Permeability and thermal conductivity of host compressed natural graphite for consolidated activated carbon adsorbent

Abstract

Permeability and thermal conductivity test units were set up to study the heat and mass transfer performance of the host material, i.e. expanded natural graphite (ENG), for consolidated activated carbon (AC) adsorbent. The permeability was tested with nitrogen as the gas source, and the thermal conductivity was studied using steady-state heat source method. The results showed that the values of permeability and thermal conductivity were 10^-15 to 10^-12 m² and 1.7 to 3.2 W/(m·K), respectively, while the density compressed expanded natural graphite (CENG) varied from 100 to 500 kg/m³. The permeability decreased with the increasing density of CENG, whereas the thermal conductivity increased with the increasing density of CENG. Then the thermal conductivity and permeability of granular AC were researched. It was discovered that the thermal conductivity of samples with different grain size almost kept constant at 0.36 W/(m·K) while the density was approximately 600 kg/m³. This means that the thermal conductivity was not related to the grain size of AC. The thermal conductivity of CENG was improved by 5 to 10 times compared with that of granular AC. Such a result showed that CENG was a promising host material for AC to improve the heat transfer performance, while the mass transfer performance should be considered in different conditions for utilization of adsorbent.

Keywords

permeability / thermal conductivity / expanded nature graphite / activated carbon

Introduction

As one of the important materials for improvement of heat transfer, expanded natural graphite (ENG) has been widely utilized as a matrix. The most common use of ENG is for the development of new types of adsorbents for adsorption refrigeration and air conditioning, especially in the chemical adsorbent. Mauran et al. first introduced ENG in the chemical adsorbent CaCl₂ [1], and such a compressed compound adsorbent of CaCl₂ and ENG was termed IMPEX, in which the graphite block was impregnated with a CaCl₂ solution of 20% [1,2]. ENG is also believed to be a promising material for heat transfer enhancement in the storage of hydrogen by adsorption technology. For a pure ENG pellet with a porosity of 79.1%, the effective thermal conductivity of pure ENG pellets is approximately 8 W/(m·K) when the density of ENG is 1250 kg/m³ [3]. In gas separation, ENG has been utilized as an additive for granular adsorbents of activated carbon, in which the thermal conductivity of activated carbon is improved by over 20 times [4]. ENG has also been utilized for heat transfer intensification of phase change materials, such as paraffin, in which the thermal conductivity was improved from 0.22 to over 0.8 W/(m·K) [5]. Han and Lee studied the gas permeability by using Darcy’s law in ammonia atmosphere for the graphite-CaCl₂-nNH₃ (n = 8, 4, 2), MnCl₂-nNH₃ (n = 6, 2) and BaCl₂-nNH₃(n = 8, 0) composites for chemical heat pumps, and found that the gas permeability was in the range of 5.0 × 16^-16 to 10^-12 m² depending on the reaction pair, bulk density, and weight fraction of the graphite powder [6]. Biloe studied the permeability of compressed expanded natural graphite (CENG) by using Helium as a gas source, in which the density ranged from 20 to 200 kg/m³. They reported that the values of permeability varied from 10^-15 to 10^-12 [7]. Transient test method was used in measuring the thermal conductivity [8–10]. Wang et al. [11] measured the effective thermal conductivity of solidified expanded graphite and CaCl₂-nNH₃ (n = 2, 4, 8) compound adsorbent by the hot wire method at fixed pressures and temperatures under ammonia atmosphere, and the values were found in the range of 7.05 to 9.2 W/(m·K). The drawback of this method is that the accuracy is influenced for the reason of that the measuring point cannot be precisely fixed because of the swelling of adsorbents in the process of adsorption.

Recently the anisotropic thermal conductivity and permeability had been found for compressed expanded natural graphite, and two different directions for heat and mass transfer were studied [12]. The results showed that the direction perpendicular to the compressing direction had not only optimal performance for heat transfer, but also for mass transfer. Based on this research, the test units were designed in the Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University to test the thermal conductivity and permeability for the optimal direction perpendicular to the compressing direction. Darcy’s law in nitrogen atmosphere was used to study the permeability of CENG, and steady-state heat source method was introduced on the research of the thermal conductivity of CENG and AC.

Experiment

Preparation of compressed adsorbents

ENG is prepared by heating untreated natural graphite, manufactured in Shanghai YiFan Graphite Company, with a size of 50-80 mesh and a percentage purity of over 99%, in an oven at a temperature of 600°C for 10 min. The density of AC, produced by coconut shell (the type is K404) and manufactured by Hainan AC Company, is approximately 600 kg/m³. The pressure machine with an available pressure of 1 to 10 MPa is utilized for the production of the compressed material. The density of CENG ranged from 100 to 500 kg/m³.

Test of permeability

The permeability test unit, as illustrated in Fig. 1, is designed for CENG and activated carbon. The main components are the specimen chamber, a differential manometer, and a rotermeter.

The gas is introduced into the test unit slowly and evenly distributed in the adsorbent. The inlet and outlet of the test unit (Fig. 2) are designed as the cone structure. The metal mesh is put both at the inlet and outlet to prevent the adsorbent from being broken by the gas. The test slot is vertical for the compressing of the adsorbent. The compressing force is also vertical, as shown in Fig. 2, to let the testing direction be perpendicular to the compressing direction which is also the optimal direction for the mass transfer process [12].

Nitrogen is utilized as the experimental gas, which as Fig. 1, flows through the gas cylinder, the specimen chamber, the Rotermeter and finally enters the atmosphere. In this process the temperature is the environmental temperature, and the outlet pressure is the atmosphere pressure which is 100 kPa in calculation. The parameters measured include the pressure drop Δp across the sample and flowrate q_v. Since the samples to be tested are porous media with very low gas velocity, the Ergun model is applicable.

Because the property of nitrogen is very close to ideal gas, and assuming there is no mass accumulation inside the samples, towards the axial gas flow configuration, the intrinsic characteristics of the material are then given by the following expression [13]:

(1)Y=BX+{\displaystyle \frac{\mathrm{1}}{K}},

in which

(2)Y={\displaystyle \frac{(p_{\mathrm{1}}^{\mathrm{2}}-p_{\mathrm{2}}^{\mathrm{2}})S}{\mathrm{2}RT\mu m_{\mathrm{a}}\mathrm{\Delta }z}},X={\displaystyle \frac{m_{\mathrm{a}}}{\mu S}},m_{\mathrm{a}}=\rho S{v}_{\mathrm{a}},

where K is the permeability (m²) and B is the shape factor of the samples; p₁ and p₂ are the inlet pressure and outlet pressure of the nitrogen gas, respectively; S is the sample cross section (m²); R is the gas constant (J/(kg·K)); T is the sample temperature (K); μ and ρ are the gas viscosity (Pa·s) and density (kg/m³), respectively; m_a is gas mass flowrate (kg/s); and v_a is axial velocity of the sample (m/s).

To measure the permeability of the samples, Y and X are calculated by using the experimental data of mass flowrate, pressure drop, ambient temperature, and outlet gas pressure, etc., K is obtained from the relations between Y and X, which is linear, and 1/K is the intercept of the equation for the linear relation between them.

Test of thermal conductivity

The thermal conductivity of the adsorbent is studied by using the steady-state heat source method. The principle of the experimental unit is based on British Standard BS-874 [13].

The schematic principle of the experimental unit for thermal conductivity test is exhibited in Fig. 3. The main components include a center square plate heater sandwiched between two compressed samples, two water coolers symmetrically placed at the left and right side of the compressed sample, a quadrate guard heater radial distribution beyond the central square plate heater, and a water tank from which water is pumped through the water coolers.

The schematic design and photograph of the cooler and heater for thermal conductivity test unit is presented in Fig. 4. In the test unit there are two slots for the test of thermal conductivity, and the sample will be vertically compressed inside the slot by the pressing machine (Fig. 4(a)). In this process the testing direction is perpendicular to the compressing direction which is the optimal direction for heat transfer [12]. Such a method also has the advantage of low contact thermal resistance because of the tight contact between the material and the metal surface. Figure 4(b) shows that the spiral grooves are designed for three plates. The plate in the middle is for the central heater (Fig. 3), and the other two plates serve as water coolers (Fig. 3). The spiral grooves are designed as two neighboring groves having water or electricity flow directions alternatively arranged, as shown in Fig. 4(c), which is helpful to ensure that the temperature in the whole surface of the cooler or the heater can be evenly distributed (Fig. 4(c)). The temperature is tested at two points, as shown in Fig. 4(c), and the difference between the two points is compared. The difference is less than 0.2°C.

The experiments are conducted under steady-state conditions. The central heater is heated by a stabilized voltage supply, and the electric resistance of the electric heat wire is controlled at 14.1 Ω. The cooler is cooled by the cooling water with the environmental temperature. The determination of the effective thermal conductivity λ is calculated by the measurement of the average temperature gradient ΔT produced through the compressed samples by a known axial heat flux Q, which can be calculated by the electric current and the electric resistance of the heating wire. When the working conditions (heat flux determined by the electric current of central square plate heater, water flowrate, and temperatures) are set up and the equilibrium is reached, the effective thermal conductivity λ (W/(m·K)) is given by

(3)\lambda ={\displaystyle \frac{Q\mathrm{\Delta }z}{\mathrm{2}S\mathrm{\Delta }T}},

in which Q is calculated by the power (W) of the central square plate heater, Δz is the thickness of the compressed sample, ΔT is the temperature difference across the sample and S is the effective heating area of the central square plate heater (m²).

Results and discussion

Permeability of CENG

The permeability of CENG is demonstrated in Fig. 5. The pressure drop increases faster with the gas flowrate while the density of CENG is larger. For example, when the density is 300 kg/m³, the pressure drop ranges from approximately 60 to 220 kPa. However, when the density is 450 kg/m³ the pressure drop ranges from 320 to 690 kPa. The main reason for this is that the mass transfer resistance for the nitrogen gas is larger while the density is larger.

The difference of pressure can be shown by the permeability of CENG. When the density is smaller, the permeability of the sample will be larger, and it will be easier for the gas to flow through the sample. That is, a small pressure drop will have a reasonable flowrate. When the density is larger, the permeability will be small, and it will be difficult for the gas to flow through the sample. That is, under the condition of similar pressure drop with the sample of small density will have a small flowrate.

The permeability of CENG under the condition of different values of density is listed in Table 1, where the permeability varies from 8.914 × 10^-12 to 8.391 × 10^-15 m² while the density changes between 100 kg/m³ and 500 kg/m³. The permeability of the sample with a density of 500 kg/m³ is decreased by approximately 1000 times compared with the sample with a density of 100 kg/m³.

Thermal conductivity of CENG

In the research of the thermal conductivity of CENG, two important parameters are the heat flux and temperature drop at both sides of the sample. The heat flux is dependent on the change of electric current supplied by the stabilized voltage supply. The relation between thermal conductivity, heat flux, and density of samples are shown in Fig. 6.

Figure 6(a) shows that the thermal conductivity did not change with the heat flux when the heat flux changed from 3.5 to 14 W. However, it can be seen in Fig. 6(b) that the thermal conductivity of CENG progressively increases linearly when the density varies from 100 to 500 kg/m³. The smallest thermal conductivity is 1.72 W/(m·K) when the density of the sample is 100 kg/m³. The largest thermal conductivity is 3.41 W/(m·K) when the density of the sample is 500 kg/m³. The thermal conductivity is improved significantly compared with the thermal conductivity of granular ENG, which is generally 0.2 W/(m·K).

Thermal conductivity of AC

In the research of AC, six different grain diameter of the samples, i.e. with mesh of 6-20, 20-40, 40-60, 60-80, 80-100, and more than 100, are prepared. The results of thermal conductivity are shown in Fig. 7.

The results indicate that the thermal conductivity of AC changed little with the heat flux varying from 1.73 to 5.1 W, although the thermal conductivity of AC at the heat flux of 1.73 W is slightly larger than other samples. The average thermal conductivity of AC almost keeps a constant at 0.36 W/(m·K), as shown in Fig. 8. The thermal conductivity of CENG is improved by approximately 5 to 10 times compared with that of granular AC.

Experimental error analysis

The error transfer function of permeability is

(4)\left|{\displaystyle \frac{\mathrm{d}K}{K}}\right|=\left|{\displaystyle \frac{\mathrm{d}Y-B\mathrm{d}X}{Y-BX}}\right|\le \left|{\displaystyle \frac{\mathrm{d}Y}{Y-BX}}\right|+\left|{\displaystyle \frac{B\mathrm{d}X}{Y-BX}}\right|.

The pressure is calculated by the environmental pressure and the differential pressure meter (the type is Dwyer477A-7) with an error of±0.1%, and the gas mass flowrate is tested by the flowmeter (the type is Dwyer MMA-23) with an error of±4%. The maximal error of K is calculated, whose error is 4.6%. The error transfer function of thermal conductivity is

(5)\left|{\displaystyle \frac{\mathrm{d}\lambda }{\lambda }}\right|=\left|{\displaystyle \frac{\mathrm{d}Q}{Q}}+{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }z}{\mathrm{\Delta }z}}-{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }T}{\mathrm{\Delta }T}}\right|\le \left|{\displaystyle \frac{\mathrm{d}Q}{Q}}\right|+\left|{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }z}{\mathrm{\Delta }z}}\right|+\left|{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }T}{\mathrm{\Delta }T}}\right|.

The temperatures are tested by the thermal couples with a measuring error of±0.5°C. The heat flux is calculated by the electric current and electric resistance, in which the electric resistance has a relative error of±1% after calibration and the electric current is controlled by the stabilized power supply with a relative error of±1%. The thickness of the sample is measured by a micrometer with an error of±0.01 mm. The thickness of the sample is 20 mm, the minimum temperature difference is 5.31°C, the electric current is 1 A, and the electric resistance is 14.1 Ω. According to these parameters the maximal relative error of the thermal conductivity is 13.83%.

Conclusions

To evaluate the performance of heat and mass transfer on the host material of CENG for AC for adsorption refrigeration, both permeability and thermal conductivity of the CENG and AC were researched, and the conclusions are as follows:

1) The permeability of compressed expanded natural graphite changes from 10^-15 to 10^-12 when the density varies between 100 kg/m³ and 500 kg/m³. The permeability decreases dramatically with the increasing density, especially when the density is higher than 450 kg/m³.

2) The thermal conductivity of CENG increases from 1.7 to 3.2 W/(m·K) when the density varies from 100 to 500 kg/m³. The thermal conductivity of CENG does not change with the heat flux but changes linearly with the density of samples.

3) The thermal conductivity of AC is not related to the mesh. The average value keeps constant at 0.36 W/(m·K). The thermal conductivity of CENG is improved by approximately 5 to 10 times compared with that of granular AC. Such a result shows that CENG is a promising host material for AC to improve the heat transfer performance. But the mass transfer performance of CENG is worse than that of granular AC. Thus CENG will be a good host for the refrigeration pair with high pressure, such as ammonia refrigerant. For the refrigerant works under vacuum condition, such as methanol and water refrigerant, it will have more requirements on mass transfer than heat transfer because the pressure drop between the adsorber and the condenser/evaporator is very small. For such condition, especially for the freezing condition with very low pressure drop, pure granular AC and the host of CENG with low density should have better performance.

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