Constraints
Constraint Templates
Constraint templates help simplify data wrangling across multiple Petro Flow formulations by providing an abstraction layer between the network data and network constraint definitions. The constraint template's job is to extract the required parameters from a given network data structure and pass the data as named arguments to the Petroleum Flow formulations.
These templates should be defined over AbstractPetroleumModel and should not refer to model variables. For more details, see the files: core/constraint_template.jl and core/constraint.jl.
Junction Constraints
Volume flow balance constraints
The primary constraints related to junctions ensure that volume flow is balanced at these nodes.
PetroleumModels.constraint_junction_volume_flow_balance — FunctionConstraint for balancing volumetric flow a function (nodes)
Constraint for balancing volumetric flow at junctions (nodes) in the pipeline system. Given junction $i$, this constraint takes the form of $\sum_{j \in Producers_i} qg_j - \sum_{j \in Consumers_i} ql_j = \sum_{ij \in Pipes^f_{ij}} q_{ij} - \sum_{ij \in Pipes^t_{ji}} q_{ji} + \sum_{ij \in Pumps^f_{ij}} q_{ij} - \sum_{ij \in Pumps^t_{ji}} q_{ji} + \sum_{ij \in Tanks^f_{ij}} q_{ij} - \sum_{ij \in Tanks^t_{ji}} q_{ji}$ where $qg$ and $ql$ includes variable and constant demand and production as defined by the $is\_dispatchable$ flag
Pipe Constraints
Bernoulli equation
The primary constraints related to pipes ensure that that head change and flow across a pipe is represented by Bernoulli equation. In this constraint head loss across a pipe is related through the Leibenzon relationship.
PetroleumModels.constraint_leibenzon — FunctionLeibenzon model for pipeline physics
Constraint for computing the relationship between volumetric flow and head difference at either end of a pipe. For a pipe $(i,j)$, this constraint is computed as $(h_i - h_j) = (z_j - z_i) + \frac{\beta * \nu^m}{D_{ij}^{5.0-m}} * L_{ij} * 1.02 * q_{ij}^{2.0-m}$. The constraint adopts the Leibenzon model
Pump Constraints
Operation constraints
The primary constraints related to pumps ensure that the pumps operate within the limits of their capability (head difference, volume flow, rotational speed and pump efficiency).
PetroleumModels.constraint_pump_head_difference_bounds — Functionconstraints that limit pump head difference
Constraints that bound the head difference when fluids are pushed through a pump $\underline{h}_{ij} \le h_j - h_i \le \overline{h}_{ij}$
PetroleumModels.constraint_pump_efficiency — Functionconstraint for computing the efficiency of the pump
Constraint for computing the efficiency of a pump $\eta = \overline{\eta} - (\frac{q_{ij}}{\hat{q_{ij}}} - \frac{w_{ij}}{\hat{w}_{ij}})^2 * (\frac{\hat{w}}{w_{ij}})^2 * \overline{\eta})$
PetroleumModels.constraint_pump_head_difference — FunctionConstraints for computing the head difference for a pump
Constraint for computing the head difference when pushing fluids through a pump $h_j - h_i = \frac{w_{ij}}{\hat{w}_{ij}}^2 * a - q_{ij}^2 * b$
Tank Constraints
Flow balance constraints
Tanks are used to model storage nodes in a pipeline system. The primary constraint ensures the head and flow on both sides of tanks are within the limits capability of the tank's intake and offtake pipes.
Missing docstring for constraint_tank_volume_balance. Check Documenter's build log for details.