Experimental determination of the kinetics of sorption and gas filtration in coal

To measure the temperature changes during sorption and desorption of carbon dioxide on hard coal, resistive thermometers were used. A sensor was made from platinum–rhodium (PtRh) with the initial diameter wire of 10 µm diameter. By flattening the wire, the author obtained sensors with thicknesses in the range of 1.0–1.3 µm. Subsequently, the thermometer was covered with coal grains of size 4–26 µm. In order to ensure better thermal contact and mechanical bonding to the thermometer, these grains were glued to it with a nitrocellulose lacquer. The time constant of resistance thermometers is ~5 ms.

Two thin-walled steel tubes were soldered, and their internal walls were sawed (Fig. 1). It allowed for the insertion of the thermometer inside the tube and its transfer from one tube to the other. On one of the tubes, a radiator was wound, which made it possible to heat the gas flowing through the pipe by several degrees. The radiator was used to equalise the temperatures in the streams of gases flowing through both tubes, as well as to measure the time constant of thermometers.

Figure 1

The thermometer with the glued coal was attached to the cross-table, so that it could be quickly moved from the initial position in the axis of one of the tubes to the axis of the other tube. The time of moving the thermometer measured using appropriately set contacts was ~20 ms.

For the experiment, carbon dioxide and argon were selected (CO₂ as the gas sorbed on coal). These gases have similar molecular weights of 44 and 40, respectively. Argon sorption on hard coal was found to be low compared to the sorption of carbon dioxide. The gas from the bottle flowed through a reducer and a copper coil placed in water, and then, it flowed into the atmosphere through a steel tube. The usage/flow rate of both gases was measured using liquid manometers with a sloping tube (M₁, M₂). The gas usage/flow rate was selected so that the temperature in the streams was the same.

After the thermometer with coal was placed in carbon dioxide, the adsorption process started [18]. As a result of the release of sorption heat, the coal was heated up and, at the same time, it was cooled down by the gas stream. The temperature rose to a certain value and then decreased to the initial value.

When the thermometer with the coal was moved in the opposite direction from carbon dioxide to argon, the temperature changes took the opposite sign. During desorption, the coal cooled down, and then its temperature increased to its initial value.

The solution of the thermal conductivity equation with gas sorption as the source is the following function:

where τ_s is the time constant of sorption; τ_t is the time constant for temperature equalisation; and A, B and T _k are constants.

As the above formula shows, in the experiment, there are two opposing processes with different time constants. During adsorption, due to heat release, the thermometer is heated together with the coal. The time constant of this process is τ_s . At the same time, due to the temperature difference between the gas stream and the thermometer with coal, temperature equalisation occurs. The time constant of this process is τ_t.

Fig. 2 shows the temperature changes recorded when transferring the thermometer with coal from argon stream to the carbon dioxide stream (adsorption), and vice versa – from the carbon dioxide stream to the argon stream (desorption). These charts show the theoretical curve, adjusted to experimental data, which was used to determine the constants of sorption time and constants of temperature equalisation. Such charts, obtained in the experiments, were the bases for the determination of the sorption time constant.

Figure 2

The lowest sorption time constant (10 ms) was obtained for a 1.3-μm-thick resistance thermometer and a thickens of coal 6.5 μm. However, with very thin coal layers, the temperature changes are not very high, and therefore, the sorption time constant may be determined with high measurement uncertainty. In most experiments, this constant was ~50 ms. Therefore, it can be concluded that the sorption time constant is not greater than 50 ms. The sorption process itself is therefore a very fast process.

The scheme of the experiment is shown in Fig. 3. Experiments were carried out at an initial gas pressure of 0.25 MPa. During the experiments, it was assumed that desorption would occur at a relatively low final pressure, i.e. around 30 Pa.

Figure 3

The large chamber was connected by a valve with a vacuum system. This connection made it possible to de-gas the chamber to 1 Pa. The coal was saturated with gases (CO₂, He) that flowed from a cylinder connected to the pneumatic system through a pressure-reducing valve. Gas pressure measurement was made through a precise pressure gauge. The valve system made it possible to de-gas the coal and then saturate it with a selected gas.

In the top cover of the chamber, there were sockets in which were placed the following:

In the chamber, there was a vessel, where coal spilt after ‘destruction’ of the closing partition of the cell. The vessel was set directly under the cell with carbon. Inside the vessel, there was a thermocouple T_w measuring the temperature of coal during gas release. The thermocouple measuring the gas temperature T_g was placed in the chamber at the height of the membrane separating the chambers. The pressure transmitter lay slightly above the partition. In order to protect it from contamination by coal dust, it was separated from the large chamber by a filter. The cell with coal was mounted on the top cover of the large chamber, in a socket sealed with rubber gaskets.

There was a rod in the axis of the cell. Its one end protruded outwards and the other end ended with a knife and rested on the membrane. The dislocation of the rod caused the diaphragm to rupture, pouring coal into a large chamber. To measure the gas pressure, a piezoresistive pressure sensor was used (sensor with a silicon diaphragm with vaporised strain gauge bridge). The changes in coal and gas temperatures were measured using specially made thermocouples from constantan–manganese wire with thickness of ~3 μm and sensitivity of 40 μV/K.

Voltage signals were recorded by two analogue-to-digital cards, namely ‘fast’ and ‘slow’. Such a solution makes it possible to register voltages in a large range of time. One of the cards recorded the voltage from the pressure sensor in the time range of up to 0.4 s, and the other recorded the same for much longer time periods, i.e. up to 100 min.

The coal was pre-crushed using a laboratory stirrer and then milled in an impact mill to obtain very fine grains. The following grain classes were selected: 25–32, 63–71, 90–100 and 200–250 μm.

In further considerations, we assume that the permeability coefficient k is constant, and that it does not depend on the radius or time.

We assume that the equation of motion is in the form of the Darcy equation, gas is a perfect gas and the sorption isotherm is linear (Henry’s law). By introducing dimensionless gas density, as in Equation (2), we get Equation (3) [20].

where ρ_max is the maximum initial gas density;

where D is filtration coefficient, and

It is a non-linear filtration equation. The above equation will be considered in the spherical coordinate system. According to the experimental conditions, this equation should be solved with the following initial boundary conditions:

The first condition means that at the initial moment inside the grain, the density of free gas is as shown in Equation (6):

where: ψ is the porosity, H is the Henry’s constant, p₀ is the pressure of the gas that saturates the coal, C = 1/RT, R is the universal gas constant and T is the absolute temperature.

The second condition means that on the outside of the grain, the density of the gas is equal to zero (the seeds are in the chamber where the pressure is ~1 Pa). The third condition is a condition for the symmetry of the density distribution of the free gas relative to the centre of the coal grain.

Fig. 4 shows the relationship between pressure and time in the large chamber in the case of the experiments wwith carbon dioxide and helium. Grains of size 25–32 μm were used in the experiment. The pressure of saturation with both helium and carbon dioxide was 0.25 MPa. From these graphs, it can be seen that for a period of ~10 ms, the pressures of CO₂ and helium increase equally. Next, the increase in helium pressure is stopped, and after 15 ms, it settles. This character of pressure change of helium released from coal confirms the assumption that the gas is non-sorbable on coal. Fig. 5 shows the amount of desorbed CO₂ in the initial desorption period. After 0.4 s, a relatively large amount of gas is released from the grains.

Figure 4

Figure 5

The total amount of gas released is shown in Fig. 6. The dotted curve shows the calculated theoretical amounts of the released gas.

Figure 6

To understand the filtration and sorption processes accompanying the propagation of pressure waves in coal that is saturated with gas, it is necessary to measure the time and space distributions of the physical quantities that determine the course of the phenomenon. A set-up created especially for this purpose (Fig. 7) (its detailed description is presented in a previous paper [22]) makes it possible to measure the pressure in the macropores of coal samples and the temperature of its skeleton. Test samples in the form of specially prepared briquettes (B) were formed in a briquetting machine using a hand-operated screw press.

Figure 7

The sidewalls of the briquetting machine had sockets in which pressure transducers P_i and conduits for the assembly of thermocouples T_i were mounted. The thermocouples were put inside the briquette during its formation process (pressing).

A system of joints and valves connected the briquetting machine with the pneumatic system. The pneumatic system consisted of a rotary vacuum pump PR, a gas cylinder with a manostat (CO₂, He) and an electro-pneumatic pressure transmitter PEP.

The transmitter, controlled by the voltage generator (G), made it possible to set periodically changing gas pressure at the front of the briquette [23]. The pneumatic system made it possible to saturate the briquette with gas or empty it by implementing various pressure conditions on the edges of the briquette. The saturation pressure was measured by a precise manometer M.

Electrical signals from the pressure and temperature transmitters were fed to amplifiers AP and AT and then recorded by analogue-to-digital (A/C) cards. The analogue-to-digital card allowed for recording signals in a digital form in a computer PC.

The card was controlled by a software that was specially developed for this experiment. It enabled setting the following parameters: the sampling rate, the recording time and the number of voltage signals recorded. Recorded voltages, through relevant characteristics, were converted into pressure and temperature values. During the experiment, the current pressure and temperature values were measured on the monitor screen. After the experiment, the time of the next measurement and the values of measured pressures and temperatures were saved in a text file.

The presented set-up was used to produce the following boundary and initial conditions in the briquette:

The positive pressure jump in the briquette was triggered by manually opening the valve between the briquette front and the cylinder filled with gas up to the pressure p_o. Examples of the changes in pressure over time are shown in Fig. 8. Before the experiment, the briquette was de-gassed. The time of the pressure rise in the chamber in front of the briquette, measured by a pressure gauge p₀, was of the order of 0.1 s. The negative pressure jump was triggered by opening the valve between the front of the gas-saturated briquette and a large tank connected to the vacuum pump. The applied saturation pressures ranged from 0.3 to 0.45 MPa. Examples of changes in pressure over time are shown in Fig. 9.

Figure 8

Figure 9

The sinusoidal, changing pressure at the front of the briquette was obtained by joining the front of the briquette with an electro-pneumatic converter. The converter was controlled by an voltage generator (G). The sinusoidal changing pressure had a frequency from 0.05 to 0.0005 Hz and an amplitude of ~0.05 MPa. The values of the constant component were ~0.16 MPa. The time of settling the pressure courses in the briquette depended on the frequency and type of gas and varied from several to several dozen minutes.

When implementing the boundary conditions in condition 3, the briquette was first fully de-gassed. De-gassing was carried out from the front and bottom of the briquette simultaneously. Then, after closing the valve connecting the briquette face with the pump, de-gassing of the briquette from the bottom continued, and at the briquette front, a positive pressure jump up to the value p₀ was applied. The experiments with the boundary condition in condition 4 were carried out in a similar way. The difference was that the bottom of the briquette was opened to atmospheric pressure. In the case of the boundary condition in condition 5, the pressure at the front of the briquette was applied using an electro-pneumatic transmitter.