Volume 1, Year 2014 - Pages 1-10

DOI: TBD

### Waste Heat Energy Supercritical Carbon Dioxide Recovery Cycle Analysis and Design

Kevin R. Anderson^{1}, Trent Wells^{1}, Daniel Forgette^{1}, Ryan Okerson^{1}, Matthew DeVost^{1}, Steve Cunningham^{2}, Martin Stuart^{2}

^{1}California State Polytechnic University at Pomona, Mechanical Engineering Dept. Solar Thermal Alternative Renewable Energy Lab, 3801 West Temple Ave, Pomona, CA, 91768, USA

kranderson1@csupomona.edu

^{2}Butte Industries, Inc. Burbank, CA, 91501, USA

**Abstract** - *The US Department of Energy has estimated that 280,000 MW of recyclable waste heat is expelled annually by U.S. industries. Further estimates suggest that harvesting it could result in a savings of $70 billion to $150 billion per year [1]. Thus, any efficiency increase will result in savings to energy producers. Supercritical Carbon Dioxide (SCO _{2}) provides unique advantages over alternative waste heat recovery systems however; it also produces unique design challenges. We propose a novel energy recovery device based on a SCO_{2} regenerative Rankine cycle for small-scale (1kW to 5kW) heat recovery. This study presents a thermodynamic SCO_{2} cycle analysis for waste heat recovery from low temperature (200°C - 500°C) sources using small mass flow rates (20 – 60 grams/sec). This paper will present a prototype SCO_{2} cycle architecture including details of key system components. Preliminary modeling suggests that SCO_{2} systems are viable for low temperature waste heat recovery applications.*:

** Keywords:** waste heat to power, supercritical carbon dioxide, regenerative Rankine cycle, renewable energy.

© Copyright 2014 Authors - This is an Open Access article published under the Creative Commons Attribution License terms. Unrestricted use, distribution, and reproduction in any medium are permitted, provided the original work is properly cited.

Date Received: 2013-11-11

Date Accepted: 2014-03-24

Date Published: 2014-04-09

Nomenclature

*b*: pump width, m*D*: diameter, m*D*: hydraulic diameter, m_{h}*D*: characteristic diameter, m_{s}*e*: effectiveness, %*h*: heat transfer coefficient, W/m^2-K, specific enthalpy, kJ/kg*H*: head, m*k*: thermal conductivity, W/m•K*ṁ*: SCO^{2}flow rate, kg/sec*N*: pump revolution, rpm*N*: specific speed, dimensionless_{s}*P*: power, kW*p*: initial pressure, MPa_{i}*p*: final pressure, MPa_{o}*Pr*: Prandtl number, dimensionless*Q*: heat flux into the system, W/m^{in}^{2}*Q*: heat flux leaving the system, W/m^{out}^{2}- : Energy, kW
*Re*: Reynolds number, dimensionless*SCO*: Supercritical Carbon Dioxide, kg_{2}*s*: entropy, kJ/kg•K*s*: isentropic entropy, kJ/kg•K_{i}*t*: plate thickness, m*T*: cold temperature, °C_{cold}*T*: hot temperature, °C_{hot}*V*: volumetric flow rate, m_{F}^{3}*w*: Plate width, m, specific work, kJ/kg*W*: Work, kJ_{R}- : Power, kW/kg
*η*: cycle efficiency, %*η*: Carnot efficiency, %_{carnot}*ξ*: power coefficient, dimensionless*ρ*: density, kg/m^{3}*σ*: maximum stress, MPa_{max}*φ*: flow coefficient., dimensionless*y*: head coefficient., dimensionless

#### 1. Introduction

According the American Council on Renewable Energy (ACORE) [2], there is an abundant source of emission-free power in the U.S. which is currently being overlooked. This source of power is known as waste heat, a by-product of industrial manufacturing processes which can potentially revitalize U.S. manufacturing, stimulate economic growth, lower the cost of energy, and reduce the carbon imprint due to emissions used for
electricity generation. If not harnessed to generate emission-free, renewable
equivalent power, waste heat is released into the atmosphere via stacks, vents,
and other mechanical equipment. Waste Heat to Power (WHP) captures waste heat
with a recovery unit, and converts the waste heat into electricity through a
heat exchange process. WHP produces not emissions because no fuel is burned.
The American Council on Renewable Energy (ACORE) estimates that there are
approximately 575 MW of installed WHP capacity in the US alone, while the EPA
[3] estimates that there is approximately 10 GW of WHP capacity in the U.S.,
enough to power 10 million U.S. homes. From the Heat is Power (HiP) Association
[4], WHP is included in 15 state renewable energy portfolio standards. By using
WHP to generate emission-free power, users can re-route the power back to the local
infrastructure grid or sell it to the host grid in order to support clean
energy production, distribution and usage. The primary technologies employed by
WHP systems are Organic Rankine Cycle (ORC), Supercritical Carbon Dioxide (SCO_{2}),
the Kalina Cycle, the Stirling Engine, and other emerging technologies such as
thermo-electrics. In this current paper, we demonstrate the use of SCO_{2}
technology as a viable resource for the generation of emission-free
electricity, which is clearly a renewable energy breakthrough.

Supercritical Carbon Dioxide, SCO_{2}
has been considered a viable alternative working fluid for power cycles since
the 1960s because it provides several advantages over steam and helium [5-9].
The density of SCO_{2} allows energy extraction devices to have a much
smaller footprint than comparable steam and helium based turbo machinery [9].
Additionally, the critical point of CO_{2} is very low (31.1 °C and 7.4
MPa) compared to other fluids, allowing for heat transfer from low temperature
(200 °C – 500 °C) sources to the supercritical state [10]. Operating in the
single supercritical phase throughout the proposed cycle reduces the need for
two-phase hardware [9]. However, due to the operating pressure and highly
variable, non-linear fluid properties, suitable hardware for industrial use did
not exist until recently [7, 8]. Advancements in compact heat exchangers and
turbo machinery coupled with the drive for business to become "green" has
revived interest in SCO_{2} power cycles leading to new solutions for energy
addition and extraction [7, 8]. More recently, the investigations of [11-13]
have advanced the applicability of SCO_{2} cycles for use in low-grade
waste heat recovery. The studies of [14-17] afford comprehensive comparative
thermodynamics analyses comparing the feasibility of using SCO_{2} for
low-grade waste heat recovery. The work of [18] offers a parametric
optimization study of the SCO_{2} power cycle for waste heat recovery
maximization. The breakthrough work of [19,20] has led to the year 2013
unveiling of a 8 MW SCO_{2} EPS100 commercially available heat recovery
system from Echogen Power Systems, LLC. Studies addressing the attraction of
SCO_{2} cycles for other applications including Solar Thermal,
Geothermal and automobile fuel consumption applications include the works of
[21-25]. From the literature review presented herein, the relation of the
current paper and the arena of renewable energy has been properly placed into
context. The objective of this current paper is to investigate the waste heat
regenerative SCO_{2} Rankine cycle performance and feasibility with low
flow rate through mathematical modeling and to compare our results with
previous findings and offer a hardware selection guidelines in the form of a
novel expander device which can be used to generate electricity via a SCO_{2}
Rankine regenerative cycle.

#### 2. Regenerative Rankine Cycle Layout

The waste heat regenerative Rankine cycle is made up of six components as shown in Figure 1.

The SCO_{2} cycle starts at a low side pressure above 7.5 MPa
and a low side temperature of 35 °C, slightly above the critical point. After
compression the SCO_{2} is brought to the high-side pressure of 20 MPa
and a temperature of 36 °C, approximately 1 °C higher than the pre-compressed
state. An internal heat exchanger then heats the pressurized SCO_{2} by
exchange with low-pressure, post-expansion SCO_{2}. After exiting the
internal heat exchanger the SCO_{2} is heated in a second heat exchanger
where addition is done via waste heat, raising the temperature to its ultimate
value of approximately 200 °C. The heated and pressurized SCO_{2} is
then expanded near isentropically to produce rotational energy. The rotational
energy is converted to electricity by coupling the expander's output shaft to a
permanent magnet alternator. The fluid exits at a low-side pressure of 12.4 MPa
and a temperature of 163 °C. The expanded fluid is then run through the
internal heat exchanger where it is cooled by high-pressure, pre expansion SCO_{2}.
The cooled supercritical CO_{2} is finally passed through a radiator
where it exits at the pre-compressed pressure and temperature.

The following steady-state, steady-flow
thermodynamic relations given in Eqn. (1) through Eqn. (9) relate the hardware
components of Figure 1 to the various operating points labeled on the p-h
Mollier state diagram of the SCO_{2} working fluid as shown in Figure 1.

Compressor:

Expander:

Waste Heat:

Condenser:

Specific Work Output:

Cycle Efficiency:

Heat Exchanger Effectiveness:

#### 3. Mathematical Modeling

3.1. Cycle Analysis and Optimization

In order to determine the most efficient
operating point, a parametric analysis is performed using first order thermodynamics.
For the prototype cycle, limits are chosen to be 35°C and pressure
above 7.4 MPa to maintain the fluid above the critical point and avoid
two-phase flow. Temperature on the high side is dictated by input from a low
quality heat source, which generally originates at 200 °C - 500 °C [26]. Pump and expander efficiencies
are determined from assumptions outlined in section 4. The remaining fixed
parameters are determined based on system requirements of recovering energy
from low-quality heat using SCO_{2}.

The three degrees of freedom considered for the parametric analysis are: volumetric
expansion ratio, high side pressure, and the temperature drop across the
cooler. In order to close the thermodynamic cycle the temperature drop across
the cooler was assumed to be a function of all other parameters. A MATLAB
program is used to vary the three degrees of freedom, discard any physically
impossible cycles, then determine the most efficient parameter combination. The
flow chart for this program is shown in Figure 2. In order to eliminate two
degrees of freedom, the Carnot efficiency *η _{carnot} *as
given in Eqn. (10) dictates that the greatest efficiency will be achieved when

*T*is minimized and

_{cold}*T*is maximized. Therefore, maxima and minima for these values are selected where

_{hot}*T*is above the supercritical region and

_{cold}*T*is lower than the waste heat source.

_{hot}
Figure 3 is generated using the same MATLAB code and shows the dynamic relationship
dictated by the governing equations and boundary conditions (i.e. high-side and
low-side pressure, and state-points from the p-h diagram). Using Figure 3 the
required temperature drop across the heat exchanger, cooler, and cycle
efficiency may be determined for a given heat exchanger effectiveness. Figure 3
can thus be viewed as a road-map in SCO_{2} waste heat recovery cycle
component design and selection. Using MATLAB on a 64-bit workstation the one
source of possible numerical error is round-off error. Herein round-off error
is estimated to be 10%, which is bounded by the at least 15~20% uncertainty
associated with the SCO_{2} thermo-physical properties as obtained from
REFPROPS [10].

After our design optimization was concluded, the state points shown in Table 1 were recorded to document the optimized SCO2 Rankine Regenerative Cycle. Table 1 is an itemized tabulation of where the state points fall on the p-h and T-s phase diagrams for optimum performance of our proposed cycle. These points are tabulated in Table 1 in order to provide future guidance for researchers who desire to springboard from our current analysis. Given conservative device efficiencies an overall cycle efficiency is found to be 11% with an optimum volumetric expansion ratio to be between 1.4 and 1.5. Furthermore, to achieve this cycle the heat exchanger need only be 78% effective.

Table 1. Operating Points Defined by Cycle Optimization

State Points | T (K) |
P (MPa) |
ρ (kg/m ^{3}) |
h (kJ/kg) |
s (kJ/kg-K) |

1 | 308 | 12.4 | 776.61 | 278.19 | 1.23 |

2 | 319 | 20 | 810.4 | 289.38 | 1.24 |

3 | 417 | 20 | 338.83 | 513.32 | 1.86 |

4 | 473 | 20 | 258.82 | 597.79 | 2.05 |

5 | 436 | 12.4 | 176.78 | 577.23 | 2.08 |

6 | 328 | 12.4 | 537.76 | 353.29 | 1.47 |

3.2. Results Comparison

These current findings are in qualitative and quantitative agreement with the studies of
[11-13, 15, 16]. When comparing our current findings of 11% efficiency it
should be kept in mind that herein we have assumed a nominal pinch-point in our
heat exchanger on the order of 10 °C
(from Figure 3) in comparison to a pinch-point of 5 °C assumed in [11,15]. A larger pinch-point translates into a
smaller heat-exchanger, such as the ones physically realized by the commercial
hardware of [19, 20]. Nevertheless, our efficiency of 11% for the cycle given
by the state-points of Table 1 and Figure 1 agree with the findings of [15]
where high-side and low-side pressures of 200 bar, and 60 bar afford an
efficiency of 13%. Furthermore, our current findings agree with the high
pressure limiting behavior of efficiency for SCO_{2} regenerative waste
heat recovery cycles reported by [12, 13], where efficiencies on the order of
9% are reported for high side pressures of 150 bar. Finally, the asymptotic
trends of cycle efficiency versus SCO_{2} mass flow rates reported in
[16] asymptotically limit the cycle efficiency to 10% which is in qualitative
agreement with the current findings of this paper. With the above comparison of
our results to available data in the literature, the accuracy of our present
calculations has been demonstrated.

3.3. Heat Exchanger Sizing

Current heat exchanger analysis techniques call for evaluation of fluid properties using bulk average temperatures. However, this assumption is only valid for fluids with properties that vary linearly within the heat exchanger. Evaluating fluid properties at the bulk average temperature severely overestimates specific heat throughout the heat exchanger [10], as shown by the "Conventional" line in Figure 4. Furthermore, there has been little research done to improve the analysis of such fluids other than computational simulations. To avoid overestimation, the heat exchangers were sized using a piecewise technique and the heat exchanger was split into dimensionless axial nodes where fluid properties varied more linearly as shown by the "Piecewise" line in Figure 4. The technique involves iteratively stepping through the heat exchanger at different nodal points. Once solved, the fluid properties are updated until error is minimized before the analysis steps to the next node. Depending on the design configuration, appropriate convective correlations were used from standard heat transfer analysis [27, 28]. This technique allows one to account for variation in fluid properties to approximate heat exchanger size without costly and time- consuming testing.

#### 4. Component Selection

4.1. Pump

Supercritical Carbon Dioxide, SCO_{2}
systems present not only thermal design challenges but also gives rise to
special considerations for the pump. There have been multiple attempts
that address the optimization of a pump for SCO_{2} applications [15,
29, 31, 32] that indicate an efficiency of 85% to be reasonable and
conservative. Efficiency may often be increased through later optimization,
however, for the purpose of this paper an 85% efficiency is assumed to
determine the work required to compress the SCO_{2} from 12 MPa to 20
MPa. In order to determine an initial pump design the concepts of the Cordier
diagram are used determine an optimal type of pump for the cycle. By comparing
non-dimensional parameters such as the flow coefficient ϕ, head coefficient ψ, and power
coefficient ξ a suitable speed and characteristic
diameter may be calculated using N_{s} and D_{s}. Combining ϕ, ψ, and ξ allows
an efficiency to be specified per η [32,
33]. Equations (11) through (16) define the non-dimensional parameters used in
the turbo-machinery component selection. Utilizing these results for an 85%
efficiency yields a relatively small specific speed and a large specific
diameter requirement. The Cordier diagram dictates that for this combination of
operating points reciprocating pump is the optimal starting choice for the
compression cycle [32, 33]. This determination was also repeated for the
expander selection discussed later and shown in Figure 5.

Where *N* is rotations per minute, *V _{f}* is volumetric flow rate of the fluid in cubic meters per second,

*H*is effective head in meters,

*D<*is the effective diameter in meters,

*P*is power in Watts, and

*ρ*is density in kg/m

^{3}.

Isentropic compression assumes ideal
conditions with no losses. However, losses are incurred by leaks, heat transfer
between the pump and fluid, and under or over compression leads to examination
of the enthalpy difference between the compression state points. The
compression cycle of SCO_{2} occurs between state points 1 and 2,
raising the pressure from 12 to 20 MPa. Work is determined as the enthalpy
difference in the isentropic and polytropic compression of the fluid as shown
in Eqn. (17). This analysis yields an energy requirement of 0.2 kW to raise the
pressure to the 20 MPa operating condition.

4.2. Expander

The SCO_{2} in the expander
undergoes near isentropic expansion in order to create mechanical energy to turn
a permanent magnet alternator. The initial design was a toroidal engine with
opposing pistons however, this architecture was found to be too difficult to
fabricate. Therefore the expander design was revised into a more linear
hexagonal variation. The latest iteration of the expander design is shown in
Figure 6. This type of expander was chosen over a more conventional turbine expander due to the low volumetric flow rates within the cycle and results from calculating the specific speed and specific diameter similar to the pump selection methodology shown in Figure 5. The expander alternates intake and exhaust cycles to create axial piston movement. Each bank of three pistons is attached to a mounting plate that converts axial motion into rotational motion. A cam and a gear system is implemented to output power to a permanent magnet alternator. The design is still undergoing revision in order to optimize the expander for SCO2.

The cycle of the expander includes three optimal points: injection, expansion, and exhaust. Assumptions were made to neglect frictional losses, thermal losses through the expander itself, and steady state conditions. Figure 7 shows the ideal expansion cycle of the expander from start to finish. The cycle begins with the piston at top dead center as SCO2 is injected into the expander at 20 MPa and 200°C. This raises the pressure from 12 MPa to 20 MPa and the operating temperature of the previously expanded fluid from 90°C to 200°C within a relatively short amount of time. After the SCO2 is injected into the chamber the fluid is naturally allowed to expand, thus pushing the piston to bottom dead center. This expansion allows the pressure and temperature to drop while ideally maintaining constant enthalpy, and providing work for the system. The final leg of the cycle is a constant pressure evacuation of the piston chamber. This exhaust portion comes from the driving force done by the other side of the piston cycling through the expansion portion of the cycle. As the piston now slides back to top dead center, valves open inside the chamber allowing the SCO2 to evacuate back into the supply loop at reduced pressure and temperature of 12 MPa and 90°C. Once the expander has been built, careful testing will yield empirical data with which the theoretical results can be correlated.

4.3. Internal Heat Exchanger

The required heat transfer area from the heat exchanger analysis led to very large length requirements for a standard counter flow concentric pipe configuration. Plate-based heat exchangers are desirable for large area requirements because of their large surface-area to volume ratio. Therefore, the compact plate heat exchanger architecture was chosen to reduce the overall size of the heat exchanger. The MATLAB code in section 3.2 was modified to arrive at a new area requirement using the plate convection correlation, h [28] given by Eqn. (18).

Due to the operating pressures and temperatures aluminum and copper heat transfer interfaces were
not viable. The high side temperature is in the aging range of aluminum, which
leads to eventual embrittlement and weakening below an acceptable level. Copper
has acceptable temperature performance, but was not viable due to its low
material strength. Therefore, stainless steel was selected because it provided
the best compromise between strength and thermal conductivity at the operating
pressure and temperature. Plate thickness was determined by calculating *σ _{max}*.
[34] via the relationship of Eqn. (19).

#### 5. Conclusions

The above analysis examines the feasibility of a regenerative Rankine cycle utilizing SCO_{2}
for waste heat recovery in small-scale systems. Initial analysis suggests that recovery
from low temperature sources approximately 200°C and above is feasible with an
operating efficiency of 11% given the conservative operating parameters in
Table 1. Agreement between the present results and those of [11-13,15,16] has
been demonstrated offering validity to the current study. Further analysis and
experimental validation is required for optimal development of hardware that
may be used for low flow rates. It is notable that the overall thermodynamic
efficiency of the system is highly dependent on the internal heat exchanger
effectiveness and it is expected that higher system efficiencies may be
achieved after development and optimization of the system.

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