IO4 - course : Long term production optimization

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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.

Course material can be tailored to participant background and desired duration.

Course modules developed through IO

IO4 - course : Long term production optimizationPossible modules and dependencies

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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

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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.

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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

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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.

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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

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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

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Modules 4/5 : Adjoint-based techniques

Recent research on speeding up reservoir simulations in optimization loops in MRST:

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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)