Multistage oilfield design optimization under uncertainty

A system for oilfield management comprising:

• a computer processor;
• an oilfield design tool that, when executed on the computer processor:
• obtains a subsurface model comprising a fracture design model having a fracture property with an uncertain value;
• obtains a set of representative values that represent uncertainty in the fracture property;
• and
• generates an oilfield design based on a solution;
• an oilfield simulator that, when executed on the computer processor:
• executes a fracture forecast model with a control variable value and a model parameter sample to obtain an objective function value in a plurality of objective function values;
• and
• a solver that, when executed on the computer processor:
• solves an oilfield optimization problem with a control variable using the set of representative values for the fracture property to obtain the solution comprising an optimal value for the control variable with respect to an objective function, wherein solving the oilfield optimization problem comprises:
• for a plurality of model parameter samples, generating the plurality of objective function values by, for each of the plurality of model parameter samples:
• sampling the set of representative values for the fracture property to obtain a respective model parameter sample in the plurality of model parameter samples, and
• issuing a call to the oilfield simulator with the control variable value and the respective model parameter sample;
• and
• calculating a mean of the plurality of objective function values.

A non-transitory computer readable medium for managing oilfield operations comprising computer readable program code for:

• obtaining a subsurface model comprising a fracture design model having an fracture property with an uncertain value;
• obtaining a set of representative values that represent uncertainty in the fracture property, wherein the set of representative values comprises a plurality of model parameter samples;
• solving an oilfield optimization problem with a control variable using the set of representative values of the fracture property to obtain a solution comprising an optimal value for the control variable with respect to an objective function, wherein solving the oilfield optimization problem comprises:
• for each of the plurality of model parameter samples, executing a fracture forecast model with a respective value of the control variable and a respective model parameter sample of the plurality of model parameter samples to obtain a respective objective function value of the objective function;
• and
• determining the optimal value for the control variable based on the respective objection function value obtained with each of the plurality of model parameter samples;
• generating an oilfield design based on the solution;
• and
• storing the oilfield design.