Transient Problem Specifications

Optimal Gas Flow

The transient optimal gas flow problem optimizes a linear combination of the total compressor power and the total load shed in the system subject to the time-varying pipeline dynamics modeled as ordinary-differential equations (ODEs), discretized using Backward Euler scheme. The readers are referred to this paper or its (arxiv version) for a derivation of the ODEs. Also, note that the Optimal Gas Flow problem currently can work with only time-periodic time-series data. If the data is not time-periodic, then GasModels will try to fit a time-periodic spline to the data and then run the transient optimal gas flow problem.

Model

GasModels.build_transient_ogf — Function

Builds the transient optimal gas flow Nonlinear problem

Variables

GasModels.variable_density — Function

variables associated with density (transient)

GasModels.variable_compressor_flow — Function

variables associated with compressor mass flow (transient)

GasModels.variable_c_ratio — Function

variables associated with compression ratio (transient)

GasModels.variable_compressor_power — Function

variables associated with compression power (transient)

GasModels.variable_pipe_flux_avg — Function

variables associated with pipe flux average (transient)

GasModels.variable_pipe_flux_neg — Function

variables associated with pipe flux negative (transient)

GasModels.variable_injection — Function

variables associated with injection in receipts (transient)

GasModels.variable_withdrawal — Function

variables associated with withdrawal in deliveries (transient)

GasModels.variable_transfer_flow — Function

variables associated with net withdrawal in transfers (transient)

GasModels.variable_storage_flow — Function

variables associated with storage flows

GasModels.variable_storage_c_ratio — Function

variables associated with well compressor/regulator ratio

GasModels.variable_reservoir_density — Function

variables associated with reservoir density

GasModels.variable_well_density — Function

variables associated with the nodal densities of the well

GasModels.variable_well_flux_avg — Function

variables associated with the average well fluxes for the storages

GasModels.variable_well_flux_neg — Function

variables associated with the neg. well fluxes for the storages

Expressions

The following linear and non-linear expressions are created by the formulation for ease of formulating the constraints

GasModels.variable_pipe_flux_fr — Function

variables associated with pipe flux (from)

GasModels.variable_pipe_flux_to — Function

variables associated with pipe flux (to)

GasModels.variable_well_flux_fr — Function

variables associated with the (from) well fluxes for the storages

GasModels.variable_well_flux_to — Function

variables associated with the (to) well fluxes for the storages

GasModels.expression_density_derivative — Function

density derivative

GasModels.expression_net_nodal_injection — Function

net nodal injection

GasModels.expression_net_nodal_edge_out_flow — Function

net nodal edge flow out

GasModels.expression_compressor_power — Function

compression power

GasModels.expression_well_density_derivative — Function

density derivative for well nodal densities

GasModels.expression_reservoir_density_derivative — Function

density derivative for storage reservoir

Constraints and Constraint Templates

GasModels.constraint_slack_junction_density — Function

Constraint: fixing slack node density value

Template: fixing slack node density value

GasModels.constraint_nodal_balance — Function

Constraint: nodal balance

Missing docstring.

Missing docstring for constraint_nodal_balance. Check Documenter's build log for details.

GasModels.constraint_pipe_mass_balance — Function

Constraint: pipe mass balance

Template: pipe mass balance

GasModels.constraint_pipe_momentum_balance — Function

Constraint: pipe momentum balance

Template: pipe momentum balance

GasModels.constraint_compressor_physics — Function

Constraint: compressor physics

Template: compressor physics

GasModels.constraint_compressor_power — Function

Constraint: compressor power

Template: compressor power

GasModels.constraint_storage_compressor_regulator — Function

Template: storage compression/pressure-reduction

Constraint: well compression/pressure-reduction

GasModels.constraint_storage_well_momentum_balance — Function

Template: well momentum balance

Constraint: well momentum balance

GasModels.constraint_storage_well_mass_balance — Function

Template: well mass balance

Constraint: well mass balance

GasModels.constraint_storage_well_nodal_balance — Function

Constraint: storage well nodal balance

GasModels.constraint_storage_bottom_hole_reservoir_density — Function

Constraint: equivalence of bottom hole density and reservoir density

GasModels.constraint_storage_reservoir_physics — Function

Constraint: reservoir physics

Objective

Three types of objectives are supported by the transient OGF problem (i) a load shedding objective, (ii) a compressor power objective, and (iii) a linear combination of both controlled by the optional argument economic_weighting in the Matlab static file.

GasModels.objective_min_transient_load_shed — Function

minimum load shedding objective for transient OGF problem

GasModels.objective_min_transient_compressor_power — Function

minium compressor power objective for transient OGF problem

GasModels.objective_min_transient_economic_costs — Function

transient objective for minimizing a linear combination of compressor power and load shed