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### Managing petcoke slurry

There is a good economic case for petcoke slurry as a refinery fuel, but first you need to deal with the rheology

**PRAFULL PATIDAR and AJAY GUPTA**

Reliance IndustriesReliance Industries

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**Article Summary**

The term slurry commonly refers to solid-liquid mixtures covering a wide variety of particulate solids in the liquid phase. In slurry, the voids between particles are filled with liquid, and this makes it easier to handle and transport using pumps. Fuel slurries such as coal-water slurry (CWS) or petroleum coke-water slurry (PCWS) have gained attention over recent years. Converting coal or petcoke into a liquid form simplifies the delivery and dispensing of the fuel and may be a cost-efficient alternative to oil and natural gas. A typical PCWS consists of 60-75 wt% petcoke particles, about 1 wt% chemical additive, and the rest water. From the point of view of easier handling and pumping of these highly concentrated mixtures, it is desirable to have a lower slurry viscosity since the higher viscosity of the slurry increases the pumping energy requirement.

There are various problems associated with handling PCWS. These are summarised in Table 1.

Newtonian fluids with an added component can show non-Newtonian behaviour. The same is true for a suspension of solid particles in a Newtonian liquid such as that demonstrated in everyday life by concentrated corn starch solution. PCWS exhibits similar non- Newtonian behaviour. The presence of particles within the flow increases viscous dissipation compared with the pure fluid phase viscosity, which leads to an increase in the apparent viscosity. The apparent viscosity is mainly dependent on the volume fraction of particles and the extent to which the particles are flocculated. Viscosity increases with increasing volume fraction of solids and degree of flocculation. Einstein showed that, for dilute suspensions, the effective viscosity depends only on the solid loading. Analytically solving the hydrodynamics around a single sphere, he arrived at the following relationship to predict the viscosity of the suspension:

(1)

where η is the apparent viscosity of the suspension, φ is the volume fraction of solids, the coefficient 2.5 is a constant originally referred to as the intrinsic viscosity, although often called the Einstein coefficient. This equation assumes that the suspension is extremely dilute (φ <0.01) so that the flow fields that form around the particles do not interact with each other. This equation was later improved upon by including additional terms in order to consider the interaction of the flow field created around one particle with another particle. Batchelor gave the following relationship that can be used for an increased solids loading up to φ <0.25:

(2)

The Einstein and Batchelor models, although helpful for understanding dilute suspensions, suffer from the drawback that they break down for concentrated suspensions as is evident from the fact that as φ → 1, the viscosity approaches a finite value even though the viscosity of a solid is infinite (see Figure 1). This can be understood from the fact that the underlying assumptions of these models no longer hold in concentrated regime due to significant interparticle interactions. From experiments, it is well known that the relative viscosity continuously increases with increasing volume fraction and exhibits a singular behaviour at a value <1, the point of divergence commonly referred to as the maximum packing fraction. The viscosity of a suspension is more appropriately expressed in the form of a power law, which takes account of the fact that, beyond φmax, the viscosity of the slurry is effectively infinite and flow ceases. Taking cognisance of this, Krieger and Dougherty improved Einstein’s model by taking into account φmax:

(3)

where φmax is the maximum packing fraction, η0 is the viscosity of the liquid medium and η1 is the intrinsic viscosity or Einstein coefficient. The value of η1 differs from 2.5 for non-spherical particles.

Many other models exist to describe the behaviour of concentrated suspensions, and these are summarised in Table 2. These equations predict the correct limiting behaviour. Although none of these semi-empirical models can capture all of the complex behaviours exhibited by concentrated suspensions, with correct parameter values obtained from fitting available experimental data reasonably accurate predictions of viscosity can be obtained that are fit for practical applications. The Krieger and Dougherty model is the most popular amongst all of these and is commonly used.

The viscosity of a suspension increases with increasing concentration of solids. This is attributed primarily to the physical particle interactions that occur when a solid is dispersed in a liquid. There are three main categories of these physical interactions according to Cheng1:

(a) Hydrodynamic interactions that give rise to viscous dissipation in the liquid

(b) Particle-particle contact, bringing in frictional interactions

(c) Interparticle interaction, prompting the formation of flocs and aggregates, especially in fine particle suspensions.

The effects of hydrodynamic interactions dominate at low to medium solids concentrations where viscosity roughly increases linearly with increasing solids concentration. From medium to high solids concentration, particle frictional interactions become important while at very high solids concentration the particle effect predominates over hydrodynamic effects. After a certain solids concentration, further small increments of the concentration result in a significant increase in viscosity.

The viscosity of a slurry is affected by particle size distribution in the slurry. A narrow particle size distribution characterised by similar sizes of particles in a concentrated slurry would result in higher interparticle void spaces. As the particle size distribution increases, this allows for a greater packing fraction and thus reduced interparticle void spaces. This means that for a given solids concentration the same amount of solid particles can now be packed into a smaller volume, thus leading to greater availability of free water which provides better fluidity for the slurry and reduced viscosity.

Figures 2a and 2b show that the monodisperse mixture has interparticle void spaces whereas in a polydisperse mixture the smaller particles fill up the interparticle voids.

Figure 3 shows the variation of relative viscosity of suspensions with polydispersity. It can be seen that the same relative viscosity can be achieved with higher solids concentration when using polydisperse particles in suspension.

**Slurry handling challenges**There are various problems associated with handling PCWS. These are summarised in Table 1.

**Rheological behaviour of solid suspensions**Newtonian fluids with an added component can show non-Newtonian behaviour. The same is true for a suspension of solid particles in a Newtonian liquid such as that demonstrated in everyday life by concentrated corn starch solution. PCWS exhibits similar non- Newtonian behaviour. The presence of particles within the flow increases viscous dissipation compared with the pure fluid phase viscosity, which leads to an increase in the apparent viscosity. The apparent viscosity is mainly dependent on the volume fraction of particles and the extent to which the particles are flocculated. Viscosity increases with increasing volume fraction of solids and degree of flocculation. Einstein showed that, for dilute suspensions, the effective viscosity depends only on the solid loading. Analytically solving the hydrodynamics around a single sphere, he arrived at the following relationship to predict the viscosity of the suspension:

(1)

where η is the apparent viscosity of the suspension, φ is the volume fraction of solids, the coefficient 2.5 is a constant originally referred to as the intrinsic viscosity, although often called the Einstein coefficient. This equation assumes that the suspension is extremely dilute (φ <0.01) so that the flow fields that form around the particles do not interact with each other. This equation was later improved upon by including additional terms in order to consider the interaction of the flow field created around one particle with another particle. Batchelor gave the following relationship that can be used for an increased solids loading up to φ <0.25:

(2)

The Einstein and Batchelor models, although helpful for understanding dilute suspensions, suffer from the drawback that they break down for concentrated suspensions as is evident from the fact that as φ → 1, the viscosity approaches a finite value even though the viscosity of a solid is infinite (see Figure 1). This can be understood from the fact that the underlying assumptions of these models no longer hold in concentrated regime due to significant interparticle interactions. From experiments, it is well known that the relative viscosity continuously increases with increasing volume fraction and exhibits a singular behaviour at a value <1, the point of divergence commonly referred to as the maximum packing fraction. The viscosity of a suspension is more appropriately expressed in the form of a power law, which takes account of the fact that, beyond φmax, the viscosity of the slurry is effectively infinite and flow ceases. Taking cognisance of this, Krieger and Dougherty improved Einstein’s model by taking into account φmax:

(3)

where φmax is the maximum packing fraction, η0 is the viscosity of the liquid medium and η1 is the intrinsic viscosity or Einstein coefficient. The value of η1 differs from 2.5 for non-spherical particles.

Many other models exist to describe the behaviour of concentrated suspensions, and these are summarised in Table 2. These equations predict the correct limiting behaviour. Although none of these semi-empirical models can capture all of the complex behaviours exhibited by concentrated suspensions, with correct parameter values obtained from fitting available experimental data reasonably accurate predictions of viscosity can be obtained that are fit for practical applications. The Krieger and Dougherty model is the most popular amongst all of these and is commonly used.

**Factors affecting viscosity of slurry**

Concentration of solidsConcentration of solids

The viscosity of a suspension increases with increasing concentration of solids. This is attributed primarily to the physical particle interactions that occur when a solid is dispersed in a liquid. There are three main categories of these physical interactions according to Cheng1:

(a) Hydrodynamic interactions that give rise to viscous dissipation in the liquid

(b) Particle-particle contact, bringing in frictional interactions

(c) Interparticle interaction, prompting the formation of flocs and aggregates, especially in fine particle suspensions.

The effects of hydrodynamic interactions dominate at low to medium solids concentrations where viscosity roughly increases linearly with increasing solids concentration. From medium to high solids concentration, particle frictional interactions become important while at very high solids concentration the particle effect predominates over hydrodynamic effects. After a certain solids concentration, further small increments of the concentration result in a significant increase in viscosity.

Particle size distributionParticle size distribution

The viscosity of a slurry is affected by particle size distribution in the slurry. A narrow particle size distribution characterised by similar sizes of particles in a concentrated slurry would result in higher interparticle void spaces. As the particle size distribution increases, this allows for a greater packing fraction and thus reduced interparticle void spaces. This means that for a given solids concentration the same amount of solid particles can now be packed into a smaller volume, thus leading to greater availability of free water which provides better fluidity for the slurry and reduced viscosity.

Figures 2a and 2b show that the monodisperse mixture has interparticle void spaces whereas in a polydisperse mixture the smaller particles fill up the interparticle voids.

Figure 3 shows the variation of relative viscosity of suspensions with polydispersity. It can be seen that the same relative viscosity can be achieved with higher solids concentration when using polydisperse particles in suspension.

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