A demand-driven, capacity-constrained, adaptive algorithm for computing steady-state and transient flows in a petroleum transportation network.

We developed an algorithm to perform simulations of a supply network for crude oil and refined products in order to estimate the consequences of disruptions to components of the network. Components include oil fields, import terminals, refineries, transmission pipelines, tank farms, and distribution terminals. The physical system is represented as network connections, capacities, and inventories. The governing equations describe mass balance in a non-linear diffusive system in which flows in the network are along gradients in a potential field. Each node in the network has a defined storage capacity and desired storage amount. The potential at each node is a function of the difference between the actual and desired amount of fluid stored. The potential can be thought of as the balance between the desire to increase inflows to maintain the desired storage level and the willingness to provide fluid for consumption or outflow to downstream nodes.