Integrating Mathematical Optimization and Decision Making in Intelligent Fields

In this paper a decision-making approach that can be applied to problems that are relevant to the oil and gas industry is presented. This methodology is supported by state-of-the-art mathematical optimization algorithms, and is based on the formal integration of the decisions in question with well-studied optimization procedures. The integration of the methodology with the application adds to its robustness. Two different types of problems are formulated and solved. The first kind is based on deciding which wells have to be shut in during a given production interval whilst simultaneously optimizing the controls for each selected well. The second category involves deciding for a group of wells which ones have to be injectors or producers, and at the same time searching for optimal well locations. In all the results obtained we can systematically see that the set of decisions proposed by the integrated approach mean substantial improvement in field production. For example, in the first class of problems studied, the production oil target is satisfied, and up to 50 percent of produced water is saved with respect to the reference case. The huge amount of information available, for example, in Intelligent/Smart Fields or Closed-Loop Reservoir Management can be utilized for rigorously making solid decisions. In this work we put an emphasis on integration of real-life decisions with a realistic simulation-based mathematical optimization framework. This framework can be also useful for establishing a common language for decision makers and researchers within a given organization, and as a consequence endowing the decision-making process with agility and robustness. It should be stressed that ultimately it is human interpretation and intuition that drives the making of crucial decisions. Automated tools should be understood as an additional (and hopefully valuable) source of information for making these important decisions.

[1]  Louis J. Durlofsky,et al.  A New Well-Pattern-Optimization Procedure for Large-Scale Field Development , 2011 .

[2]  Efstratios N. Pistikopoulos,et al.  A mixed integer optimization formulation for the well scheduling problem on petroleum fields , 2005, Computers and Chemical Engineering.

[3]  Reidar Brumer Bratvold,et al.  Making Good Decisions , 2010 .

[4]  Michael Lev Litvak,et al.  Prudhoe Bay E-Field Production Optimization System Based on Integrated Reservoir and Facility Simulation , 2002 .

[5]  Luís N. Vicente,et al.  A particle swarm pattern search method for bound constrained global optimization , 2007, J. Glob. Optim..

[6]  Ignacio E. Grossmann,et al.  An outer-approximation algorithm for a class of mixed-integer nonlinear programs , 1986, Math. Program..

[7]  M. Powell The BOBYQA algorithm for bound constrained optimization without derivatives , 2009 .

[8]  Todd D. Plantenga,et al.  HOPSPACK 2.0 user manual. , 2009 .

[9]  Huifen Chen,et al.  Stochastic root finding via retrospective approximation , 2001 .

[10]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[11]  Charles Audet,et al.  Pattern Search Algorithms for Mixed Variable Programming , 2000, SIAM J. Optim..

[12]  Tamara G. Kolda,et al.  Asynchronous Parallel Generating Set Search for Linearly Constrained Optimization , 2008, SIAM J. Sci. Comput..

[13]  Emad Ahmed Elrafie,et al.  Overview of Saudi Aramco's Intelligent Field Program , 2010 .

[14]  Reidar Brumer Bratvold,et al.  Value of Information in the Oil and Gas Industry: Past, Present, and Future , 2009 .

[15]  Tapan Mukerji,et al.  A derivative-free approach for the estimation of porosity and permeability using time-lapse seismic and production data , 2010 .

[16]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[17]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[18]  Jan Dirk Jansen,et al.  Dynamic Optimization of Waterflooding With Smart Wells Using Optimal Control Theory , 2004 .

[19]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[20]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[21]  Thomas Stützle,et al.  Ant Colony Optimization Theory , 2004 .

[22]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[23]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[24]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[25]  Katya Scheinberg,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[26]  Louis J. Durlofsky,et al.  Optimal Well Placement Under Uncertainty Using a Retrospective Optimization Framework , 2012 .

[27]  P.J.P. Egberts,et al.  Optimal waterflood design using the adjoint method , 2007 .

[28]  Michael Andrew Christie,et al.  Application of Particle Swarms for History Matching in the Brugge Reservoir , 2010 .

[29]  Mrinal K. Sen,et al.  On optimization algorithms for the reservoir oil well placement problem , 2006 .

[30]  L. Durlofsky,et al.  Production Optimization with Adjoint Models under Nonlinear Control-State Path Inequality Constraints , 2008 .

[31]  Louis J. Durlofsky,et al.  Optimization of Nonconventional Well Type, Location, and Trajectory , 2003 .

[32]  L. Durlofsky,et al.  Application of a particle swarm optimization algorithm for determining optimum well location and type , 2010 .

[33]  Frans G. Van Den Berg,et al.  Business value from intelligent fields , 2010 .

[34]  Katya Scheinberg,et al.  A derivative free optimization algorithm in practice , 1998 .

[35]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[36]  R. Bratvold,et al.  I would rather be vaguely right than precisely wrong: A new approach to decision making in the petroleum exploration and production industry , 2008 .

[37]  J. Jansen,et al.  Closed-loop reservoir management , 2005 .

[38]  B. Foss,et al.  Nonlinear Output Constraints Handling for Production Optimization of Oil Reservoirs , 2010 .

[39]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[40]  O. Pironneau On optimum design in fluid mechanics , 1974 .

[41]  Roman B. Statnikov,et al.  Multicriteria Optimization and Engineering , 1995 .

[42]  Tapan Mukerji,et al.  Derivative-Free Optimization for Oil Field Operations , 2011, Computational Optimization and Applications in Engineering and Industry.

[43]  L. Durlofsky,et al.  Optimization of nonconventional wells under uncertainty using statistical proxies , 2006 .

[44]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[45]  Martin Grötschel,et al.  Solution of large-scale symmetric travelling salesman problems , 1991, Math. Program..

[46]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[47]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[48]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[49]  Oliver Kramer,et al.  Derivative-Free Optimization , 2011, Computational Optimization, Methods and Algorithms.

[50]  P. Toint,et al.  A brief history of filter methods. , 2007 .

[51]  Louis J. Durlofsky,et al.  Application of derivative-free methodologies to generally constrained oil production optimisation problems , 2011, Int. J. Math. Model. Numer. Optimisation.

[52]  Ronald A. Howard,et al.  Readings on the Principles and Applications of Decision Analysis , 1989 .

[53]  Omprakash K. Gupta,et al.  Branch and Bound Experiments in Convex Nonlinear Integer Programming , 1985 .

[54]  Lalit M. Patnaik,et al.  Adaptive probabilities of crossover and mutation in genetic algorithms , 1994, IEEE Trans. Syst. Man Cybern..

[55]  Charles Audet,et al.  A MADS Algorithm with a Progressive Barrier for Derivative-Free Nonlinear Programming , 2007 .

[56]  Pengju Wang,et al.  Development and applications of production optimization techniques for petroleum fields , 2003 .

[57]  Charles Audet,et al.  Analysis of Generalized Pattern Searches , 2000, SIAM J. Optim..

[58]  A. Cominelli,et al.  Production Optimization under Constraints Using Adjoint Gradients , 2006 .

[59]  Tamara G. Kolda,et al.  Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods , 2003, SIAM Rev..

[60]  Tor Arne Johansen,et al.  Real-Time Production Optimization of Oil and Gas Production Systems: A Technology Survey , 2007 .

[61]  Bjarne A. Foss,et al.  Oil production optimization - A piecewise linear model, solved with two decomposition strategies , 2010, Comput. Chem. Eng..

[62]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[63]  G. Seber Multivariate observations / G.A.F. Seber , 1983 .

[64]  Robert T. Clemen,et al.  Making Hard Decisions with Decisiontools Suite , 2000 .

[65]  Ali Ahmed Jama,et al.  Intelligent Field Centers (IFCs): Integrating People, Processes and Technologies to Optimally Manage Giant Fields , 2010 .

[66]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[67]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[68]  L. Durlofsky,et al.  Efficient real-time reservoir management using adjoint-based optimal control and model updating , 2006 .

[69]  Gérard Cornuéjols,et al.  An algorithmic framework for convex mixed integer nonlinear programs , 2008, Discret. Optim..

[70]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[71]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[72]  David K. Smith Theory of Linear and Integer Programming , 1987 .

[73]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.