CFD Modeling of Slurry Bubble Column Reactors for Fisher-Tropsch Synthesis
By Andrey A. Troshko, Franz Zdravistch
Chemical Engineering Science 64 (2009) 892-903
The Fischer–Tropsch process (or Fischer–Tropsch Synthesis) is a catalyzed chemical reaction in which synthesis gas, a mixture of carbon monoxide and hydrogen, is converted into liquid hydrocarbons of various forms.
Franz Fischer (left) and Hans Tropsch (right)
This reaction is an exothermal reaction.
Catalysts are needed for this reaction. Catalysis is the process in which the rate of a chemical reaction is either increased or decreased by means of a chemical substance known as a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. The catalyst may participate in multiple chemical transformations. Catalysts that speed the reaction are called positive catalysts. Catalysts that slow down the reaction are called negative catalysts or inhibitors.
The most common catalysts are based on iron and cobalt, although nickel and ruthenium have also been used.
So there are liquids (Products), gases (reactants), and solids (catalysts) in the reaction, the bubble column reactor is suitable for this kind of reaction.
There is more information about this reaction in: http://www.fischer-tropsch.org/.
Importance of this reaction:
The principal purpose of this process is to produce a synthetic petroleum substitute, typically from coal, natural gas or biomass, for use as synthetic lubrication oil or as synthetic fuel. This synthetic fuel runs trucks, cars, and some aircraft engines.
2. Bubble Column Reactor:
The reactants for the Fischer-Tropsch synthesis reaction are both gases (hydrogen and carbon monoxide) and have to interact with a solid catalyst particle for a reaction to take place. This can be achieved by designing a bubble column reactor. In this type of reactor the catalyst particles are suspended in a solvent (water, ethanol, toluene, etc) to create a homogeneous mixture called a slurry. The reactant gases are pumped through the bottom of the column and form bubbles. As they rise through the column, gas from the bubble absorbs into the slurry causing the bubble to shrink. These reactors are usually run in semi-batch mode as opposed to a continuous mode. The reactor is considered semi-batch because the reaction products are removed from the solvent using a separation device.
Other Bubble Column Reactors:
Structured Bubble Column Reactors:
Structured bubble column reactors combine a traditional bubble column with a packed or trickle bed reactor. The packing consists of wire mesh sheets, which are patterned to maximize surface area and develop channels for gas and liquid flow. Instead of the catalyst particles being suspended in the slurry phase, they are now sandwiched between sheets of the wire mesh, shown in Fig Y. Some of the key advantages of a structured bubble column reactor over a traditional bubble column are:
i. ease of separation between catalyst particles and liquid
ii. increased selectivity to desired products
iii. increased conversion of products to reactants
There is a lot of interest in developing structured bubble column reactors for several industrial chemical processes including Fischer-Tropsch synthesis.
Aside from the chemicals industry bubble column reactors are used in the biological/pharmaceutical industry for fermentation reactions. In these systems the reactant gas, usually oxygen, is pumped into a broth of water and cells. Bubble columns allow for increased dissolved oxygen in the reactor broth, which leads to higher cell concentrations and productivity.
3. CFD Modeling
Computational fluid dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the millions of calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions.
An example of CFD modeling: A computer simulation of high velocity air flow around the Space Shuttle during re-entry.
If we have developed the model, we can use computer to do some simulation and present the results intuitively. In this paper, a CFD model of FT reactors have been developed.
Developing the model:
1. Coalescence and Breakup
As the bubbles move through the slurry they may experience coalescence and breakup. Coalescence is when two bubbles merge to form one larger bubble. Breakup occurs when turbulent eddies (pockets of energy formed by the bubbles moving through the slurry) within the slurry impact a bubble. The presence of catalyst particles hinders the formation of eddies strong enough to cause bubble breakup.
2. Developing a Bubble Size Distribution:
At any point in time a bubble column reactor will contain a large distribution of bubble sizes. This is attributed to gas absorbing into the slurry and coalescence and breakup taking place. To characterize this distribution and its behavior over time with respect to specified parameters a population balance equation must be developed. The distribution must be approximated by dividing the range of bubble sizes into a discrete number of subclasses, ex. 0.5 cm < bubble dia. < 1.5 cm is subclass 6.
Conservation equations, specifically mass, can then be evaluated for each of these subclasses.
The conservation equation accounts for absorption into the slurry gs,i and coalescence/ breakup rates Sgi, thereby characterizing the bubble size distribution. One of the key assumptions made for this system is that coalescence and breakup do not occur at heights below 0.4 column diameters.
3. Mass Transfer of Gas to Catalyst Surface:
Reactants located inside the bubble must travel to the catalyst particle’s surface by a series of mass transfer steps. It is important to quantify these steps into an overall mass transfer rate equation to evaluate the performance of the reactor. Since both the bubble and catalyst particle are moving in the solvent thin films form on their surfaces’. Mass transfer across a film is known as convective diffusion.
The overall mass transfer for a bubble column reactor is described in two major steps: diffusion out of the bubble and adsorption onto the particle surface. Based on a series of assumptions (well-mixed fluid, relative diffusion rates in gas and liquid, etc.) several of the mass transfer steps can be neglected because of their limited effect on the overall mass transfer rate. From this we find that the overall mass transfer rate is only a function of the convective diffusion at the bubble-liquid interface and is described using the form:
Where kLa and Hg are constants (Volumetric mass transfer coefficient and Henry’s constant) and cg and cs are the gas and slurry concentrations.
4. FT Reaction Rate
This reaction is a surface reaction, and it is considered as a Langmuir-Hinshelwood Type. It was assumed that CO was the predominant surface species, CO is more strongly adsorbed than H2.
The overall reaction rate can be expressed as: (Yates and Satterfield, 1991)
1. Air-Water Bubble Column
How the Bubble Size Distribution Evolves in a Reactor?
By using a bubble size distribution characterized by the population balance and mass conservation equation a CFD model of a bubble column reactor can simulate hydrodynamic behavior of both the bubbles and slurry.
Instant (a) and Average (b) bubble volume fraction predicted by CFD model
For a simple system like air bubbles moving through water at atmospheric conditions we can see that the CFD model predicts a majority of the bubbles to pass through the center of the column.
Instant (a) and Average (b) water velocity vector predicted by CFD model
Since a majority of the bubbles are passing through the center the solvent in the center is forced up the column. As you move towards the edge of the column there are less and less bubbles pushing the water up. Eventually the force of gravity dominates and the water flows back down the column.
Instant (a) and time- average (b) average bubble diameter predicted by CFD model
Average Bubble Diameter vs Radial Position in the column predict by the model and experiemental data
Further analysis of the simulated reactor shows that the average diameter of the bubbles increases as you move up the column. This indicates that coalescence dominates over breakup as you move up the column. The simulation also indicates that the average bubble diameter decreases as you move away from the center of the column. Therefore, it can be implied that breakup begins to dominate over coalescence as you move to the outer edge of the column. This result is in agreement with experimental data by Kulkanari, 2004.
2. Fischer–Tropsch Commercial Reactor
Compared with the air-water reactor, the simulation reactor used in the commercial FT reaction, with geometry 30m high, ID=7m, operating at 30 bar pressure and 513K. Each simulation described below was run sequentially in three stages.
First (stage1), a reaction free simulation was run to establish the base hydro-
Dynamic flow patterns.
Second (stage2), heterogeneous reactions ,were included. The reaction time scales (kLa) are of the order of 1s. This time scale is much shorter than the bubble residence time scale. Thus, the expected result is a quick saturation of the liquid species. Therefore, it is expected that the results from stages1 and 2 should be very similar.
Third, the FT reaction (stage3) was activated. Under the specified operating pressure and temperature, the time scale of the FT reaction was much longer than the time scale of heterogeneous reactions. Hence, the FT reaction rate was a limiting factor in the chemical kinetics.
Simulations were run for gas inlet velocities of 0.1 and 0.4 m/s and catalyst volume fractions of 20% and 35%.
i) Gas Phase Analysis:
Predicted instant gas volume fractions. (VOF)
Inlet velocity 0.1m/s(Left) and 0.4m/s(right). a) 20% Catalyst Concentration; b) 35%.
The comparison of stages 1 and 2 proves that, as expected, heterogeneous reactions alone lead to a quick saturation of the liquid phase by CO and H2 so that reactions stop and there is no further mass transfer from the gas bubbles. Introduction of the FT reaction leads to reduced levels of CO and H2 in the liquid, so heterogeneous reactions become active again restarting the mass transfer process from the gas bubble phase. The rate of the gas bubble phase mass transfer is dictated by the FT reaction rate. At syngas inlet velocity of 0.1m/s, virtually all the gas in the bubbles is consumed, therefore the final gas hold up at stage 3 is independent of catalyst concentration. At the higher syngas velocity of 0.4 m/s the rate of gas mass transfer is limited by the FT reaction rate so the gas holdup is lower for 35% catalyst VF due to higher FT reaction rate.
ii) Slurry Phase Analysis:
Concentration Distributions in Slurry (Liquid Phase)
0.1m/s; 20% Catalyst Concentration
Concentration Distributions in Slurry (Liquid Phase)
0.4m/s; 36% Catalyst Concentration
For Reactants: CO and H2:
For a syngas inlet velocity of 0.1m/s, Slower gas mass inlet.
A continuous distribution is observed with maximum rates near the gas sparger. For 0.1m/s gas velocity, the whole gas is consumed near the sparger, so the flow field is basically stagnant. In this case, the FT time scale is not large in comparison with the species diffusion time scale. Therefore, the liquid species have non-uniform distribution.
For product CH2:
There is a uniform distribution of product species CH2 in the slurry phase. This is a consistent pattern since the turbulent mixing time scale in the slurry is much shorter than the FT time scale. Product distributes quickly after formation.
iii) FT Reaction Rate Analysis:
Predicted time averaged FT reaction rate.
Non-uniform liquid species distribution leads to a non-uniform distribution of the FT reaction. This is the expected result as the FT reaction rate is proportional to CO and H2 slurry concentrations.
From the reactor design point of view:
This is a very important result, since the model predicts a non-uniform distribution of the FT reaction rate when the mass transfer due to the FT reaction is comparable to the gas mass inlet rate. For such a case, the placement of the cooling heat exchanger may become important. The model predicts a uniform FT reaction rate distribution for 0.4m/s inlet conditions. This is a consequence of the FT reaction time scale being much larger than the turbulent time scale of the species dispersion in slurries resulting in a uniform species distribution. In this case heat release is distributed uniformly in the reactor.
The Fischer-Tropsch synthesis reaction has significant potential to decrease our societies dependence on crude oil for the production of hydrocarbons. It is significantly faster and cheaper to design a model that simulates a reactor then to actually build and test a pilot reactor. To develop this model considerations must be made about the distribution of bubble sizes, mass transfer effects, and surface catalysis mechanisms.
This model predicts that if the inlet gas velocity is very low (0.1 m/s) the FT reaction rate is non-uniform and is unaffected by catalyst concentration. This is important when designing heat exchanger placement for the reactor. As the inlet gas velocity is increased (0.4 m/s) then the FT reaction rate becomes uniform and is affected by catalyst concentration. Experimental data needs to collected to support these findings. Future work is still needed to evaluate heat transfer effects of the system.