Gradient-based Pareto optimal history matching for noisy data of multiple types

The advantages of the simultaneous integration of production and time-lapse seismic data for history matching have been demonstrated in a number of previous studies. Production data provide accurate observations at particular spatial locations (wells), while seismic data enable global, though filtered/noisy, estimates of state variables. In this work, we present an efficient computational tool for bi-objective history matching, in which data misfits for both production and seismic measurements are minimized using an adjoint-gradient approach. This enables us to obtain a set of Pareto optimal solutions defining the optimal trade-off between production and seismic data misfits (which are, to some extent, conflicting). The impact of noise structure and noise level on Pareto optimal solutions is investigated in detail. We discuss the existence of the “best” trade-off solution, or least-conflicting posterior model, which corresponds to the history-matched model that is expected to provide the least-conflicting forecast of future reservoir performance. The overall framework is successfully applied in 2D and 3D compositional simulation problems to provide a single least-conflicting posterior model and, for the 2D case, multiple samples from the posterior distribution using the randomized maximum likelihood method.

[1]  Cor van Kruijsdijk,et al.  Semi-Automatic History Matching Using the Pilot Point Method Including Time-Lapse Seismic Data , 2001 .

[2]  Bjarne A. Foss,et al.  The Norne Field Case - A Unique Comparative Case Study , 2010 .

[3]  Alexandre Boucher,et al.  Applied Geostatistics with SGeMS: A User's Guide , 2009 .

[4]  Akhil Datta-Gupta,et al.  Streamline-based history matching of bottomhole pressure and three-phase production data using a multiscale approach , 2017 .

[5]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[6]  Louis J. Durlofsky,et al.  A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models , 2014, Mathematical Geosciences.

[7]  Baehyun Min,et al.  Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction , 2015, Appl. Soft Comput..

[8]  Olivier Gosselin,et al.  Effect of Scale Dependent Data Correlations in an Integrated History Matching Loop Combining Production Data and 4D Seismic Data , 2003 .

[9]  Roland N. Horne,et al.  A Procedure to Integrate Well Test Data, Reservoir Performance History and 4-D Seismic Information into a Reservoir Description , 1997 .

[10]  T. Mukerji,et al.  Sensitivity Analysis for Joint Inversion of Production and Time-Lapse Seismic Data of Norne Field , 2012 .

[11]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[12]  Lianlin Li,et al.  History Matching With Learned Sparse Dictionaries , 2010 .

[13]  Olivier Gosselin,et al.  History matching using time-lapse seismic , 2004 .

[14]  S. Aanonsen,et al.  History Matching Using Time-lapse Seismic (HUTS) , 2003 .

[15]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[16]  K. Deb,et al.  Understanding knee points in bicriteria problems and their implications as preferred solution principles , 2011 .

[17]  Joe M. Kang,et al.  Pareto-based multi-objective history matching with respect to individual production performance in a heterogeneous reservoir , 2014 .

[18]  Gijs Van Essen,et al.  Adjoint-based History-Matching of Production and Time-lapse Seismic Data , 2012 .

[19]  Víctor Pereyra,et al.  Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems , 2009, Math. Comput. Simul..

[20]  M. J. King,et al.  Streamline-Based Time Lapse Seismic Data Integration Incorporating Pressure and Saturation Effects , 2013 .

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

[22]  Akhil Datta-Gupta,et al.  Handling conflicting multiple objectives using Pareto-based evolutionary algorithm during history matching of reservoir performance , 2015 .

[23]  Olivier Gosselin,et al.  Integrated History-Matching of Production and 4D Seismic Data , 2001 .

[24]  Louis J. Durlofsky,et al.  Comprehensive framework for gradient-based optimization in closed-loop reservoir management , 2015, Computational Geosciences.

[25]  Tor Arne Johansen,et al.  Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter , 2005 .

[26]  Michael Andrew Christie,et al.  Multiple model seismic and production history matching: a case study , 2004 .

[27]  Yifan Zhou,et al.  Parallel general-purpose reservoir simulation with coupledreservoir models and multisegment wells , 2012 .

[28]  Ning Liu,et al.  Inverse Theory for Petroleum Reservoir Characterization and History Matching , 2008 .

[29]  Karl Dunbar Stephen.  Seismic history matching with saturation indicators combined with multiple objective function optimization , 2013 .