Apr-2017

# Combating reactor pressure drop

A refiner investigates the causes of pressure drop due to fouling in a fixed bed reactor and considers an appropriate mitigation strategy

**ANKIT A JAIN and AJAY GUPTA
Reliance Industries Ltd**

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**Article Summary**

The dominant factor that limits the run length of fixed bed units in a refinery is the build-up of pressure in the reactor. The possible causes of pressure drop in the reactor are shown in Figure 1. Pressure drop due to â€¨fouling requires scientific understanding and root cause analysis in order to develop an appropriate mitigation strategy. The typical pressure profile seen in one of our commercial fixed bed reactors is shown in Figure 2. A rapid increase in pressure drop across the catalyst bed was seen in both the single and multiphase fixed bed reactors operating in our refinery, leading to a premature shutdown of the reactor. On probing the different layers of catalyst bed, it was found that the layers of the bed were either plugged with fines (iron sulphide, coke and other inorganic compounds) or in some cases there was irregular change in the shape of the catalyst particles. In a scenario wherein each manufacturer’s aim is to increase the intrinsic activity of the catalyst and, at the same time, refiners aim to pack the maximum amount of catalyst into a given volume, it is imperative that the run length of the reactor should be governed by catalyst activity rather than by a rapid increase in pressure drop due to fouling or other factors.

This article describes an approach to quantifying pressure drop due to fouling in a reactor. The unit in question is a single phase packed bed reactor, which was experiencing a severe fouling problem and subsequent pressure drop problems. Two phenomena that led to this fouling problem have been probed in detail. These scenarios are: deposition of fines in the voids between the catalyst particles; and irregular swelling of catalyst particles in the voids due to chemical reactions (see Figures 3b-c). The pressure drop across the catalyst bed of a single phase packed bed reactor is estimated by the Ergun equation. In this article, the correlation is used to quantify with time the pressure drop due to fouling across the bed. Similarly, the approach discussed here may be extended to multiphase packed bed reactors by making appropriate changes in the governing pressure drop correlations.^{1,2}

**Case study: fouling of a packed bed reactor **

The two cases of fouling observed in the catalyst bed are shown schematically in Figures 3a-c. Case 1 represents a situation in which fouling arises due to the accumulation of fine particles in the voids (iron sulphide, carbon particles, phosphate particles, and so on) while Case 2 represents a scenario wherein the catalyst particles’ surface expands due to chemical reactions, leading to a decrease in the void space.

Figure 3a is a simplified representation of a portion of packed bed loaded with spherical particles where we have assumed a void fraction of 0.40.

The two cases represented in Figures 3b and 3c have been analysed separately in this work. The work can be easily extended to a case representing a combination of both phenomena.

The volume of fines (Vf,t) entering the reactor and the diameter of particles of fines (dp,f) is assumed. For both cases, we assume the fraction (length) of the bed (Lf) being fouled out of the total length of the bed (Lt).

For simplicity, it is assumed that the concentration of fine particles in the feed remains constant and uniform over a period of time. As the virgin fixed bed is fed with fines-laden feed, the void fraction (εB,t) will change with time according to the relationship seen in Equation 1.

It should to be noted that the volume of catalyst and total volume of bed referred to are in the localised fouled region of the bed only. For the rest of the bed (L =Lt –Lf) the voidage remains the same.

**Case 1: fouling due to accumulation of fine particles **

Assuming that the fines entering the bed are spherical and are of uniform size (rp,f), we can easily quantify the number of particles depositing in the bed with respect to time.

The number of fine particles deposited in the bed in time ‘t’ is:

(np,f,t)=

[2]

Various correlations are proposed in the literature to calculate the equivalent diameter of particles in a bed with multiple dimensions. In our studies, we have calculated the Sauter mean diameter to calculate the equivalent diameter of the particle size in the bed (see Equation 3).

For Case 1: np,c is the number of particles of main catalyst with radius rp,c.

**Case 2: accumulation of fouling products on the catalyst surface **

The number of particles in this case remains the same as the initial number of particles.

For calculating the equivalent diameter, we have assumed that the surface being formed due to the deposition of particles is hemi-ellipsoidal in each part (assuming that the catalyst particles are divided into four parts, see Figure 3c) and appropriate formulae have been used to calculate the surface area of the equivalent particle (Se,t).

For Case 2:

[4]

The pressure drop in the two cases has been calculated using the Ergun equation (see Equation 5):

[5]

ΔPt is the pressure drop across the bed at time ‘t’; L is the length of the bed (for pressure drop across the fouled fraction of bed: L = Lf and for the rest L = Lt - Lf); dp,e,t is the equivalent diameter of packing; ρ is the density of fluid; μ is the dynamic viscosity of the fluid; v is the superficial velocity; and εB,t is the void fraction of the bed. The above calculation is carried out for each iteration of time step Δt.

Various time dependent functions (rate of fine deposition, rate of swelling, and so on) may be introduced in the above procedure to take into account the more complex dynamic behaviour of the system.

**Results and analysis**

The pressure drop in the bed for the two examples of fouling phenomena is calculated as discussed earlier. Sensitivity analysis with respect to parameters including the fouled fraction of bed length and the diameter of the â€¨catalyst particles and the fine particles is carried out to understand â€¨its effect on the pressure drop profile.

**Comparison of pressure drop due to the two fouling phenomena**

The pressure drop due to fouling in the two cases (Case 1: particle deposition and Case 2: particle swelling) has been compared in Figure 4. For the same rate of fouling (in terms of volume), the same extent of fouling (length of bed) and same diameter of the particle bed, the pressure drop is higher in the case wherein fines are concentrated in the voids between the catalyst particles compared to the deposition of fines on the surface of catalyst particles. At the end of the same cycle, the pressure drop in the first case is roughly twice that in the second case.

**Effect of fraction of bed fouled**

We varied the fraction of the region in which fouling takes place (usually the topmost layer of the bed). It can be noted from Figure 5a that the increase in pressure drop is most sensitive to the increase in the fraction of fouled bed; this is evident from the slope of the increase in pressure drop for the L = 0.1 m to L = 0.3 m case. It can be seen from Figure 5b that at 0.27 of voidage an exponential increase in the pressure drop across the reactor begins. We define this as the critical voidage. Hence a reactor showing an exponential increase in pressure drop may have reached the critical voidage of 0.27 at a certain layer of the bed. It can also be inferred from Figure 5a that the distribution of fouling over the entire length of the bed, instead of being concentrated in a smaller region of the bed, is crucial to increasing the run length of the reactor. This indicates the importance of strategies that ensure the distribution of fines (fouling particles) over the entire length of the bed. Skimming of the top layer of the bed from time to time is applied in various units. The length of the bed to be skimmed can be estimated from these calculations.

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