Production optimization at Troll C

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Adjoint based gradient calculation -
advantantages and challenges
Bjarne Foss, Ruben Ringset The Norwegian
University of Science Technology NTNU IO
center

• Outline
• Motivation
• A simple example to illustrate the potential of
  adjoints
• Where are the hurdles?
• Conclusions

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Motivation
Model
Norne field StatoilHydro Eni, Petoro
Data
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Motivation
now
now
time
history
well schedule
model
simulator
forecast
for k1 to N ...simulate(k) end

Uncertainty
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Motivation
Inlet separator
Pipelines/tankers Market
Wells Pipelines
Reservoir
Process Utilities
Reservoir and well models (Eclipse)
Network model (GAP, MaxPro, OLGA)
Process model (HYSIS)
Application Value chain optimization
Optimization requires a large number of gradient
calculations Efficient gradient computations are
important
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A simple example
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A simple example
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A simple example
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A simple example
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Adjoint gradient computation
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Adjoint gradient computation
Forward simulation
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Adjoint gradient computation
One forward simulation
One reverse simulation
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Forward method
N forward simulations (nested loops)
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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)

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The output constraint challenge
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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)

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Adjoint based gradient calculation -
advantantages and challenges

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

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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
(reverse simulation)
Choose