Mixing fffects in coal processing bioreactors

Resources, Conservation and Recycling, 3 {1990) 137-148 137 Elsevier Science Publishers B.V./Pergamon Press plc - - Printed in The Netherlands

Mixing Effects in Coal Processing Bioreactors

GRAHAM ANDREWS

Idaho National Engineering Laboratory, Idaho Falls, ID 83415 (U.S.A.)

(Received February 10, 1989; accepted in revised form August 29, 1989)

ABSTRACT

Andrews, G., 1990. Mixing effects in coal processing bioreactors. In: P.R. Dugan (Editor), Bio- processing of Coals Workshop, III. Resour. Conserv. Recycl., 3: 137-148.

In the bioprocessing of high-volume, low-value products like coal it is important to minimize the size and cost of the bioreactor. Optimum reactor design requires attention to the degree to which mixing should be induced or prevented. An analysis of a simple bioprocess in plug-flow and stirred-tank reactors shows that the amount of mixing required depends critically on the amount of microorganisms available from the inoculum and from cell growth. A mixed reactor is preferable when microbes are scarce and is the only possible solution when none are available to inoculate the coal entering the reactor. However, when sufficient cells are available (usually from cell recycling) a plug-flow reactor may be an order of magnitude smaller. The best solution may be a stirred-tank reactor feeding a plug-flow reactor and reactor size estimates for this system are given.

INTRODUCTION

The costs incurred in any biotechnology process can be divided conceptually into the cost of the substrate, the cost of the reactor (capital and operating), and the costs of separating the product. For low-volume, high value products the cost of the reactor is often insignificant. Drug production by tissue culture, for example, requires specialized expensive media and produces a dilute aqueous solution that must be concentrated to high levels of purity. Also, production may be of the order of grams per year, so the reactor is quite small and its cost is much less than the costs of the media and product purification. This is not the case with high-volume, low-value products. In coal depyritization for example, the pyrite itself is the main substrate and the "substrate cost" is limited to the small amounts of nitrogen, phosphorus, etc. that must be supplied. Prod- uct separation is limited to washing and drying the finished product, relatively straightforward operations. At the same time the quantities of coal involved are huge so the bioreactor must be large, and the cost of building and operating it will be a major factor in the overall process economics. Conventional me- chanically agitated, stainless steel fermentors would obviously be far too ex-

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138 G. ANDREWS

pensive, and the process must be carried out in slurry tanks, coal piles, or other simple and inexpensive types of bioreactor.

Whatever type of reactor is chosen, a major objective in scaling it up is to minimize its size and cost. There are two complementary ways of achieving this: microbiology and reactor design. Any improvement in the growth rate of the organism (s), the efficiency with which it attaches to the coal surface, or the amount of a critical enzyme produced can accelerate the process and reduce the reactor volume required. Some of the engineering requirements to minimize the reactor size for a given throughput are as follows:

(a) For the purposes of reactor design the most important difference between coal bioprocessing and conventional fermentation is that coal processing is a heterogeneous reaction at a coal/water interface. Its rate is propor- tional to the available surface area, a = 3 S / ~ J r per unit reactor volume, where S is the coal hold-up (coal volume/reactor volume), r is the particle radius and ~/its sphericity. Maximizing the reaction rate requires maximizing S and min- imizing r, so the reactor must contain either beds or concentrated (40-50%) slurries of finely ground coal.

(b) The actual process is usually carried out by microorganisms attached to the surface of the coal, or in the case of depyritization, to the surface of the pyrite. There would be no point in providing a large surface area unless sufficient microbes can be provided to saturate this area, which may be difficult. Growing bacteria in a separate fermentor in order to inoculate the coal has been proposed [ 1 ] but would be very expensive. In conventional fermentation the inoculum can be small because large numbers of cells grow during the process. This is not the case in coal bioprocessing; the actual substrate concentration in the reactor is usually quite small (oxidizing the coal's organic matter to produce cells would obviously be counter-productive) and cell yields are often low. Cell recycling is an obvious solution to this problem, but cells can only be recycled if they can be removed intact from the coal leaving the reactor or if some coal with attached cells is recycled back to the reactor inlet.

(c) The physico-chemical conditions throughout the reactor must be main- tained close to the values that give optimum microbial activity. This introduces problems of control of pH, temperature, etc. and mass transfer of gases (02 and sometimes CO2) between the air and the microorganisms. Unfortunately, (a) and (c) are mutually exclusive. In concentrated slurries gas transfer coef- ficients are reduced and microbial inhibitors (organic compounds, heavy met- als) may leach out of the coal [2 ]. Similarly, heaps of finely ground coal would not drain properly, and waterlogging would stop oxygen transfer into a heap.

Many different types of reactors have been, or could be, proposed for coal bioprocessing, including stirred tanks, a series of stirred tanks, fluidized beds, and various arrangements of beds of coal in heaps or on trays [3]. One of the main general differences between them is the amount of mixing that is induced or allowed to happen. The objective of this paper is to present a comparative

MIXING EFFECTS IN BIOREACTORS 139

analysis of the performance of stirred-tank and plug-flow reactors, which allows recommendations to be made about when mixing should be encouraged or eliminated. It is shown that the main factor which determines this is problem (b), the ability to provide enough cells for the process.

MIXING

The "plug-flow reactor" and the "completely mixed stirred-tank" are not real reactors but idealizations made by designers so that they can study the effect of mixing on the extent of conversion in real reactors. Completely mixing a commercial-scale coal bioprocessing reactor would require prohibitive amounts of energy, and the need to distribute nutrients to all the microorganisms in the reactor also makes plug flow impossible in practice. The relation- ship between these idealizations and real reactors can be described by their residence time distributions (Fig. 1). The distribution can be determined in principle by taking fluid elements (or particles or cells) from the reactor outlet and establishing the time they have actually spent in the reactor. It can be determined in practice from tracer studies [4]. In the ideal plug-flow reactor all fluid elements have been in the reactor for exactly the same time, equal to the nominal reactor residence time, v. At the other extreme, "complete mixing" implies that all fluid elements have an equal probability of reaching the outlet, irrespective of how long they have been in the reactor. From this is can be shown that the distribution of the actual residence times of the elements follows the function e-t/~. The residence time distribution function for all real

~ . . . I - - - - IDEAL PLUG

FLO~

I TIME

NCMmAL I~SZDENCe hME T = VOLUME FLOW RATE

Fig. 1. Residence time distribution functions.

140 G. ANDREWS

reactors falls between these two extremes, so a study of their behavior can tell the reactor designer whether or not mixing should be encouraged in the real reactor.

The question of whether mixing is desirable has been extensively studied [4]. A plug-flow reactor can usually be smaller than a stirred tank for a given conversion but the difference depends critically on the details of the process kinetics and there are exceptions. For zero-order kinetics (the flat part of the Monod curve for example) the two reactors would be the same size, and for negative order kinetics, including substrate-inhibited bioprocesses, the stirred tank can be considerably smaller. Mixing can have a particularly large effect on the autocatalytic, heterogeneous reactions involved in coal bioprocessing.

Consider for example a process like pyrite decomposition in which microorganisms grow while the particle size decreases. In a plug-flow reactor the absence of mixing means that there are gradients of pyrite particle size and cell concentration along the reactor. This produces gradients in the critical parameters of surface area and the extent to which the surface is saturated with cells. Note that there can also be gradients in the physico-chemical conditions, so it is possible to vary the pH (for example) as the process proceeds if this is found to be desirable. This can not be done in a stirred tank because "complete mixing" removes all concentration gradients. Conditions throughout this type of reactor are identical to the outlet conditions. In the process considered here, "outlet conditions" mean a small average particle size and high cell concentration which implies a low surface area per unit reactor volume but a surface that is likely to be saturated with cells. The problem is to determine the conditions under which this arrangement will give a higher reaction rate than the plug-flow reactor.

THEORY

Microorganisms

A coal processing bioreactor contains two cell populations, those in the liquid and those adsorbed on the solid. It is assumed that only the adsorbed cells are active in the process. The total microbial concentration is given by*

X = X 1 ( 1 - S ) + a X a (1)

where S is the solid concentration expressed as a volume fraction and a is the solid surface area per unit volume of slurry. The adsorption and desorption of cells is a rapid process [5 ] so the two populations are in adsorptive equilibrium. Myerson and Kline [6] showed that for the adsorption of Thiobacillus on coal this equilibrium could be described by a Langmuir isotherm:

*For nomenclature see Appendix at the end of the article.


Xa -K+X~" (2)

.~ is the saturation capacity of the solid surface for microorganisms and the parameter K describes the affinity of the cells for the surface.

The production of cells from the metabolism of the solid is given by the yield equation for the reactor:

X - X i - ~ Y ( S i - S ) . (3)

Since the main interest is the activity of the adsorbed cells, the quantities X and X~ are eliminated between eqs. (2) and (3) giving a quadratic equation for the degree of saturation of the solid surface:

x---~-- ~{b+c+ 1 _+ [(b+c+l)2-4b]l/2},

b= (I+GY)d ' c - - ~ X [ 1 - S i ( 1 - y ) 1' (4)

riXi - Yr i S _ ari

I=a-s, y= l - g,

The form of the dimensionless parameters I and G is significant. I is the cell inoculum parameter, equal to the number of cells in the inoculum divided by the number of cells required to saturate the surface of the incoming solid. G is the cell growth parameter equal to the number of cells generated by complete consumption of the solid divided by the number of cells needed to saturate the surface of the incoming solid (this is clear if top and bottom are multiplied by Si).

Since eq. (4) is so complex, only the limiting case in which the affinity of the cells for the surface is very high (K-c=O) will be considered. This gives two simple solutions (x= 1 or b) whose physical significance is as follows. If b < 1 than x--b and there are not enough cells in the system to saturate the solid surface. All available cells will be adsorbed (a consequence of the high- affinity assumption) so none will be found in the liquid. If b > 1, then there are enough cells to saturate the solid (x= 1 ) and excess cells will be found in the liquid.

Particles

The particles are assumed to be spheres of uniform initial radius, ri, which are consumed by the process. This "shrinking particle" model is reasonable for coal solubilization and the direct fermentation of cellulosics by organisms like Clostridium thermocelum. It also applies to coal pyrite decomposition if

142 c . ANDREWS

the pyritic inclusions are assumed to be monosized spheres of radius ri with their entire surface area accessible to bacteria (Andrews and Maczuga [7] discuss the effect of inclusion geometry on decomposition kinetics.) None of these particles are actually exact spheres, but experience with these analyses shows that the results are not sensitive to details of the geometry.

Additional cautions are necessary in applying this model to depyritization. The quantities S, a, X, Xa now apply to the inclusions not the coal. Bacteria adsorbed on the organic coal matter form a third population that is not in the liquid yet can not attack the pyritic sulfur directly. Nevertheless, both these bacteria and those in the liquid still have a role, which may or may not be rate limiting, in oxidizing ferrous iron to ferric. Despite these complications the qualitative predictions of the model will still be valid as long as the cells adsorb fairly selectively on the pyrite [5,6].

It is assumed that all microbial nutrients are present in excess, so the solid surface itself is the limiting nutrient for the attached cells and they metabolize it at a constant specific rate q cm3/g cells.h. The conservation equation for a single solid particle is

d r = - x a q , r=ri at t=0. (5) d(4~r3) X~q4nr 2 or dt dt

The plug-flow reactor

Sampling a plug-flow reactor would show that at any point all the particles have the same radius, because they have all spent the same time in the reactor. The fractional removal of solids is therefore given by

S 3 y = l - ~ = l - f . (6)

Since the variation of r with time is the same for all particles, eq. (5) can be integrated directly to give the required reactor size for a given conversion of solids:

1

T ~:qv_ f dr- (7) r i x

( 1 - y ) l / 3

Near the reactor entrance there are usually (unless I-> 1) not enough ceils to saturate the available surface area, so the appropriate solution to eq. (4) is x = b. Substituting this into eq. (7) gives

T=~G ln(l+---~/) , b < l . (8)


As the particles move down the reactor their size and thus their surface area decreases. Knowing the number concentration of particles ( n = 3Si/4~r3i ), the surface area of each particle (4ur 2 ), and eq. (6), it can be shown that

d = (1--y)2/3. (9)

With the continuous decrease in surface area and the continuous increase in microbial concentration due to cell growth, there must be a point in the reactor at which there are enough cells to saturate the surface. This corre- sponds to b = 1, and beyond this point the solution of eq. (4) is x = 1, the surface is saturated, and excess cells can appear in the liquid. Integrating eq. (7) past this point gives the variation of removal with reactor size:

T=~-~ln 1+ + ( 1 - y c ) l / 3 - ( 1 - y ) 1/3 (10)

where Yc is the value of y that makes b = 1. Note that if I= 1 the inoculum provides enough cells to saturate the inter-

face, yc = 0, and eq. (10) applies all along the reactor. Increasing the inoculum size beyond this point would not give any increase in reactor performance. Note also that if I=1 then eq. (8) gives T = ~ . A plug-flow reactor can not operate without an inoculum of cells.

The stirred-tank reactor

In contrast to the plug-flow reactor, the mixing in the stirred tank reactor keeps the cell concentration constant throughout the reactor. This keeps Xa constant [since adsorbed and liquid-phase cells stay in equilibrium according to eq. (2) ] and allows an overall mass balance on the solids equating the rate of disappearance of the solid [ F ( S i - S ) ] to the rate of consumption by attached cells (VaXaq). In dimensionless variables this becomes

y=3~xT. (11)

The difficulty with a stirred-tank reactor is that the particles leaving it are not all the same size. Some have spent only a short t ime in the reactor and are therefore still large, while others have had a longer residence time and are therefore much smaller, and still others have been completely consumed. It follows that the surface area a, must be an average value over all these particle sizes. To find this value, eq. (5) is first solved for an individual particle:

1 - x T t for t < l / T x ~= 0 for t>_l/Tx (12)

where t-= t / z and t is the actual t ime spent in the reactor by the particle. The residence time distribution for a stirred-tank reactor is e ~. It follows

144 G. ANDREWS

from eq. (11) that of the total number of particles put into the reactor (n-- 3Si/ 4~r~ ) a fraction e- i/Tx spent so long in it that they are completely consumed and the fraction e- t dt that spends from time t to t + dt in the reactor contrib- utes a surface area 4~r2n e t dt to the effluent.

Since the particle size distribution in the effluent is identical to that in the reactor (a consequence of complete mixing) it follows by substituting for r from eq. (12) that

I lTx I ' )

d-- ) (l+Txt-)2e-~d~ (13) o

Evaluating the integral and substituting from (4) and ( 11 ) gives

6= y =l-2Tx[1-Tx(1-e-1/Tx) ]= I -b Gy. (14) 3Tx

Although not an explicit equation, this is the complete solution for the stirred- tank reactor. The calculation procedure is to pick a value for Tx, calculate y, and then (knowing the values of I and G) evaluate b. If b -_- 1 then x = 1 and the solid surfaces in the reactor are saturated, while if b < 1 then b-- x and they are not saturated. In either case the corresponding value of the reactor size parameter, T, can be found.

RESULTS AND DISCUSSION

Results calculated from eqs. (8), (10), and (14) are plotted in Fig. 2 as fractional solids removal, y, versus dimensionless reactor size, T, with the inoculum size,/, as the parameter. The graph is drawn for G= 2 which is the correct order of magnitude for coal depyritization based on an effective cell yield of 0.04 gm cells/gin pyrite, a cell dry weight of the order of 10-13 gin/cell, and the observed fact that saturation of the surface (reflected in maximum rate in batch culture) requires slightly more than 1011 cells/g pyrite [2].

Figure 2 shows that when a large inoculum of microorganisms is available (I~ 1) the plug-flow reactor is smaller for a given solids removal. Its advantage over a stirred tank is particularly large if high removal is required. The stirred tank is larger by a factor of 5 for 90% removal, and infinitely larger for 100% removal since a stirred tank, unlike a plug-flow reactor, can not produce complete removal. All this is due to the broad residence time distribution of the stirred tank. Intense mixing means that some particles go straight from the inlet to the outlet, spending very little time in the reactor even when the nominal reactor residence time is large. As the reactor gets bigger there are fewer of these virtually untreated particles, but their relative contribution to the solids in the effluent becomes more important. This is why 100% removal is impossible.

The situation is completely reversed when little or no inoculum is available


4

,_~/--oi / 001/ 0~ / I->I i/ /7 O O l ~ J ~ / / ~ I / / /- , , /

~ -

! I / I

/ I / I I

J~:o I I :o.11 I y - / / - - - ~,o~.ow

/ / ~ Complete mixing

/ / / /

J-.------r / I i i 0 0.5 1 1.5 2

Dimensionless reactor size T

Fig. 2. So l ids remova l versus reac tor size.

( I= 0). A plug-flow reactor cannot function under these conditions because cell growth is an auto-catalytic process; if none are present then none will grow. A stirred tank will function because microorganisms that have grown on ex- isting particles are automatically "back-mixed" to the reactor inlet where they can inoculate incoming particles. Note that this mechanism requires that at least some of the cells desorb from a surface back into the liquid. This will always happen, even if cell adsorption is "irreversible," because the combina- tion of cell growth and the decreasing surface area of the particle must even- tually cause the surface to be saturated with cells. It will however happen more slowly in a process like organic sulfur removal in which the particle does not shrink. The vertical line in Fig. 2 for a stirred-tank with no inoculum corre- sponds to T= 1/3G or 3= 1/qYwhich is identical to the wash-out condition for a chemostat with a soluble substrate. For T< 1/3G and I=O a stirred tank would give zero removal because the microorganisms are washed out of the reactor faster than they can grow.

146 G. ANDREWS

The value of the parameters I and G over which a plug-flow or stirred-tank reactor should be preferred are shown in Fig. 3, which is a plot of the reactor size required for 90% removal versus the size of the inoculum. For nongrowing cells (G=O) and a small inoculum (I_< 0.13) the two reactors are identical. This happens because, in both reactors, all the available cells are adsorbed on a solid surface and are metabolizing substrate. However, for a given removal, there is much less solid surface area available in a stirred tank reactor so at I= 0.13 all the available surface is saturated with cells and any additional cells must stay in the liquid where they can not accomplish anything. This surface saturation condition gives a reactor size requirement of T= 2.30 which remains the same even if more ceils are available. For G>_0.145 the solid surface is always saturated with cells generated by growth, and Tmust be 2.30 completely independent of the inoculum size. In a plug-flow reactor the particles near the reactor outlet can be saturated with ceils while those near the inlet are not. This makes the reactor size a continuously decreasing function of the amount of cells available, whether they come from the inoculum (increasing I) or are generated by growth (increasing G). In the limit of large I and G, when all the particles are saturated, the size of a plug-flow reactor approaches T= 0.53. This is less than one quarter of the size of a stirred-tank reactor, solely because the plug-flow reactor contains more than four times the surface area of substrate.

In summary, a plug-flow type of reactor is superior except when the cell inoculum available is small. For 90% removal (Fig. 3 ) "small" means I < 0.092 if G--0.1, I<0.016 if G=0.4, •<0.0004 if G=2 and I--0 with any value of G

- - Complete mixing . . . . Plug flow

O

-

.1

Reactor - ' size - X ~ ~ 0 _ T ~ ~ ~ ~

~ ' - . - - - ~ = 05 " " ~ " - - - ~ i ~ . . . . . . ~ •

] ~------- = 20

o I I 0 0.1 0.2 0.3

Inoculum size I

Fig. 3. Reactor size required for 90% solids removal.


(the plug flow lines in Fig. 3 all go to ~ as I goes to 0). There is however no reason why the entire removal need to be done in a single reactor. If no inoculum is available the best solution may be two reactors, a stirred tank feeding both solids and microorganisms in to a plug-flow reactor to complete the process. No detailed analysis of this system can be given here because the feed to the plug-flow section would no longer consist of monosized particles. However, Fig. 2 which approximates the conditions for microbial depyritization suggests that the stirred tank should have T = 0.2 to avoid cell washout and that it would give 40% removal. With the large inoculum flowing into the plug-flow section, a size of T = 0.4 ~ 0.5 should be sufficient to remove another 50% of the solids. This idea is similar to the conclusion reached by Bos et al. [8] but the present analysis suggests that the proportions of their reactor system is incorrect. Their stirred-tank cell generation reactor consisted of only one tenth of the overall reactor volume, much smaller than one third to one fourth suggested here. It fed a series of nine similar tanks which together approximate a plug-flow reactor.

CONCLUSIONS

The cost of the reactor will be a major factor determining the economic vi- ability of a coal bioprocessing operation. The type of reactor that should be used in order to minimize this cost depends critically on the amount of mi- croorganism that are available to inoculate the incoming coal. If enough cells are available, from cell recycle or some other source, to saturate the solid surface (the pyrite surface in the case of depyritization) then a plug-flow type of reactor is better. For high solids removal it need be only 10-20% the size of a stirred-tank reactor. This is due mainly to mixing causing short-circuiting of the reactor, so some solid particles appear in the effluent virtually untreated. However, if only a small inoculum is available, a stirred-tank reactor is preferable because mixing moves the microbes that grow during the process back to the reactor inlet where they can inoculate the incoming coal. This can not happen in a plug-flow type of reactor. When high solids removal is required and little or no inoculum is available the best solution is a stirred-tank reactor operating slightly above the wash-out point and feeding into a plug-flow "fin- ishing" reactor.

APPENDIX. NOMENCLATURE

a solid surface area per unit volume of G Yrl/3~:; dimensionless cell growth reactor parameter

d ari/3Si I riXi/3SiX; dimensionless cell inocu- b (I+ Gy)/d lum parameter c K( 1 - S ) laX K affinity constant for cell adsorption

148 G. ANDREWS

q specific consumption rate of solid X1 cell concentration in the liquid F r/ri Xa adsorbed cell concentration r particle radius X saturation capacity of surface for cells S volume fraction of solids x Xa/~:; degree of saturation of surface t time spent by particle in reactor y 1 - - S/Si; fraction removal of solids E t/v y¢ solution of ( I+ Gyc) -- (1 --yc) 2/3 T ~:f~q/ri; dimensionless reactor size Y cell yield per unit volume of solid

parameter z nominal reactor residence time X total cell concentration in reactor i (subscript) reactor inlet conditions

ACKNOWLEDGEMENT

This work was supported by contract No. DE-AC07-76ID01570 from the U.S. Department of Energy, Advanced Research and Technology Develop- ment Office to the Idaho National Engineering Laboratory.

REFERENCES

1 Isbister, J., 1986. Biological removal of organic sulfur from coal. Proc. Workshop on Biological Treatment of Coals, Herndon, VA, June 1986.

2 Andrews, G.F., Darroch, M. and Hansson, T., 1988. The bacterial removal of pyrite from concentrated slurries. Biotechnol. Bioeng., 32: 813.

3 0 l s e n , G. and Brinkmann, F.E., 1986. Assessment of bioprocessing of coal. Proc. Workshop on Biological Treatment of Coals, Herndon, VA, June 1986.

4 Levenspiel, 0., 1974. Chemical Reaction Engineering. Wiley, New York. 5 Bagdigian, R.M. and Myerson, A.S., 1986. Biotechnol. Bioeng., 28: 467. 6 Myerson, A.S. and Kline, P., 1983. Biotechnol. Bioeng., 25: 1669. 7 Andrews, G.F. and Maczuga, J., 1984. Fuel, 63: 297. 8 Bos, P., Huber, T.F., Kos, C.H., Ras, C. and Kuennen, J.G., 1986. A Dutch feasibility study on

microbial coal desulfurization, in: R.W. Lawrence, R.M.R. Branion and H.G. Ebner (Editors), Fundamental and Applied Biohydrometallurgy. Elsevier, Amsterdam, pp. 129-150.

Mixing fffects in coal processing bioreactors

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