Dynamic simulation of chemical processes described by distributed and lumped parameter models

Heydweiller, J.C.; Sincovec, Richard F.; Fan, L. T.

doi:10.1016/0098-1354(77)80017-3

Cited by 12 publications

(2 citation statements)

References 9 publications

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“…We use a lumped element approximation [81], [82] to characterize edge dynamics ( 5) and ( 6), with nodal conditions (9) and ( 10) and subject to injection profiles q i (t), which approximately defines the state on the network in terms of nodal densities ρ j (t). Our approach is to add enough nodes to the network so that density and flow are nearly uniform on any given segment.…”

Section: Discretized System Dynamicsmentioning

confidence: 99%

Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation

Misra¹,

Vuffray²,

Zlotnik³

2020

Preprint

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We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the network nodes, and its movement throughout the network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions, as well as time-varying parameters in the coupling conditions at vertices, provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on networks, and discuss application to subsonic compressible fluid flow with energy dissipation on physical networks. The main result and monitoring policy are demonstrated for gas pipeline test networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission networks.

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Section: Discretized System Dynamicsmentioning

confidence: 99%

Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation

Misra¹,

Vuffray²,

Zlotnik³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…More specifically, a process that can be described entirely in terms of lumped parameters will give rise to a model composed of a mixed set of ordinary differential and algebraic equations . On the other hand, a process that also contains unit operations with variables distributed in one or more spatial dimensions will typically yield a mixed set of partial differential, ordinary differential, and algebraic equations (Heydweiller et al, 1977). Terms that must be integrated over one or more spatial dimensions, or particulate system modeling by means of population balances, may also add integrals to the above set of equations (Marquardt, 1991).…”

Section: Mathematical Formulation Of the Combined Process Simulation mentioning

confidence: 99%