Adjoint based gradient calculation advantantages and challenges Bjarne

Adjoint based gradient calculation - advantantages and challenges Bjarne Foss, Ruben Ringset The Norwegian University of Science & Technology – NTNU IO center Outline 1. Motivation 2. A simple example to illustrate the potential of adjoints 3. Where are the hurdles? 4. Conclusions 1

Motivation Model Norne field Statoil. Hydro Eni, Petoro Data 2

Motivation now history well schedule model simulator for k=1 to N. . . simulate(k) end + Optimize Parameter estimation Uncertainty 3 forecast time

Motivation Reservoir and well models (Eclipse) Inlet separator Wells Pipelines Process Utilities Network model (GAP, Max. Pro, OLGA) Pipelines/tankers Market Process model (HYSIS) Application Value chain optimization Optimization requires a large number of gradient calculations Efficient gradient computations are important 4

A simple example 5

A simple example 6

A simple example 7

A simple example 8

Adjoint gradient computation 9

Adjoint gradient computation Forward simulation 10

Adjoint gradient computation One forward simulation One reverse simulation 11

Forward method N forward simulations (nested loops) 12

The output constraint challenge – possible remedies Reducing the number of constraints • Enforcing them on parts of a prediction horizon • Lumping output constraints together – One interesting application of this is found in the Standford GPRS reservoir simulator (Sarma et al, 2006) 13

The output constraint challenge 14

The output constraint challenge – possible remedies Reducing the number of constraints • Enforcing them on parts of a prediction horizon • Lumping output constraints together – One interesting application of this is found in the Standford GPRS reservoir simulator (Sarma et al, 2006) Taking advantage of barrier or interior point optimization methods • Removing output constraints without introducing slack variables • Model constraints (i. e. equality constraints) can be removed by a single shooting method (in eg. MPC) 15

Adjoint based gradient calculation - advantantages and challenges Conclusions • Adjoint based gradient calculation may give huge improvements in run-time • Output constraints is a challenge 16

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Once again - A very simple example Let Lagrangian function and assume that is the independent variable, i. e. Compute the gradient wrt Choose 18 (”reverse simulation”)