A Simple Control Parameter for Combustion Retorts
A strategy is proposed for operation of modified in situ oil shale retorts to achieve high recovery. The operating conditions required for a maximum pyrolysis time in front of a stable deflagration wave are defined by means of intuitive argument and a simplified analysis. An evaluation of this strategy by comparison to published data suggests that this approach is valid.
Introduction The establishment of external control parameters for shale-oil combustion retorting to obtain high oil recoveries must be on an a priori basis. It is not possible, particularly in the case of large underground operations, to control retorting gas composition or flow rates by means of a classical feedback scheme based on continuous measurement of the product gas composition. A principal objective of the USBM work on oil shale at the Laramie Energy Research Center has been directed a t establishing meaningful control variables, and data from the operations of their 150ton combustion retort (Harrak et al., 1974) are used here to develop a possible control parameter. An important result of the previous studies is the recognition that high recovery of the volatile materials from direct-combustion-heated oil shales can be achieved only if the residual carbon and not the volatile material is the fuel for the combustion process. A rubblized oil shale bed would be of very nonuniform particle size, and probably the only way to achieve high yields would be to ensure a rather large separation between the pyrolysis zone and the combustion zone in the advancing thermal wave. The best way to produce this separation seems to be to produce large quantities of hot gases at the combustion zone. Some degree of control of the quantity of hot gases leaving the combustion region could be achieved either by recycling combustion gases, as was done on the 150-ton retort tests, or perhaps by introducing steam with the air forced into the bed. It thus appears that the relationship between the retorting gas flow rate and the velocity of the deflagration wave is important, and the nature of this relationship is developed in the following paragraphs. Development By use of an approximate description for the temperature field preceding a deflagration wave, it is possible to gain some insight. Although some thermal energy is required to pyrolyze and gasify the shale oil, a much greater quantity is required to heat the shale and organic matter to a high temperature. Thus, to a first approximation, the equations describing the one-dimensional heat flow for passage of a constant property fluid through a solid apply. If it is also assumed that axial conduction and temperature gradients in the solid may be neglected, the following set of coupled partial differential equations should apply to the region from where the combustion products enter the solid at temperature Tc to where only the virgin material exists at To
aT
+ riz C
aT
pscs at + m,C,
aT
pgCg2 at
ax
+ ah(T,- T,)= 0
(1)
+ ah(T,- T,) = 0
(2)
and
aT
ax
Here the subscripts g and s refer to the gas and solid respectively, p is a density, C is heat capacity per unit mass, 82
Ind. Eng. Chem., Fundarn., Vol. 15, No. 1, 1976
T is temperature, m is the mass flux density (mass velocity) of the phase relative to an arbitrary reference, h is the gas-to-solid heat-transfer coefficient, and a is the surface area of contact per unit volume of bed. For the purposes of this discussion, a complete solution to eq 1 and 2 is not sought. If the frame of reference with r = 0 is chosen as the end of the combustion zone where T = Tc,a steady-state solution or temperature profile could exist for appropriate values of h, and m, (now taken relative to the deflagration front), m, being taken as negative. In the region from x = 0 to x = a,the steady-state gas temperature is given as (3) where 1 = Hg/(l - R ) , and is interpreted to be a measure of the separation between the combustion and pyrolysis zone in the oil shale bed;
I
I
R = mgCg,msCs ; H, =
c,riz,
ha often called the height of a gas transfer unit. If R is less than 1,a steady-state solution exists. The condition that R is greater than 1 implies that the thermal wave ahead of the deflagration front becomes increasingly thick with time. At this point, an intuitively plausible but ad hoc postulate is required. As this thermal wave becomes thicker, the stability of a planar deflagration front is impaired, and canting of the front and channeling of the gas flow ensues. By-passing of areas of the bed could occur and oil recovery would be low. This postulate could certainly be tested experimentally. An analytical evaluation of the stability of such a wave or of the gas flow uniformity in the bed appears to be possible to test this assumption. Thus, a condition for a stable, steady-state combustion and pyrolysis wave in the bed is that R be less than 1. No claim of proof is made, but if it is postulated that this condition is a valid criterion, a working hypothesis (to be later proved or disproved) is established. It is very likely that high recovery requires large values of I , the pyrolysis zone thickness, and it is of interest first to estimate 1 for the Laramie tests and then to consider techniques for producing large values of 1. First, for the reported conditions of these tests, it is found, by use of a correlation for heat transfer in packed beds (Gamson et al., 1943), that 1 is essentially equal to the mean-surface diameter of the bed (about 1 in.). Such a sharp thermal wavein a bed containing 0.5-m diameter (20-in.) material is likely not realistic. In fact, the neglect of axial conduction to yield eq 1 and 2 is probably not justified in this case where U s is quite small; however, because of the high heat-transfer rates in packed beds, sharp temperature gradients can exist, and small combustion-pyrolysis zone separations would be expected unless special techniques are employed. The obvious method for increasing 1 is indicated by the definition under eq 3. An increase in the gas flow velocity, m, increases 1 both by increasing H , and R.Since h is pro-
-
3
0 17.3
05 1.o 2.0 CONTROL PARAMETER, R
3.0
Figure 1. A summary of ’the USBM data from the 150-ton retdrt tests as fractional Fischer assay shale oil recovery as a fiinction of a
proposed control parameter. portional to the square root of mi, the increase in H, is proportional on mg1/2, and a large increase in 1 would not be easily obtained as a result of changing H,. The increase in 1 by increasing R as R approaches 1should be very effective. However, the deflagration velocity, -ms/ps, is coupled to m, by the combustion process, and the best method for increasing riz, without also increasing the deflagration velocity would be to reduce the oxygen content of the retorting gas. Obviously, this approach has its limits. If the oxygen content is too low, h, goes to zero and retorting stops. It appears that an operating value of the control parameter R of 0.90 to 1should be sought.
Discussion Figure 1 is a plot of the fractional oil recovery as a function of the control parameter R from data of the 150-ton
retort for the ten runs reported by Harrak et al. (1974). The prediction, based upon the arguments presented above, appears to be confirmed. Here, fractional recovery is the volume fraction of Fischer assay. To calculate R , the values of the deflagration velocity, -m,/p,, and the gas mass velocity, m,, were obtained from Table I of Harrak et al. (1974). A value of 1280 kg/m3 (80 lb/ft3) was used for the “dumped” density, ps, of the shale, and over the temperature range of interest, it was assumed that the solid-gas heat capacity ratio C,/C, was 1. The data presented in Figure 1represent a wide range of operating conditions, and the validity of the proposed control parameter is rendered plausible. In the range of values of R between 0.9 and 1.0, very high oil recoveries might be obtained. In practice, one could select the retorting advance rate desired by setting oxygen (air) flux density, and then by measurement of the actual retorting rate, the recycle rate of burned gas would be adjusted to ensure an R value near 1 to ensure maximum recovery.
Literature Cited Gamson. B. W., G. Thodos. Hougen. 0. A,, Trans. Am. Inst. Chem. Eng., 39, 1-21 (1943). Harrak, A. E., Dockter, L., Long, A., Sohns, H. W.. “Oil Shale Retorting in a 150-Ton Batch Type Pilot Plant,” U.S. Bur. Mines Rep. Invest., No. 7995
(1974).
Department of Chemical Engineering University of Utah Salt Lake City, Utah 84112
Alva D. Baer* Norman W. Ryan
Received for review June 9,1975 Accepted November 10, 1975
Diffusion in Mixed Polymer Solutions
Mass transport in solutions containing various polystyrenes in toluene was investigated in order to determine the effects of the polymers on the diffusivity. Although the addition of a polymer of a different molecular weight than those already in solution sometimes does, and sometimes does not, change the diffusivity of a third component through the solution, the results can be predicted a priori.
Introduction and Background Diffusion through polymer solutions is encountered many times in the polymer processing industry. Since diffusion is always a slow process, many times it is the ratecontrolling step in a diffusion-reaction sequence. The effect on the diffusivity of altering the polymer concentrations has been studied previously (Navari et al., 1971; Osmers and Metzner, 1972) and equations have been presented for the a priori prediction of the effect. Frequently the solutions contain polymers having widely different molecular weights. This will obviously alter the molecular weights and viscosities of the solutions. Thus, one might expect there to be different effects on the diffusion when varying the concentration of single polymer in solution than when varying the concentration of that polymer in the presence of other polymers having different molecular weights. Indeed such a result is apparently present in protein solutions. Varying the concentration of the pro-
tein albumin alone in solution appears to have little effect on the diffusivity, but the same variation results in rather large changes in the diffusivity if other proteins are present (Navari et al., 1970). Later studies (Gainer and Chisolm, 1973) have shown that this effect appears to be dependent on the types of proteins present in the solutions. In the work presented here, we have investigated the effect of changing the concentrations of polystyrene in toluene on the diffusion of cyclohexane in order to see if an effect similar to that seen in protein solutions exists. In addition, we have applied the equations of Navari et al. (1971) to determine if a priori predictions of the behavior can be made.
Theory The complete theory for diffusion in protein and polymer solutions proposed by Navari et al. (1971) is available elsewhere in the literature and will be discussed only briefInd. Eng. Chem., Fundam., Vol. 15, No. 1, 1976 83
