the website http://www.ipt.ntnu.no/~norne.  Participants were required to history match the model until the end of 2004 and predict the production (oil, water and gas rates) performance until end of 2008.  Using the history matched results from above, create an optimal production strategy for the remaining recoverable resources for the future period. Participants might also suggest techniques to enhance recovery, since significant amount of the recoverable reserves were already produced by the end of October 2008.  The format for the production strategy should contain time, pressure (BHP) or flow rates for the wells.  The following constraints should apply to the strategy: 1. For each injector well the maximum FBHP = 450 bar 2. For each producer well the minimum FBHP = 150 bar 3. For each injector well the maximum water rate = 12000 Sm/day 4. For each producer well the maximum liquid rate = 6000 Sm/day 5. Maximum water-cut = 95% 6. A maximum of two wells can be sidetracked to increase recovery  The following economic parameters were given : Oil price 75 US

Adjoint Methods for Multicomponent Flow Simulation

per bbl Discount rate 10% reference time is January 2005 Cost of water handling/injection 6 US

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

per bbl Cost of gas injection 1.2 US

Enhancing the scalability of selected inversion factorization algorithms in genomic prediction

per Mscf (M = 1000) Cost of a new side-tracked well 65 million US

Towards Parallel Large-Scale Genomic Prediction by Coupling Sparse and Dense Matrix Algebra

Participants could also assume their own parameters related to other EOR methods, e.g., surfactants, polymers and low salinity water flooding.  Discuss and compare results of the achieved recovery factor. General Methods for all the Groups As stated before, four groups presented their results in the applied technology workshop in June 2011 in Trondheim. In this paper we present the details of the work from three groups, namely Texas A&M University, the Norwegian University of Science and Technology (NTNU) and Stanford University. The history matching results from TU Delft were previously published (Szklarz S et al. 2011). They used the Ensemble Kalman Filter (EnKF) method for history matching and did not perform an optimization or an enhanced oil recovery (EOR) strategy; therefore, this paper does report the results from TU Delft. A summary of the methods applied for history matching and recovery optimization by each group is in Table 2. To perform history matching, Stanford University started by dimensionality reduction of the reservoir parameters using their principal component analysis (PCA) and then application of particle swarm optimization (PSO) for history matching. For subsequent optimization they used a derivative free method, Hook Jeeves Direct Search (HJDS). The group from Texas A&M first engaged in multiscale reparameterization of the permeability field using the Grid Connectivity-based Transform (GCT) and calibrated the reduced permeability to production data using a Quasi-Newton method. Thereafter they applied a streamline-based method to integrate the 4D seismic data. Last, the Texas A&M group increased recovery and optimized the production forecast by first draining the oil pockets through side tracking, and by second applying a streamline-based method to equalize the arrival time of fluid phase fronts at all producers. The group from NTNU applied manual history matching techniques that included qualitative

Balanced Graph Partition Refinement using the Graph p-Laplacian

The focus of the present work is on efficient computation of gradients using adjoint methods. In contrast to finite-difference methods, where the number of forward simulations required to estimate the desired derivatives grows linearly with the number of control variables, adjoint techniques provide all the required derivatives of the objective function in a fraction of the computational time of one forward simulation run. However, from an implementation viewpoint they are significantly more involved than, for example, finite-difference methods. This is due to the fact that the computation of gradients through adjoints requires a deep understanding of the simulation code. While the discrete adjoint formulation is most commonly employed in the reservoir simulation community, little is known about the continuous adjoint formulation, which is usually preferred in aerodynamics. Both continuous and discrete adjoint formulations are discussed in this work, and implemented for a compositional reservoir simulator. They are applied to several optimization problems of practical interest and compared with respect to their efficiency and the quality of the gradients they provide. The computed gradients are then forwarded to standard optimization software packages to determine optimal well settings for maximizing any specified objective function, as the net present value.

Toward the Next Generation of Multiperiod Optimal Power Flow Solvers

Starting from the inexact interior-point framework from Curtis, Schenk, and Wachter [SIAM J. Sci. Comput., 32 (2012), pp. 3447--3475], we propose an effective Schur-complement slack-control preconditioner for the full Lagrangian Hessian matrix needed at each Newton iteration. Together they yield a scalable, robust, and highly parallel method for the numerical solution of large-scale nonconvex PDE-constrained optimization problems with inequality constraints. Because it uses the full Hessian matrix, modifying it whenever needed, the method not only is globally convergent, but also converges fast locally. Our preconditioner is not tailored to any particular class of PDEs or constraints, but instead judiciously exploits the sparsity structure of the Hessian. Numerical examples from PDE-constrained optimal control, parameter estimation, and full-waveform inversion demonstrate the robustness and efficiency of the method, even in the presence of active inequality constraints.