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### Modelling the processing of gasifier feed

Inlet particle size distribution is crucial to the performance of a gasifier. A simulation exercise determines the performance of a rod mill processing gasifier feed

**ANKIT A JAIN and AJAY GUPTA**

Reliance Industries LimitedReliance Industries Limited

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**Article Summary**

The importance of crushing is well known in the mining and cement industries wherein the particle size distribution (PSD) of the feed is extremely important in order to minimise process costs and maximise the efficiency of the process.

The rod mill is widely used to grind petcoke (received from the coker unit of a refinery) into fine particles. Thus, understanding the effect of various inlet properties on the operation, working and performance of the rod mill is of utmost importance to the entire gasification process. An understanding of the performance of the rod mill with respect to the properties of the petcoke (Bond Work Index, BWI),2 feed inlet rate and inlet size is important too as these properties may change along with a change in crude slate processed in the refinery (see Figure 2). A model for the rod mill is an essential tool to develop an insight into the effect of these parameters on the performance of the rod mill and in its efficient operation.

In this article, we use the comminution model to predict the outlet PSD from the rod mill. The model results, validated with experimental results, were later used to understand the sensitivity of various factors. The model discussed in the article can also be used to understand various scenarios including deciding on the rod filling degree (power required) and the requirement for a crusher before the rod mill (pre-crusher). It may also be useful in the design of a new rod mill.

A schematic of the comminution model applied in this work is shown in Figure 3. The comminution laws postulated by Kick, Rittinger and Bond can be described by the following differential equation:

(1)

(2)

W = the work input on a mass basis

C = coefficient (also known as work index) given in work units

dp = characteristic particle diameter of the produced particles (a reliable value for the particle size is d80)

n = exponent (depends on comminution law)

P = power input

m ̇= feed mass flow.

The application of Kick’s, Rittinger’s, and Bond’s laws is limited to a certain range of particle size: Rittinger’s Law <0.05 mm (fine grinding); Bond’s Law 0.05-50 mm (transition); and Kick’s Law >50 mm coarse grinding). The comminution laws are evaluated based on the BWI.

The macro parameter to understand the performance of the rod mill is F80 and P80 (particle diameter which is larger than 80% of the inlet/outlet mass). The other parameters are the power input to the rod mill which in turn is closely related to the filling degree (% of rods) in the rod mill.

Various experimental data were simulated using the model developed. A specimen input PSD to the model is shown in Figure 4. The BWI and the net power in the particular trial are given as an input to the model. A comparison of the output data between the simulation and experimental results showed a good match (see Figure 5). A comparison of the macro parameter P80 showed a good match with experimental data; the comparison is listed in Table 1.

BWI is a measure of resistance of the material to grinding in a rod mill. The BWI of the petcoke depends on the type of crude being processed (generally, BWI is directly related to the metal content in the crude). Thereby, one of the major issues with the operation of the rod mill may be the dynamically changing BWI of the feed to the mill. Simulations were done in order to understand the sensitivity of BWI and P80. These simulations give an insight into the cut-off BWI for a particular feed rate to meet the required product specifications. As shown in Figure 6, for a feed rate of 1.3 ratio the cut-off BWI is 1.01, while for 1 it is 1.3.

Feed inlet size is one of the most important operating parameters affecting the performance of a rod mill. A sensitivity analysis with respect to F80 and P80 was carried out to understand the effect of inlet feed composition (see Figure 7a). It can be noted from Figure 7a that the feed inlet size would not meet the product specifications if it was fed to the rod mill. In such a case, the feed F80 was further reduced in order to determine the cut-off (max) F80 that, if it was fed to the rod mill at the specified BWI and power inlet, would meet the product specifications. The results of these simulations are shown in Figure 7b. It can be inferred from the graph that as the BWI increases, the sensitivity with respect to change in feed size decreases, especially after 1.2 (ratio). This graph also gives us an insight into the scenario wherein we need to make a decision regarding the kind of pre-conditioning required before the feed is fed into the rod mill in order to achieve the required product specifications.

Power supplied to the rod mill depends on the filling degree (% volume of rod) in the rod mill. Thereby it is important to understand the sensitivity of power on the product size outlet (P80). As Figure 8 shows, the change in power to the rod mill is quite sensitive to change in P80; a 25% increase in power brings a decrease of 55% in the product outlet P80. Understanding this is important in order to decide the ideal filling degree of rods in the rod mill for a particular feed F80 and BWI.

^{1}Similarly, the PSD of the feed to a gasifier is of high importance in the overall efficiency and reliability of the gasification process (see Figure 1). This is especially so in the case of an entrained bed gasifier wherein residence time is the least compared to other gasification technologies (fixed bed, fluidised bed). Studies have shown that the critical range of particles for a two-stage upflow entrained bed gasifier is 120-300 µm.^{2 }The rod mill is widely used to grind petcoke (received from the coker unit of a refinery) into fine particles. Thus, understanding the effect of various inlet properties on the operation, working and performance of the rod mill is of utmost importance to the entire gasification process. An understanding of the performance of the rod mill with respect to the properties of the petcoke (Bond Work Index, BWI),2 feed inlet rate and inlet size is important too as these properties may change along with a change in crude slate processed in the refinery (see Figure 2). A model for the rod mill is an essential tool to develop an insight into the effect of these parameters on the performance of the rod mill and in its efficient operation.

In this article, we use the comminution model to predict the outlet PSD from the rod mill. The model results, validated with experimental results, were later used to understand the sensitivity of various factors. The model discussed in the article can also be used to understand various scenarios including deciding on the rod filling degree (power required) and the requirement for a crusher before the rod mill (pre-crusher). It may also be useful in the design of a new rod mill.

**Comminution model for a rod mill**A schematic of the comminution model applied in this work is shown in Figure 3. The comminution laws postulated by Kick, Rittinger and Bond can be described by the following differential equation:

(1)

(2)

W = the work input on a mass basis

C = coefficient (also known as work index) given in work units

dp = characteristic particle diameter of the produced particles (a reliable value for the particle size is d80)

n = exponent (depends on comminution law)

P = power input

m ̇= feed mass flow.

The application of Kick’s, Rittinger’s, and Bond’s laws is limited to a certain range of particle size: Rittinger’s Law <0.05 mm (fine grinding); Bond’s Law 0.05-50 mm (transition); and Kick’s Law >50 mm coarse grinding). The comminution laws are evaluated based on the BWI.

^{3}Five efficiency factors^{4}were introduced to correct the measured BWI and apply it to a rod mill. A breakage function is used to determine the fraction of material in crushed particles from inlet particle size ‘i’ which end up in particle size interval ‘k’. The model has the capability to choose various distribution functions reported in the literature.^{5}^{ }**Performance evaluation of the rod mill**The macro parameter to understand the performance of the rod mill is F80 and P80 (particle diameter which is larger than 80% of the inlet/outlet mass). The other parameters are the power input to the rod mill which in turn is closely related to the filling degree (% of rods) in the rod mill.

**Comparison of simulation results with experimental data**Various experimental data were simulated using the model developed. A specimen input PSD to the model is shown in Figure 4. The BWI and the net power in the particular trial are given as an input to the model. A comparison of the output data between the simulation and experimental results showed a good match (see Figure 5). A comparison of the macro parameter P80 showed a good match with experimental data; the comparison is listed in Table 1.

**Sensitivity analysis with respect to BWI and feed rate**BWI is a measure of resistance of the material to grinding in a rod mill. The BWI of the petcoke depends on the type of crude being processed (generally, BWI is directly related to the metal content in the crude). Thereby, one of the major issues with the operation of the rod mill may be the dynamically changing BWI of the feed to the mill. Simulations were done in order to understand the sensitivity of BWI and P80. These simulations give an insight into the cut-off BWI for a particular feed rate to meet the required product specifications. As shown in Figure 6, for a feed rate of 1.3 ratio the cut-off BWI is 1.01, while for 1 it is 1.3.

**Sensitivity analysis with respect to inlet PSD**Feed inlet size is one of the most important operating parameters affecting the performance of a rod mill. A sensitivity analysis with respect to F80 and P80 was carried out to understand the effect of inlet feed composition (see Figure 7a). It can be noted from Figure 7a that the feed inlet size would not meet the product specifications if it was fed to the rod mill. In such a case, the feed F80 was further reduced in order to determine the cut-off (max) F80 that, if it was fed to the rod mill at the specified BWI and power inlet, would meet the product specifications. The results of these simulations are shown in Figure 7b. It can be inferred from the graph that as the BWI increases, the sensitivity with respect to change in feed size decreases, especially after 1.2 (ratio). This graph also gives us an insight into the scenario wherein we need to make a decision regarding the kind of pre-conditioning required before the feed is fed into the rod mill in order to achieve the required product specifications.

**Sensitivity analysis with respect to power**Power supplied to the rod mill depends on the filling degree (% volume of rod) in the rod mill. Thereby it is important to understand the sensitivity of power on the product size outlet (P80). As Figure 8 shows, the change in power to the rod mill is quite sensitive to change in P80; a 25% increase in power brings a decrease of 55% in the product outlet P80. Understanding this is important in order to decide the ideal filling degree of rods in the rod mill for a particular feed F80 and BWI.

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- Process Modelling and Simulation

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