Proceedings of the 6th International Conference on Process Systems Engineering (PSE ASIA)
25 - 27 June 2013, Kuala Lumpur.
STEADY STATE AND DYNAMIC MODELING
OF AN ORGANIC RANKINE CYCLE
M. J. Proctor, W. Yu*, B. R. Young
Department of Chemical and Materials Engineering, The University of Auckland, New
Zealand
*Corresponding Author’s E-mail: w.yu@auckland.ac.nz
Abstract
The organic Rankine cycle (ORC) has attracted attention over the last decade as a useful
tool for eco-friendly power production from waste heat or other low enthalpy sources.
The use of computer simulation can help engineers with process design, control and
trouble-shooting. In this paper an ORC system is modeled using the process simulator
VMGSim. Both steady state and dynamic models were built so that they can be used for
further investigation of optimization and process control for these plants. The steady
state model is validated using design data from a real geothermal ORC process and
results from the dynamic model are shown.
Keywords: Organic Rankine Cycle (ORC), Dynamic Modeling.
1. Introduction
In this paper a model of a geothermal power plant with an organic Rankine cycle (ORC)
is presented. The model aims to be a useful resource for understanding the processes
inside a geothermal plant and assist with their optimization and the development of
control systems.
A wide range of ORC applications have been investigated, such as waste heat recovery
(Kanoglu 2002; Schuster et al. 2002; Ozturk et al. 2006), geothermal systems (Talbi and
Agnew 2002), solar energy use (Camacho and Bordons 2004), combined heat and
power (Casella 2004) and engine exhaust gases (Seferlis and Georgiadis 2004; Sinnot
2005). More comprehensive literature reviews are provided by Gnuteck and
Bryszewska-Mazurek (2001) and Kaplan (2007).
This manuscript is organized as follows. After this introduction the ORC process is
described and the modeling procedure for the steady state and dynamic models is
explained. Validation of the steady-state model using plant design data is presented and
results from the dynamic model are shown, followed by conclusions.
2. Organic Rankine Cycle
Geothermal power plants can be broadly divided into two categories: those that use the
geothermal fluid directly in a turbine to generate power and those that use a secondary
working fluid into which heat is transferred by the geothermal fluid. ORC geothermal
plants fall into this latter category.
Figure 1 is a process flow diagram of an ORC system using a generic heat source. In
this process a hot fluid is used to vaporize an organic working fluid. The vapor passes
through a turbine which produces work, in turn driving a generator to produce
electricity. The low pressure vapor from the turbine is condensed using water or air
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Proctor et al.
cooling. The liquid organic working fluid is then pumped to a higher pressure and flows
back to the vaporizer to complete the cycle.
Figure 1: A schematic of an organic Rankine cycle
3. Organic Rankine Cycle Modeling
Examination of the literature in this area reveals that the general approach to modeling
geothermal power plants is to use equations derived from thermodynamic relationships
and heat and mass balances (Casella 2004; Ozturk et al. 2006; Aneke et al. 2011;
Jalilinasrabady et al. 2012). A literature search was only able to discover one paper that
contained a dynamic model (Casella 2004), which was for a flash geothermal plant. The
other papers found were for steady state models, and included ORC geothermal plants
(Jalilinasrabady, Itoi et al. 2012; Xiao, Wu et al. 2012), as well as flash plants (Ozturk,
Atalay et al. 2006).
3.1. VMGSim Software
VMGSim is a process simulator developed by Virtual Materials Group, which was
originally based on the Sim42 open source simulator developed by Young's group at
Calgary (Cota et al., 2003). Subsequently our group, the Industrial Information and
Control Centre (I2C2) at Auckland has developed an add-in process utility simulation
module for steam optimization at PETRONAS (Currie et al., 2011).
In VMGSim models are constructed using a graphical interface by connecting unit
operations representing a process together in the appropriate order. There are two
distinct modes of operation within VMGSim, steady state and dynamic, which use
different solvers to calculate the results of a model. The steady state solver works on a
unit by unit basis and requires all specifications to meet the degrees of freedom before it
solves the model. The dynamic solver works differently for pressure-flow relationships
as it solves on a network basis taking into consideration the resistance to flow across
multiple unit operations and will solve a model by calculating a series of dynamic states
separated by a user-defined step size. Both solvers work on a unit by unit basis to
calculate heat and composition balances.
3.2. Steady State Model
The steady state model was built by connecting unit operations together in the
appropriate order, as seen in Figure 2. The specifications for the steady state model
were based on design temperature, pressure and flow values provided by a geothermal
ORC plant and the layout of the unit operations was determined by examining the plant
drawings and talking with the plant operators. These values were used directly in an
initial model, which then calculated equipment related data, such as UA (Heat Transfer
Coefficient × Contact Area) values and pressure drops across the heat exchangers.
Dynamic Modelling of Organic Rankine Cycles
3
These in turn provided the basis for the final steady state model. Equipment based
specifications were used where possible so the model could be more flexible in
determining the effect of changes to the input conditions.
Expander
Separator 1
Separator 2
Recuperator
Vaporizer
Pump
M2
Waste
M1
Preheater
BrinePreheater
Heat
source
NCGPreheater
Air_cooler
Figure 2: ORC steady state model in VMGSim
For the steady state model the specifications were: the pump curve, pentane flowrate,
heat exchanger UA values and pressure drops, turbine output power, geothermal fluid
composition, flowrate, pressure and temperature, vapor fraction after the vaporizer and
condenser, and the constraint that the temperature output of the NCG (non-condensable
gas) Preheater and Brine Preheater must be equal. Due to the particular configuration of
the preheating heat exchangers it was also necessary to provide the temperature after the
first preheater, not as a specification but rather as a starting point for iteration to solve
the model.
In order to simplify the model configuration the UA value for the Brine Preheater was
allowed to vary when solving the model. The desired UA value for the Brine Preheater
was known however, and in order to obtain the correct value the condenser pressure and
pentane flowrate specifications were varied manually. This exception to providing
equipment based specifications was allowed as attempting to specify the UA value for
this heat exchanger resulted in a great amount of difficulty in getting the model to
converge. It was decided that varying these specifications manually in order to obtain
the correct UA for the heat exchanger was acceptable since it would yield the same
results because the same underlying thermodynamic relationships would still be present
in the model. This problem is not present in the dynamic model since as described in
Section 3.1, the dynamic solver for VMGSim determines the pressure-flow relationship
differently to the static model.
3.3. Dynamic Model
Due to the differences in the solvers the dynamic model was specified differently to the
steady state model, and contained some extra valves and controllers, as seen in Figure 3.
Details unique to the dynamic model included reconfiguring the turbine to use the
default “simple” curve present in VMGSim. This involved specifying the design
parameters for the turbine which were the speed, power, volumetric flow and efficiency
as well as specifying the actual speed and efficiency to be used while the model was
running (in this case the actual and design values were identical). The pump curve was
still present in the model but instead of specified pressure drops across the heat
exchangers values representing resistance to flow were used instead.
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Proctor et al.
In order for the model to exhibit the correct boiling and condensing processes the
vaporizer and condenser were configured to determine their output vapor fraction based
on the location of the input and output nozzles, which for the vaporizer were set at 0 and
100 % elevation and vice versa for the condenser. This allowed these heat exchangers to
have a liquid level which was essential for determining the upper and lower pressures of
the pentane loop without the need to define these separately as occurred in the steady
state model.
The sections of the control system essential to regulating the plant were also included
and consisted of level control for the geothermal separators (valves V1 and V2), level
control for the pentane side of the vaporizer (controlled by the pentane flow rate using
valve V3) and pentane temperature control for the preheaters (valve V4, which ensures
the temperature from the Brine and NCG preheaters are the same).
Vaporizer
Expander
Heat source
S32
Sep2
CN3
Sep3
CN2
CN1
V1
V2
Recuperator
Preheater
BrinePreheater
M3
V3
Pump
M1
Waste
Heat
Condenser
AmbTCN
Water
Or air
SP1
NCG
Preheater
V4
CN4
Figure 3: ORC dynamic model in VMGSim
4. Results and Discussion
The results from the steady state model are compared with the design values on a T-S
diagram in Figure 4. Examination of this diagram shows the changes in the condition of
the pentane as it undergoes the processes that comprise the Rankine cycle, which are
labeled on the diagram.
Although the T-S plot shows reasonable agreement between the design and model data,
differences are visible upon close inspection. One way to measure the difference
between the design and model data is to take the root mean square difference in
temperature for the points shown in Figure 4, which is 4.6 °C. This value can be put into
context by comparing it with the typical accuracy of a calibrated thermocouple, which is
around 2 °C. Deviations from the design data can be seen for the recuperator, condenser
and preheaters. The amount of combined cooling for the condenser and recuperator is
approximately equal (although there is slight sub-cooling in the design data) but the
balance between the two is different. The reason for this is the cooling on the
recuperator was dictated by the amount of heating the pentane leaving the pump
requires to reach 59.5 °C. In the design data the temperature leaving the pump is slightly
lower (due to the sub-cooling) so more heating is required, producing more cooling on
the back-end of the turbine. In addition the thermodynamic model used by the plant
Dynamic Modelling of Organic Rankine Cycles
designers may have given different results than the one within VMGSim, or the design
data may be imprecise. The difference in the preheating stages is likely to do with the
differences in the thermodynamic model used by VMGSim as well as how the
geothermal fluid was represented in the model. The model represented non-condensable
gas as CO2 which impacts the vapor fraction calculations in the separators. The plant
designers may have used a different model for the geothermal fluid which would have
impacted the heat transfer relationships in the preheating heat exchangers.
Figure 4: Comparison between steady state model results and design values on a T-S diagram.
Selected results from the dynamic model are shown in Figure 5. The ambient
temperature was varied over the course of several simulated hours in a 15 °C swing and
the effect of this change for the turbine power and condenser pressure was monitored.
As the pentane within the condenser exists in a state of vapor-liquid equilibrium the
condenser pressure will increase with the ambient temperature and this effect was
observed in the model.
Figure 5: Dynamic model results showing the change in Turbine Power and Condenser Pressure
caused by a 15 °C change in ambient temperature.
5. Conclusion
The steady state model shows a reasonable agreement with the design data, the main
differences are likely caused by a different composition being used for the noncondensables in the geothermal fluid, resulting in different amounts of vapor and liquid
passing through the preheaters in the model.
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Proctor et al.
The results from the dynamic model exhibit the expected dynamic behavior,
qualitatively, and due to the method the dynamic solver uses to calculate the pressureflow relationships this model could be useful for the investigation of changes in the
input conditions of the plant. However the dynamic model should be explicitly verified
once specific dynamic plant data is collected. This will require cooperation with a
specific operating plant.
Provided that an accurate model for a plant is available it can be used to test potential
improvements to the control system configuration or the addition of new equipment at
very low cost prior to implementing changes physically. It is hoped that these models
will be useful as a stepping stone to producing generic base models for an ORC plant
which can be customized to approximate particular plants for the purposes of
optimization and control system design.
Acknowledgements
The authors would like to acknowledge the Heavy Engineering Research Association of
New Zealand for their support of this research.
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