# Proof of Concept of a Novel Solid–Solid Heat Exchanger Based on a Double L-Valve Concept

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}capture technology. The operational objective of the solid–solid heat exchanger is to heat up the relatively cold solid stream coming from the carbonator reactor by absorbing heat from the hotter stream coming from the calciner. This novel solid–solid heat exchanger concept has been constructed on a small scale to study the hydrodynamic response of the system experimentally at different designs and airflow rates in its cold state. Based on the experimental data from the small prototype, a scaled-up hydrodynamic model is proposed that provides estimations for the operational requirements at an industrial scale. Apart from the cold flow pilot model, the heat exchanger is being assessed in the current work for an industrial case study in terms of the following: (a) the heat transfer via rigorous one-dimensional thermal modelling, (b) the structural integrity of the design through Finite Element Method (FEM) analysis, and (c) a parametric study for its expected cost. The purpose of this work is to provide a holistic approach of this novel solid–solid heat exchanger concept, the main advantage of which is its simple design and relatively low cost.

## 1. Introduction

_{2}) shows great potential as a method for Carbon Capture and Storage (CCS) applications [1,2]. This process is known as Carbonate Looping (CaL). The overall reaction can be represented as follows [3]:

_{2}⇌ CaCO

_{3}

- Carbonation, which is the forward reaction, where Calcium oxide (CaO) reacts with carbon dioxide (CO
_{2}) to form calcium carbonate (CaCO_{3}). This reaction is exothermic, releasing heat. - Calcination, which is the reverse reaction, where the calcium carbonate (CaCO
_{3}) is heated to a high temperature, which decomposes it back into calcium oxide (CaO) and carbon dioxide (CO_{2}). This reaction is endothermic and requires an external heat source (e.g., in situ combustion of a fossil fuel inside the calciner, indirect heating of the calciner through the side walls or heat pipes, etc.).

_{2}from the exhaust gases of a power station or any other CO

_{2}emitting industry, such as cement, steel or lime. The captured CO

_{2}can then be separated and stored for geological sequestration or utilized for other purposes such as enhanced oil recovery or the production of chemicals and materials [4,5].

_{2}reacts with the CaO obtained from the return stream of the sorbent loop, resulting in the formation of CaCO

_{3}. The resulting mixture of solid and gas exits the carbonator through the top and it is then separated using a cyclone. The gas phase, consisting of a CO

_{2}-lean flue gas, exits through the top of the cyclone, while the solids exit through the bottom. The solids from the carbonator move into the calciner, where they undergo calcination due to the high temperatures.

_{2}capture include the abundance of calcium oxide (CaO) and the relatively low cost compared to other capture technologies. Additionally, the captured CO

_{2}is obtained in a concentrated form, making it easier to handle for storage or utilization [6]. However, it is important to note that CaL is still an emerging technology and has some challenges to overcome, such as the energy requirements for the calcination step and the long-term stability of the calcium-based sorbent [7,8]. Further research and development are ongoing to optimize and scale up this process for practical implementation in large-scale industrial applications [7,9].

- It has no moving mechanical parts, which can be subject to wear and/or seizure. This feature is especially beneficial when operating at elevated temperatures as in the Calcium Looping Process.
- It has a rather low construction cost, because this type of heat exchanger is constructed from ordinary pipes and fittings, and low operating expenditures, since the absence of moving parts reduces the number of breakdowns and hence the downtime and maintenance costs.

_{2}capture using 37 EB-PEI/SiO

_{2}sorbent, where the absorber and desorber have significant temperature variation in beds, unlike CaL. In the CaL process, the outlet flow temperature is considered 900 °C, as the calciner walls are considered adiabatic and only transfer heat through heat pipes. The calciner’s operating temperature is ~900 °C to ensure complete calcination within a nearly pure CO

_{2}atmosphere, based on the models proposed by Baker and García [28]. A heat transfer model along the vertical tubes under hot conditions is a necessity to reveal several aspects, i.e., heat transfer efficiency, radiation effect on heat transfer, vertical tube length and diameter for an optimum heat transfer.

## 2. Experimental Setup

#### 2.1. Test Rig Design and Construction

- A piping system of granular material;
- A pneumatic system of inlet air;
- An electronic system of measuring instruments.

#### 2.2. Experimental Results

**.**In reality, however, the working medium is a granular material. That means that a fraction of the supplied airflow is passing through the porosity of the packed granular without transferring energy to it. The real power of the aeration at every experiment is calculated by Equation (7) at the narrow part of the venturi tube, where the total pressure (${P}_{tot}$) is given by Equation (8).

#### 2.3. Scale-Up Model

## 3. Thermal Analysis

#### 3.1. Governing Equations

- Uniform temperature distribution at each circular cross section, since the radius of the tubes is significantly smaller than their length.
- Constant temperature along wall thickness, since the resulting Biot numbers are much smaller than 0.1 [30].
- Adiabatic insulated outer walls, so that there are no heat losses to the environment.

^{th}finite element of fluid in the j

^{th}finite element of inner tube:

#### 3.2. Heat Transfer Coefficients

#### 3.3. Critical Mass Flow

^{2}/s

^{2}].

#### 3.4. Inputs and Boundary Conditions

#### 3.5. Thermal Simulation Results

## 4. Structural Analysis

#### 4.1. Tube Material Parameters

#### 4.2. FEM Model Setup

#### 4.3. FEA Simulation Results

## 5. Cost Analysis

^{2}, is proportional to the outer surface of the outer tube. Hence, designs of tubes with small diameters will be preferred by the algorithm because they result in low material and insulation costs. However, the narrower the Double L-Valve, the more Double L-Valves will be needed to circulate the required flux. Hence, these designs are going to have increased assembly costs.

## 6. Conclusions

- The experimental data indicated that a smaller air supply leads to less effective transfer of granular material.
- The thermal model results showed that the heat exchange that takes place is due approximately 94% to radiation and 6% to convection, resulting in a 110 °C temperature increase for the studied case (${T}_{hot}=900\xb0\mathrm{C},{T}_{cold}=650\xb0\mathrm{C},{\dot{m}}_{hot}=31.54\frac{\mathrm{kg}}{\mathrm{s}},{\dot{m}}_{cold}=35.91\mathrm{kg}/\mathrm{s}$).
- The structural integrity of the proposed design under the resulting thermal loads has been checked via FEA models, proving the manufacturability of the concept at an industrial scale. In this design, each HE is mounted at the bottom by a flange and at the top by a suspension so that it does not buckle.
- All these features were costed parametrically, but the main costs are the tube material and insulation. The resulting CAPEX of the industrial case studied is 0.279 EUR/Watt.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic representation of the Double L-Valve HE concept [19].

**Figure 4.**Photos of the constructed cold model: (

**a**) side view of the apparatus, and (

**b**) zoomed view of the intersection.

**Figure 6.**(

**a**) Airflow rate, and (

**b**) granular mass in weighing device in a random experiment of a tube with hydraulic diameter of 20 mm with horizontal length of 300 mm.

**Figure 7.**Effectiveness at different airflow rates into L-Valve with hydraulic diameter of 20 mm and horizontal length equal to (

**a**) 0.2 m, (

**b**) 0.3 m and (

**c**) 0.4 m.

**Figure 8.**Effectiveness at different airflow rates into L-Valve with hydraulic diameter of 40 mm and horizontal length equal to (

**a**) 0.2 m, (

**b**) 0.3 m and (

**c**) 0.4 m.

**Figure 9.**Fitted curve and experimental results with hydraulic diameter equal to (

**a**) 20 mm and (

**b**) 40 mm.

**Figure 10.**(

**a**) A top section of the heat exchanger; (

**b**) a part of the heat exchanger divided into finite elements.

**Figure 11.**(

**a**) Temperature along vertical tubes at steady state, (

**b**) transient response of upper and lower elements of tubes and (

**c**) radiation percentage to the total heat transfer at the upper and the lower elements as a function of time.

**Figure 13.**AISI 310s (

**a**) thermal expansion coefficient as a function of temperature; (

**b**) stress–strain graph for different temperatures.

**Figure 15.**Imported temperature load from the thermal model oft: (

**a**) the inner tube, and (

**b**) the outer tube.

Parameter | Symbol | Unit | Value |
---|---|---|---|

Tube hydraulic diameter | ${D}_{h}$ | m | 0.02–0.04 |

Granular material apparent viscosity | $\mu $ | Pa s | 0.3 |

Area of tube cross section | $A$ | m^{2} | 3.14·10^{−4} |

Granular material apparent density | $\rho $ | kg/m^{3} | 1100 |

Vertical length of L-Valve | ${L}_{1}$ | m | 0.4–0.7–1–1.3 |

Horizontal length of L-Valve | ${L}_{2}$ | m | 0.2–0.3–0.4 |

Parameter | Symbol | Parameter | Symbol |
---|---|---|---|

Inner tube radius | ${R}_{i1}$ | Granular material density | ${\rho}_{si}$ |

Outer tube radius | ${R}_{i2}$ | Granular average voidage | ${e}_{s}$ |

Length of HE | $L$ | Radiation coefficient | $\sigma $ |

Mass flux through tube | ${\dot{m}}_{i}$ | Granular material emissivity | ${e}_{i}$ |

Input granular temperature | ${{T}_{i}}_{0}$ | Tube material emissivity | ${e}_{m}$ |

Initial tube temperature | ${{T}_{mi}}_{0}$ | Tube material density | ${\rho}_{m}$ |

Thermal conductivity of granular | ${k}_{{gr}_{i}}$ | Tube material heat capacity | ${C}_{pm}$ |

Thermal conductivity of gas | ${k}_{{gas}_{i}}$ | Tube material thermal conductivity | ${k}_{m}$ |

Granular apparent heat capacity | ${C}_{pi}$ | Mean granular particle diameter | ${d}_{p}$ |

Parameter | Symbol |
---|---|

Granular temperature distribution as a function of time | ${{T}_{i}}_{j}\left(t\right)$ |

Temperature distribution to tube material as a function of time | ${{T}_{mi}}_{j}\left(t\right)$ |

Symbol | Unit | Value |
---|---|---|

${{T}_{1}}_{0}$ | °C | 900 |

${{T}_{2}}_{0}$ | °C | 650 |

${\dot{m}}_{1}$ | kg/s | 31.54 |

${\dot{m}}_{2}$ | kg/s | 35.91 |

Parameter | Symbol | Unit | Value |
---|---|---|---|

Inner radius of inner tube | ${R}_{11}$ | mm | 280 |

Outer radius of inner tube | ${R}_{12}$ | mm | 282 |

Inner radius of outer tube | ${R}_{21}$ | mm | 391 |

Outer radius of outer tube | ${R}_{22}$ | mm | 393 |

Length of HE | $L$ | m | 50 |

Mass flux in inner tube | ${\dot{m}}_{1}$ | kg/s | 3.26 |

Mass flux in outer tube | ${\dot{m}}_{2}$ | kg/s | 2.87 |

Inner granular material density | ${\rho}_{s1}$ | kg/m^{3} | 1478 |

Outer granular material density | ${\rho}_{s2}$ | kg/m^{3} | 1734 |

Input temperature of inner granular | ${{T}_{1}}_{0}$ | °C | 900 |

Input temperature of outer granular | ${{T}_{2}}_{0}$ | °C | 650 |

Initial temperature of inner tube | ${{T}_{m1}}_{0}$ | °C | 22 |

Initial temperature of outer tube | ${{T}_{m2}}_{0}$ | °C | 22 |

Thermal conductivity of granulates | ${k}_{gr}$ | W/m/K | 2.6 |

Thermal conductivity of gas | ${k}_{gas}$ | W/m/K | 0.026 |

Inner fluid average voidage | ${e}_{s1}$ | - | 0.4 |

Outer fluid average voidage | ${e}_{s2}$ | - | 0.4 |

Inner granular heat capacity | ${C}_{p1}$ | J/kg/K | 996.7 |

Outer granular heat capacity | ${C}_{p2}$ | J/kg/K | 920.2 |

Inner granular emissivity | ${e}_{gr1}$ | - | 0.9 |

Outer granular emissivity | ${e}_{gr2}$ | - | 0.35 |

Tube material emissivity | ${e}_{m}$ | - | 0.9 |

Tube material density | ${\rho}_{m}$ | kg/m^{3} | 8000 |

Temperature (°C) | Young’s Modulus (Pa) | Poisson’s Ratio | Bulk Modulus (Pa) | Shear Modulus (Pa) |
---|---|---|---|---|

20 | 1.95 × 10^{11} | 0.25 | 1.3 × 10^{11} | 7.8 × 10^{10} |

100 | 1.91 × 10^{11} | 0.26 | 1.33 × 10^{11} | 7.58 × 10^{10} |

200 | 1.86 × 10^{11} | 0.275 | 1.38 × 10^{11} | 7.29 × 10^{10} |

300 | 1.8 × 10^{11} | 0.315 | 1.62 × 10^{11} | 6.84 × 10^{10} |

400 | 1.73 × 10^{11} | 0.33 | 1.7 × 10^{11} | 6.5 × 10^{10} |

500 | 1.64 × 10^{11} | 0.3 | 1.37 × 10^{11} | 6.31 × 10^{10} |

600 | 1.55 × 10^{11} | 0.32 | 1.44 × 10^{11} | 5.87 × 10^{10} |

700 | 1.44 × 10^{11} | 0.31 | 1.26 × 10^{11} | 5.5 × 10^{10} |

800 | 1.31 × 10^{11} | 0.24 | 8.4 × 10^{10} | 5.28 × 10^{10} |

900 | 1.17 × 10^{11} | 0.24 | 7.5 × 10^{10} | 4.72 × 10^{10} |

1000 | 1 × 10^{11} | 0.24 | 6.41 × 10^{10} | 4.03 × 10^{10} |

1100 | 8.1 × 10^{10} | 0.24 | 5.19 × 10^{10} | 3.27 × 10^{10} |

1200 | 5.1 × 10^{10} | 0.24 | 3.27 × 10^{10} | 2.06 × 10^{10} |

Material Costs | Value | Unit | |
---|---|---|---|

Tube material | Total mass | 5 | EUR/kg |

Insulation | Outer surface | 500 | EUR/m^{2} |

Assembly costs | Value | Unit | |

Tube cutting and welding | Number of Double L-Valves | 2000 | EUR/piece |

Upper suspensions | Number of Double L-Valves | 500 | EUR/piece |

Axial expansion joint | Number of Double L-Valves | 300 | EUR/piece |

Flange mounting | Number of Double L-Valves | 2000 | EUR/piece |

Tube spacers | Heat exchange total length | 100 | EUR/m |

Machining of tubes | Heat exchange total length | 500 | EUR/m |

HE Thermal Parameters | Unit | Value |
---|---|---|

${{T}_{1}}_{0}$ | °C | 900 |

${{T}_{2}}_{0}$ | °C | 650 |

${\rho}_{s1}$ | kg/m^{3} | 1478 |

${\rho}_{s2}$ | kg/m^{3} | 1794 |

${a}_{s}$ | - | 0.6 |

${{C}_{p}}_{1}$ | J/kg/K | 920.2 |

${{C}_{p}}_{2}$ | J/kg/K | 996.7 |

${\dot{m}}_{1}$ | kg/s | 31.54 |

${\dot{m}}_{2}$ | kg/s | 35.91 |

Temperature at the calciner inlet | °C | 760 |

Heat recovery | MW | 3.93 |

Design parameters of Double L-Valves | Unit | Value |

Inner tube diameter | mm | 560 |

Outer tube diameter | mm | 728.5 |

Length of tubes | m | 50 |

Number of Double L-Valves | - | 11 |

Costs | Unit | Value |

Material costs | EUR | 875,800 |

Assembly costs | EUR | 221,800 |

Total CAPEX | EUR | 1,097,600 |

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**MDPI and ACS Style**

Papalexis, C.; Stefanitsis, D.; Zeneli, M.; Nikolopoulos, N.; Tzouganakis, P.
Proof of Concept of a Novel Solid–Solid Heat Exchanger Based on a Double L-Valve Concept. *Energies* **2023**, *16*, 6156.
https://doi.org/10.3390/en16176156

**AMA Style**

Papalexis C, Stefanitsis D, Zeneli M, Nikolopoulos N, Tzouganakis P.
Proof of Concept of a Novel Solid–Solid Heat Exchanger Based on a Double L-Valve Concept. *Energies*. 2023; 16(17):6156.
https://doi.org/10.3390/en16176156

**Chicago/Turabian Style**

Papalexis, Christos, Dionisis Stefanitsis, Myrto Zeneli, Nikolaos Nikolopoulos, and Panteleimon Tzouganakis.
2023. "Proof of Concept of a Novel Solid–Solid Heat Exchanger Based on a Double L-Valve Concept" *Energies* 16, no. 17: 6156.
https://doi.org/10.3390/en16176156