(215f) Simplification of the Inviscid Navier-Stokes Equations for Dynamic Simulation of Nonisothermal Gas Flow Networks

Accurate gas dynamics representation is required to simulate different processes in chemical engineering, some examples are the formaldehyde production process [5] and the nuclear hydrogen production process [6]. A very accurate representation of gas dynamics in a pipe can be achieved by using the inviscid Navier-Stokes equations with a friction term [2]. However, this system of equations produces computationally expensive simulations not suitable for the simulation of chemical process operations involving nonisothermal gas flow networks. The problem lies in the fact that information is propagated through the gas at widely different time scales. The time scales depend on the characteristics of the hyperbolic system. Two of these characteristics are related to the speed of sound and the speed of the gas, and one characteristic is related only to the speed of the gas. The characteristics related to the speed of sound are very fast (transients take less than 0.1 s) and an accurate dynamic simulation of the system requires the use of very small time steps with an explicit integrator and high-resolution methods [2].

One way to avoid this complicated and computationally expensive implementation is to simplify the equations taking into account only the relevant time scales for the simulated phenomena [3]. The fast time scale phenomena are often not of importance when studying the dynamics of chemical process operations, because discrete disruptions in the flow of the gas are not expected. As changes in pressure propagate with the speed of sound, we can make a quasi-equilibrium approximation (singular perturbation) for the equations related to the fast dynamics. These equations are the equations for mass conservation and momentum conservation. This simplified system with a dynamic energy balance can be solved by using a cheaper and faster implicit integrator like JACOBIAN® [4]. Moreover, the equations are much easier to integrate with a plant-wide dynamic simulator.

This paper presents the implementation of this framework to represent the transients in a heat transfer loop using helium. A heat transfer loop is used in a nuclear hydrogen production facility to transfer the heat generated in the nuclear reactor to the hydrogen production plant. The nuclear reactor and the hydrogen plant are at least 90m apart [1] and an accurate representation of the system is required to understand the behavior of the system. The important transients have a time scale larger than 1s and no sudden changes are expected to occur. Therefore, the simplified system of equations can be used to simulate the helium behavior in the system. Additional models for compressors and heat exchangers were considered, and the whole system of models was implemented in JACOBIAN®[4]. This framework allows the accurate representation of gas dynamics in complex chemical processes without dramatically increasing the computational cost.

1. C. B. Davis, R. B. Barner, S. R. Sherman, D. F. Wilson. Thermal-Hydraulic Analyses of Heat Transfer Fluid Requirements and Characteristics for Coupling a Hydrogen Product Plant to a High-Temperature Nuclear Reactor. Technical Report INL/EXT-05-00453, Idaho National Laboratory, 2005.

2. R. J. Leveque. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge, U. K., 2002.

3. J. E. Meyer. Hydrodynamic Models for the Treatment of Reactor Thermal Transients. Nuclear Science and Engineering, 10:269-277, 1961.

4. Numerica Technology LLC, 2005 Numerica Technology LLC (2005). JACOBIAN dynamic modeling and optimization software. http://www.numericatech.com/.

5. D. Sedes. Modelling, Simulation and Process Safety Analysis. A case study: The formaldehyde process. Technical Report, Massachusetts Institute of Technology, 1994.

6. R. B. Vilim. Dynamic Modeling Efforts for System Interface Studies for Nuclear Hydrogen Production. Argonne National Laboratory, ANL-07/16, 2007.