Method and apparatus for determining optimal control settings of a pipeline

A method for computing a cost gradient for a control set for use in generating an optimal control set to transit a pipeline from an initial state to a sustainable target state over a preselected time period having a plurality of discrete intermediate times, said method comprising the steps of:

• simulating a state of the pipeline at each of the plurality of discrete intermediate times from the start of the preselected time period to the end of the preselected time period using the set of controls, the state of the pipeline having a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;
• calculating a cost associated with the state of the pipeline at each of the plurality of discrete intermediate times and at the end of the preselected time period;
• evaluating, with respect to the plurality of state variables, derivatives of the cost associated with the state of the pipeline at each of the plurality of discrete intermediate times and with the state of the pipeline at the end of the preselected time period;
• evaluating an adjoint solution for each of the plurality of discrete intermediate times with the evaluated derivatives beginning at the end of the preselected time period and proceeding back to the start of the preselected time period time by incorporating the evaluated derivatives from each of the plurality of discrete intermediate times;
• and
• combining the adjoint solutions evaluated at the plurality of discrete intermediate times from the end of the preselected time period to the start of the preselected time period to generate a cost gradient.

A method of transitioning a pipeline from a first state to a second state over a predetermined time period comprising the steps of:

• dividing the predetermined time period into a plurality of discrete time segments;
• calculating a first state of the pipeline at the start of the predetermined time period, the state of the pipeline having a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;
• calculating a second state of the pipeline to be achieved at the end of the predetermined time period;
• generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the predetermined time period;
• simulating a state of the pipeline at each of the plurality of discrete time segments from the first state of the pipeline at the start of the predetermined time period to the final state of the pipeline at the end of the predetermined time period using the valid and feasible set of controls;
• calculating a cost associated with the state of the pipeline at each of the plurality of discrete time segments and with the final state of the pipeline at the end of the predetermined time period and summing each of the calculated costs to determine a total cost for the valid and feasible set of controls;
• evaluating, with respect to the plurality of state variables, first derivatives and second derivatives of the cost associated with the state of the pipeline at each of the plurality of discrete time segments and with the final state of the pipeline at the end of the predetermined time period;
• evaluating an adjoint solution for each of the plurality of discrete time segments with the evaluated first derivatives beginning at the end of the predetermined time period and proceeding back to the start of the predetermined time period time by incorporating the evaluated first derivatives from each of the plurality of discrete time segments;
• combining the adjoint solutions evaluated at the plurality of discrete time segments from the end of the predetermined time period to the start of the predetermined time period to generate a gradient;
• modifying the set of controls using the gradient and the second derivatives to generate an updated set of controls having a lower total cost;
• and
• repeating said steps of simulating, calculating, evaluating first and second derivatives, evaluating an adjoint solution, combining the adjoint solutions and modifying with updated sets of controls until the updated set of controls is an optimal set of controls, wherein the optimal set of controls has a minimum total cost.

A computer program product embodied on a computer readable medium and executable by a computer for determining an optimal set of controls for devices in a pipeline to transition the pipeline from a first state to a sustainable second state over a preselected time period, said computer program product comprising instructions for executing the steps of:

• dividing the preselected time period into a plurality of discrete intermediate times;
• generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the preselected time period;
• simulating a state of the pipeline at each of the plurality of discrete intermediate times from the first state of the pipeline at the start of the preselected time period to the final state of the pipeline at the end of the preselected time period using the valid and feasible set of controls, the state of the pipeline including a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;
• calculating a total cost for the simulated set of controls using a cost functional;
• computing a gradient of the cost functional;
• modifying the set of controls using the gradient to generate an updated set of controls having a lower calculated total cost;
• and
• repeating said steps of simulating, calculating, computing and modifying with updated sets of controls until the updated set of controls is an optimal set of controls, wherein the optimal set of controls has a minimum total cost.

A system for determining an optimal set of control values for control devices in a pipeline to transition the pipeline from a first state to a second state over a predetermined time period, said system comprising:

• a plurality of sensors located on the pipeline to measure characteristics of the pipeline;
• a control and data acquisition system to receive measurements from said plurality of sensors and to apply control values to the control devices of the pipeline;
• a pipeline state calculator to generate the first state of the pipeline at the start of the predetermined time period using said measurements received by said control and data acquisition system;
• a load forecaster to predict future loads at specific points along the pipeline;
• a control set optimizer to generate an optimal control set for the control devices of the pipeline, said control set optimizer using a starting control set, the first state of the pipeline from said pipeline state calculator, the second state of the pipeline and said predicted future loads from said load forecaster to generate said optimal control set, and said control set optimizer comprising:
• means for dividing the predetermined time period into a plurality of discrete time segments;
• means for generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the predetermined time period;
• and
• means for iteratively modifying said valid and feasible set of controls until the optimal set of controls is obtained;
• and
• said optimal control set being transmitted to said control and data acquisition system for application to the control devices of the pipeline.