VolumeVLEGas L3

Created Monday 22 October 2012

Basic two-zone model taking into account heat and mass storage as well as convective heat transfer and pressure differences due to friction and geostatic effects for each of the zones. Variable number of inlet and outlet ports.

1. Purpose of Model


The model is recommended in case that two distinct phases (gas and liquid) are present and no mass transfer between the phases is expected. The gas phase is expected to be always gaseous while the VLE phase may be subcooled, superheated and in the two-phase region. However, the model's common application case is a storage tank somehow connected to the atmosphere.

2. Level of Detail, Physical Effects Considered and Physical Insight


2.1 Level of Detail


Referring to Brunnemann et al. [1], this model refers to the level of detail L3 because the system is modelled with the use of balance equations for two distinct zones, namely the zone of liquid and gas volume.

2.2 Physical Effects Considered


2.3 Level of Insight


Heat Transfer

Currently, only simple models for heat transfer are supported. Future versions will support more models.

Pressure Loss

Currently, only simple models for pressure loss are available. Future versions may support more models. However, the geometric interpretation of the pressure loss is not always clear.

Spacial Distribution


3. Limits of Validity


4. Interfaces


4.1 Physical Connectors


Basics:Interfaces:FluidPortIn inlet[geo.N_inlet] - an arbitrary number of inlet ports
Basics:Interfaces:FluidPortOut outlet[geo.N_inlet] - an arbitrary number of outlet ports
Basics:Interfaces:HeatPort a heat

5. Nomenclature

6. Governing Equations


6.1 System Description and General model approach


The general model structure is defined as illustrated below: Two distinct volumes are considered referring to the liquid and gas volume in the system. The two volumes can exchange heat between each other but no mass, i.e. there is no evaporation or condensation. Furthermore, heat can be transferred with the surrounding which is handled using replaceable models, see section 2.3 Heat Transfer. Pressure losses are also addressed with replaceable models, see section 2.3 Pressure Loss. The entering and outgoing enthalpy flows are allocated according to the respective media, i.e. the vent mass flow is allocated to the gas medium while inlet and outlet VLE mass flows are allocated to the liquid volume.


6.2 Governing Model Equations


Conservation of Mass

The mass balance for each of the zones considers evaporation and condensation mass flow rates, volume changes and mass flows through the inlet and outlet connectors. These mass flows are allocated to the vapour and liquid zone according to the replaceable model PhaseSeparation, see section 2.3 Spatial Distribution. The balance equations read:


Conservation of Momentum

The momentum balances applied for each of the ports allow a calculation of a pressure distribution at the model boundaries. Two major simplifications are applied:

The three aspects considered are friction force, static pressure forces and gravity. No friction is assumed at the outlet ports while inlet ports may have friction terms according to the replaceable pressure loss model applied, see section 2.3 Pressure Loss.

Conservation of Energy

The energy balances for both zones consider entering and leaving enthalpy flow rates as well as energy transport between the zones due to heat and mass transfer. The mass flows entering and leaving are allocated to the vapour and liquid zone according to the replaceable model PhaseSeparation, see section 2.3 Spatial Distribution. Please note, there are three terms in the equations below that take the derivatives of volume, density and pressure into account. These terms are derived from the total derivative of the inner energy of the zone and appear here due to the special choice of state variables as discussed in Basic Concepts of Modelling


In the above equations two cases are distinguished to handle vanishing zones, i.e. if we have only liquid or only gas in our component. In these cases the enthalpy of vanishing zone follows the other remaining zone's enthalpy. This concept allows to simulate completely filled or void tanks. The heat flow rates to the surrounding are determined by applying a replaceable heat transfer model, see section 2.3 Heat Transfer.

The model's density is taken as an explicit function of the states. Its total derivative should be used for completeness of the model given by:

Chemistry

No chemical reactions are considered leading to the following species mass balances for the two zones. Note that these equations are only valid (and evaluated) when a mixture of fluids is used, i.e. the number of species . In case of vanishing zones the derivatives of the mass fractions become zero.

Mass Transfer between the Zones

Evaporation and condensation is not supported, i.e. there is no mass transfer between the two zones.

Heat Transfer between the Zones

The model for the inter-phase heat transfer assumes constant values for heat phase surface and heat transfer coefficient:


Summary

A summary is available including the following:


7. Remarks for Usage

This model is applied in a number of component models either via instantiation of inheritance, see Components:MechanicalSeparation:BalanceTank L3.

9. References

[1] Johannes Brunnemann and Friedrich Gottelt, Kai Wellner, Ala Renz, André Thüring, Volker Röder, Christoph Hasenbein, Christian Schulze, Gerhard Schmitz, Jörg Eiden: "Status of ClaRaCCS: Modelling and Simulation of Coal-Fired Power Plants with CO2 capture", 9th Modelica Conference, Munich, Germany, 2012
[2] Sebastian Meinke and Friedrich Gottelt, Martin Müller, Egon Hassel: "Modeling of Coal-Fired Power Units with ThermoPower Focussing on Start-Up Process", 8th Modelica Conference, Dresden, Germany, 2011

10. Authorship and Copyright Statement for original (initial) Contribution

Author:
DYNCAP/DYNSTART development team, Copyright 2011 - 2022.
Remarks:
This component was developed during DYNCAP/DYNSTART projects.
Acknowledgements:
ClaRa originated from the collaborative research projects DYNCAP and DYNSTART. Both research projects were supported by the German Federal Ministry for Economic Affairs and Energy (FKZ 03ET2009 and FKZ 03ET7060).
CLA:
The author(s) have agreed to ClaRa CLA, version 1.0. See https://claralib.com/pdf/CLA.pdf
By agreeing to ClaRa CLA, version 1.0 the author has granted the ClaRa development team a permanent right to use and modify his initial contribution as well as to publish it or its modified versions under the 3-clause BSD License.

11. Version History

Date - Version - Description of changes - author/revisor
25.06.2013 - v0.1 - initial implementation of the model - Friedrich Gottelt, XRG Simulation
21.12.2015 - v0.2 - updated species balances covering vanishing zones - Friedrich Gottelt, XRG Simulation
04.05.2017 - v1.2.2 - fixed bug in summary for expertSummary==true - Timm Hoppe, XRG Simulation


Backlinks: ClaRa:Components:MechanicalSeparation:BalanceTank L3