IO4 - course : Long term production optimization 1 Focus on reservoir simulation-based techniques partially studied and developed at IO-center: –Formulation of long-term (> 6 months) optimization problems –Gradient-based methods and adjoint reservoir simulations –Model reduction and upscaling for optimization –Flow-based proxies for rapid optimization and visualization Strongly linked to the open-source simulation software MRST, and includes examples/scripts in Matlab.MRST Course material can be tailored to participant background and desired duration.

Course modules developed through IO IO4 - course : Long term production optimization Possible modules and dependencies 2 Reservoir modelling and simulation basics using MRST Simulator prototyping using automatic differentiation Formulation of optimization problems Focus on simulation-based optimization of recovery/NPV Adjoint-based techniques Formulation and derivation Implementing objectives Gradient-based optimization –Search directions and line- search –Constraints Flow diagnostics Using efficient flow-based proxies for optimization and visualization Upscaling and model reduction Upscaled model tuning for optimization

Course 2 : Long term production optimization 3 Modules contain three main ingredients: 1.Theory and mathematical formulations – emphasis on understanding rather than proofs 2.Implementation – using MRST 3.Examples – Code that can be run during course. +

Quick overview of MRST / Getting started Grids and Petrophysical Parameters Mathematical models for single- and multiphase flow in porous media Discretization of equations Well models for reservoir simulation Examples 4 Modules 1/5 : Reservoir modelling and simulation basics using MRST

Background on classes in Matlab MRST-AD: –Basic functionality –Discrete operators –Recommendations for efficient implementations –Complete example implementing a single phase solver Components of a complex reservoir simulator: –model equations and discretization –Wells and handling of well-equations –linear- and non-linear solvers –time-step control Adding new properties/equations to existing solvers AD-based implementations for adjoint simulations. 5 Modules 2/5 : Simulator prototyping using automatic differentiation (AD) function eq = F(xn, xn-1) if forward xn = initAD(xn) elseif reverse xn-1 = initAD(xn-1) end …

Short module containing background/basics: Compact mathematical formulation of Long Term Reservoir Optimization (LTRO) problems Long – term objectives: –Recovery –NPV –Misfit Analysis of NPV for a simple example using MRST 6 Modules 3/5 : Formulation of optimization problems

Derivation of discrete adjoint equations: –Background on constrained max/min, implicit functions and total derivatives –Discrete adjoint equations for time-dependent problems –Control-steps vs time-steps Optimization using adjoint-based gradients –Objective implementation in MRST using automatic differentiation –Problem scaling –Line search: Wolfe conditions –Search directions: steepest ascent vs quasi Newton (BFGS) Constraints –Handling of linear (input) constraints for steepest ascent and BFGS –Discussion of constraints typically present for a LTRO problem –Constraint handling in simulator vs optimizer 7 Modules 4/5 : Adjoint-based techniques

Recent research on speeding up reservoir simulations in optimization loops in MRST: 8 Modules 5/5 : Flow-based proxies, upscaling and model reduction for optimization loops Flow-based proxies: Background on flow-diagnostics equations Visualization Flow diagnostics and derived quantities related to recovery and NPV Proxy-optimization Real-field example (NPV- optimization) Upscaling for optimization: Upscaling background Local vs global upscaling Transmissibility upscaling for optimization purposes Real-field example (NPV- optimization)