Computers & Chemical Engineering Vol. 8, No. 6, pp. 329-338, 1984 Printed in the U.S.A.

0098-1354184 $3.00 + .OO o 1985 Pergamon Press Ltd.

SIMULATING THE EFFECTS OF CHANGING PARTICLE CHARACTERISTICS IN SOLIDS PROCESSING

G. L. JONES Gulf Research & Development Company, P.O. Drawer 2038, Pittsburgh, PA 15230, U.S.A.

(Received 11 January 1984; receivedforpublication I February 1984)

Abstract-Solids processes are unique in that they often involve changing particle characteris- tics, i.e. size and age distributions and composition, as well as more familiar variables such as temperature, pressure, and enthalpy. These characteristics are usually coupled through chemi- cal reaction, heat and material balances, and particle flow, thus making detailed simulation of solids processing difficult or impractical. This paper explores a new approach to simulation of these effects through use of a matrix of solids attributes or descriptors incorporated into a process simulator. By combining the attribute matrix concept with detailed models, i.e. chemical reaction and particle attrition, the process model is capable of simulating a variety of effects, such as particle attrition with reaction and particle elutriation in a solids recycle process. Rules governing manipulation of matrix values and detailed models specific to particle breakup and changing composition are described. Specific application is made to a hypothetical process for extracting oil from shale. These enhanced simulation capabilities have helped to improve understanding of the way the changing particle characteristics affect overall process perfor- mance.

ScowThe problem is to find an effective and efficient means of simulating the multidimen- sional, coupled effects of changing particle size, carbon content, and residence time in the detailed simulation of an oil shale process involving recycle of solids. A technique is discussed which simulates this multidimensional combination of characteristics. The concept of a multidimensional substream attribute matrix is introduced and described in general terms. The attribute matrix is a natural extension of the vector of substream attributes which is commonly used for particle size information. The technique is applied to a hypothetical oil shale process using the two-dimensional particle size-carbon content attribute matrix. Extension of the technique to the three-dimensional case to include the influence of residence time distribution is also briefly discussed.

Conch~~ions and Significant+--The substream attribute matrix is a powerful tool in the simulation and engineering analysis of complex processes, particularly for solids handling and with solids recycle. Information which previously was outside the scope of process simulation can now be utilized and manipulated to understand complex processes better. This concept may offer an efficient means of better approximating very complex unit operations within a large process simulation with many other simple unit operations. The capability of simulating multidimen- sional effects in solids processing (residence time, particle size and composition distributions) now depends on our ability to obtain adequate data for such systems. A number of surprising results were obtained from the simulations. It was found that the shale process tends to be self-correcting which allows processing of high grade shales. This self-correcting effect is due in part to the reduction in solids residence time which results when particle attrition and, therefore, particle elutriation, increase. The simulations also show that it is at least theoretically possible to eliminate most of the fine particles with the flue gas, thus substantially reducing the recycling of fines and the entrainment of fines in the product vapor. Conditions which reduce the ratio of feed to recycle solids are beneficial in several ways which were not previously expected. These conditions reduce the average solids residence time as well as the amount of recycle solids, thus reducing the production and buildup of fine particles in the process.

1. INTRODUCTION Solids processes offer unique challenges for process simulation. Process simulators are frequently struc- tured to handle information needed to deal with fluid streams. This information includes mass and mole flows, enthalpy, density and pressure. However, this information alone may not adequately describe pro- cesses involving solids. Areas as different as microbial bioengineering, sewage treatment, mineral leaching

and synthetic fuels all deal with various kinds of solids with properties or characteristics not customarily han- dled by process simulators.

One such application of interest to Gulf Research & Development Company involves the retorting of oil shale. Generally, a surface process for extraction of oil from shale [l] involves heating crushed shale in a retort to decompose the kerogen and produce oil (Fig. 1). Decomposition of kerogen leaves behind a

329

330 G. L. JONFS

FLUE QAS l ENTRAINED SOLIDS

DISENQAQEYENT

ZONE,‘i ,“= , RAW SHALE

w3 da a0 RECYCLE

00YBU810R -SHALE OIL

\$ EXCESS VAPOR PRODUCT

is- SOLIDS ENlRAlNfD SOLIDS

;: a

RETORTED SHALE REACTOR 1

AIR -_)

Fig. 1. Hypothetical oil shale retorting process with internal heat recovery.

dense carbon residue making the retorted shale quite combustible. Heating is often accomplished by mixing raw shale with a fraction of the burned shale which is recycled from another part of the process. Fine shale particles are entrained with the product vapor from the retort and with the flue gas from the combustor. During retorting and combustion, particles breakup or attrite, causing the particle size distribution to shift toward smaller particles and producing a great many fine particles.

Attrition has been linked particularly to the removal of the hydrocarbonaceous matrix during retorting and combustion and to mechanical abrasion between particles during fluidization and flow [2]. The severity of particle breakup depends on the extent of chemical reaction, on the carbon content of the raw, retorted and burned shale, on flow conditions and solids residence time.

Entrainment of solids in the product vapor and flue gas depends on particle size, physical properties and flow conditions. Thus, solids entrainment leads to an interaction between particle attrition and the overall heat and material balances. Excessive particle attri- tion will lead to high levels of solids elutriation, resulting in a depletion of recycle solids which may cause incomplete particle heatup and then incomplete kerogen conversion. High solids entrainment in the product vapor may cause severe overloading and plug- ging of product collection systems.

Solids composition and size distribution may also be influenced by solids residence time in the recycle loop. Since shale recirculates until it is elutriated with the product vapor or flue gas or is split from the recycle, solids residence time within the loop is estab- lished by the configuration. Since elutriation is par- ticle size selective, a residence time distribution devel- ops which depends on particle size. Although solids may be in plug flow within the retort and combustor,

the overall recycle process behaves like a partially backmixed solids reactor. As in a partially backmixed reactor, solids residence time will depend on inlet and outlet flow rates and internal process details. As a

result, there is a coupling between solids residence time, particle size, composition, overall heat and mate- rial balances, and process performance characteris- tics.

Solids characteristics are thus an essential factor in describing solids process operation and improving pro- cess performance.

2. DISCUSSION

2.1. Stream and substream structure concepts One of the most important aspects of process

simulation is that of stream structure. In the stream vector is stored essentially all the information about a particular stream including extensive and intensive properties (temperature, mass and molar flow rates, pressure, enthalpy, entropy and density, vapor or liquid fraction, molecular weight) and attribute infor- mation.

The particular way in which the information is stored is less important than what information is carried in the stream vector. In ASPEN and ASPEN PLUS, the stream structure is broken down into information groups:

(1) conventional components (i.e. real or pseudo substances having molecular weights and critical properties),

(2) nonconventional components (hydrocarbon solids such as bitumen, kerogen, coke, minerals such as silicates, carbonates or pyrites),

(3) nonconventional component attributes or de- scriptors such as composition information (sulfur anal- ysis, proximate analysis and ultimate analysis), and

(4) substream attribute information.

Changing particle characteristics in solids processing 331

This last area, substream attribute information, is the feature which allows manipulation of unusual information unique to a particular process and one which offers potential for better simulation of solids processing.

The concept of substreams was introduced to dif- ferentiate primarily between gas-liquid phases on the one hand and solids on the other. The concept is quite powerful in that within a given stream there could exist multiple conventional substreams (immiscible liquids) and multiple nonconventional substreams (reactive and nonreactive solids for example).

A more complete discussion of stream structures may be found in the literature [ 34.

2.2. Substream attribute concepts Substream attributes are also quite general in

concept. Descriptors could include particle size, com- position, or age information, depending on the unique features of the process. Applications in which particle size and solids composition are important descriptors abound particularly in synthetic fuels processing (i.e. shale, coal, hydrocracking with solid catalysts). In such processes where reactions occur within or on solid particles, there is usually a relationship between the particle composition, particle size, and often residence time.

2.2.1. Attribute matrix. The multidimensional nature of the process can be treated by introducing a matrix of substream attribute values, each of which represent the mass fraction of the particular sub- stream having a unique set of attribute values as illustrated in Fig. 2. Shown is a two-dimensional matrix fi. The values in the matrix represent the weight fraction of the solid substream having the particular attribute values represented by the coordi- nates of the matrix. The specification and definition of these coordinates are quite flexible and are not funda- mental to the main computation occurring in ASPEN.

1,, M,*. . . . . . . . . . .Mlr

121 M22

h hll I

Fig. 2. Generalized 2-dimensional M x n solid substream attribute matrix.

1 n

This area is essentially a blank slate upon which the user may write.

The matrix implies a relationship (correlation) between the variables such as particle size and carbon content, although no relationship may exist. In Fig. 2 the particle size is an arbitrarily assigned value asso- ciated with each row of a. Similarly a component weight fraction value is associated with each column of R.

The present application employs only a two-dimen- sional array. However, the matrix can be expanded to three or more dimensions for processes in which a clear relationship exists between three or more solids attri- butes. For example, in combustion of hydrocarbona- ceous solids, there is a definite but very complex relation between particle size, composition, and resi- dence time. Situations where there is little interaction between variables could be handled by introducing a series of one-dimensional attribute matrices (vectors). A trivial example would be the use of various particle size distributions for various solid substreams within each stream.

In order to use the matrix concept it is necessary to choose discrete values of the otherwise continuous variables being modeled. For example the continuous particle size distribution is generally divided into discrete values by sieve analysis. Likewise the compo- sition variable must also be discretized based on estimates of the expected range of composition. Par- ticle size and composition variables have definite finite ranges allowing a reasonable choice of the number of points and the magnitude of the values. However, residence time does not have a bounded distribution. Suitable estimates of the distribution characteristics and trunction must be used to properly introduce this type of variable. In short, the values must be assigned based on some understanding of the details of the process.

Computer capacity limitations and CPU costs will usually dictate choice of the smallest size matrix consistent with modeling accuracy. The discretization of the attribute matrix does not place any limitation on kinetic models which may simulate the same reactions for heat and material balance calculations. It should be kept in mind that these two processes are essentially separate, although information will be passed between models and the results of one model will undoubtedly influence those of the other. In other words, process simulation may proceed on two levels, one based on processing of conventional information (heat and material balances, design specifications) and a second based on unconventional information such as descrip- tors and attributes. It should also be pointed out that a third but related set of information which may be manipulated is that in the component attribute portion of the stream vector.

2.2.2. Matrix operations. The elements of R are governed by simple material balance rules. The follow- ing notation is based on manipulation of a two- dimensional (m x n) matrix as shown in Fig. 2 but could be extended to systems of any dimension.

332 G. L. JONFS

Fig. 3. Simple mixer for substream attribute matrices.

The sum of all the elements of B = [Mij] is unity These types of simple processes are often handled automatically [6]. More interesting processing blocks

T $ Wj = I (1) can be constructed based on user information. Two such blocks are a selective splitter and a reactor which are discussed in general terms introducing the mathe-

where i may relate to particle size and j to carbon matical concepts. This is followed by a specific exam- content. A vector iii can be readily constructed to ple taken from actual experience with retorting of oil represent the fraction of the total solids within each shale at Gulf Research & Development Company. For particle size independent of composition. purposes of illustration, only the simulation results

pertaining to the substream attribute matrix are dis-

rrq=tM, (2) cussed.

I

Similarly a vector g can be constructed to represent the fraction of the total solids within each composition fraction independent of particle size

gj = 2 Mij (3) i

2.2.3. Mixing. In mixing one or more streams containing the same substream types, each of the mixed outlet substream attribute matrix elements is equal to the average of the inlet elements weighted by the relative mass flow rates of the substreams as shown in Fig. 3 and Eq. (4) for two input streams

j&,!‘=fM~’

+ (1 -j’)My’ (i = 1, n j = 1, m), (4)

where by mass balance

p = pou + pz) (5)

2.3. Conceptual illustration of solids processing with recycle

A conceptual process involving a number of solids processing blocks with recycle is shown in Fig. 5. In the first block, a single feed stream is mixed with a single recycle stream which flows into a reactor block. In the reactor block, particle size and composition are changed. The reactor e&rent enters another block representing particle size selective removal. The stream is then split nonselectively into a product and a recycle stream.

In general the total flows and split fractions of the streams are governed by heat and material balances and detailed design specifications for a particular process and will be assumed known in the present discussion. In converging the flowsheet, all valEes in the tear stream including the elements of M are converged by one of a variety of methods. Detail of the decomposition, storage, and convergence of M in the stream vector are outside the scope of the present discussion. These topics have been described elsewhere [7-l 11.

and

f _ F(O’)/F(‘).

The concepts are illustrated by applying a simple

(6) input-output analysis over each block. The mixer and nonselective splitter blocks in Fig. 4 were described

2.2.4. Nonselective splitting. In nonselective previously. splitting of the solids stream (Fig. 4), the elements in 2.3.1. Selective splitting. The selective splitter

M are unchanged in the various outlet streams as (Fig. 4) performs a linear transformation of the inlet

shown to the outlet matrix. Examples include cyclones, hydrocyclones, centrifuges, fluid bed elutriators, and

(7) storage bins and towers. Generally, the splitting will be

Fig. 4. Splitter for substream attribute matrices.

Changing particle characteristics in solids processing

Y (R’

. F (RI

‘I y 03

) MIXER y (A)

) REACTOR Y (R’ SELECTIVE Y (=’ ,E;g& Y tp’

F (F) F (A) F (” 8PL’TTER F (C) SPLITTER F (P)

Fig. 5. Conceptual model of substream attribute matrix in solids processing with recycle.

a strong function of particle size and a weak function of composition such as S(Di, ci). S must be defined such that

where Di and cj represent the values of particle size and composition variables. Defining the inlet mass flow of each element

F!?) = F(O) M?) 1, 1, . (9

The outlet flows of each element in the first outlet stream is defined as

F!!” = SF!!’ ‘I 1, . (10)

By mass balance

F!!2’ = F!O) _ F!!” V 1, 11 .

Then by definition of total flow

(11)

(12) 1 i

By overall mass balance

F(r2) = F’o’ _ For) (13)

and the attribute matrices in the outlet streams are readily determined

,$I) = F$‘)/F(‘O, (14)

Mj,!” = Fjj2’/F’12’. (19

333

2.3.2. Particle breakup and reaction. The power of the substream attribute matrix in simulation derives mainly from the flexibility of ASPEN to incorporate any number of user supplied subroutines (@tch as a reactor block) which transform the values of M based on process features.

In the conceptual “reactor” block, illustrated in Fig. 6, F(O) and F(l) represent the total mass flow rates and M$‘) and Mg) represent the values of the individ- ual elements in substream matrix in the inlet and outlet streams, respectively.

(a) General concepts: the approacJ used to deter- mine the general transformation of M for the “reac- tor” block is similar to that used in the selective splitter block. Expressed in operator notation, the process of reaction and particle breakup is a transfor- mation of the elements of l%“) into Go) as shown

In a practical application, the extent of particle breakup will depend on particle size, composition, residence time, and flow conditions while the extent of reaction (assuming thermal equilibrium) will depend on composition, residence time, and average solids temperature. For example, in combustion of shale containing carbon, removal of the carbon matrix causes the particles to break apart into a distribution of smaller particles. Particle breakup may also occur by mechanical abrasion which would depend on flow conditions and particle properties.

In the present case the general nonlinear coupled functionality shown in Eq. (16) is assumed to consist of two nonlinear or linear transformations, one to simulate the effect of particle breakup and the second, that of changing composition. The two transforma-

‘REACTOR’

(0) (1) (2’ MU

1 %

2 % *+ PARTICLE -‘REACTION’

(0) F BREAKUP F (” F (2’

4

Fig. 6. ‘Reactor’ for the substream attribute matrix.

334 G. L. JONFS

tions are superimposed to produce the overall effect. Particle breakup is represented by a transformation of the row values for each column while chemical reac- tion is represented by a transformation of column values for each row.

Define Fi”) as the vector of inlet mass flows

(17)

Define $’ a vector of mass fractions representing the sum of each of the column vectors of @‘I

(18)

Since particle breakup and reaction are handled sequentially, g$@ will remain invariant during the particle breakup and Fi”’ will remain invariant during reaction as illustrated in Fig. 6. Thus, during particle breakup

gj” = g?),

F!” = B(Q, cj, F!O’),

and during reaction

(19)

(20)

F!” = F(O) I I 3 (21)

gJ” = z?(gY’, Cj). (22)

(b) Particle breakup model: for illustrative pur- poses, assume that the particle size distribution into the process is log normal in Di and remains so regard- less of composition changes. It then follows that the distribution in each column of IV!;’ and Mij) are log normal in Di. Assume further that the distribution in each column of iUij can be represented by two parame- ters, the mean, pj, and the standard deviation, aj, respectively, which are defined later. Thus, the values in each column of iUij may be represented by a normalized distribution function, Pij, and by the vector gj where

Pij=Rij-R,_,j(i= 1,~ j= l,m), (23)

and R, = 0. Pij represents the discrete distribution and R, rep-

resents the discrete cumulative distribution given by

(1 + erf (x,))

RU= 1’2 (1 + erf(xmj))’ (24)

where

&j z (Ii - Pj)/(J2uj), (25)

li = log,, (DJ

and erf is the standard error function.

To normalize the cumulative distribution function xJ is introduced into R,j. The values of iUij are constructed from Pij and gj

Iuij = Pij gj. (26)

Both pj and uj may be defined from a known inlet distribution as follows

(27)

(28)

Conversely, specifying values of pj and uj, the inlet distribution can readily be constructed.

To compute the outlet distributions, models must be developed relating the change in the distribution parameters to process variables. Such models have been developed at Gulf Research & Development Company as applied to retorting of oil shale. Other research in the field has been recently presented [2]. However, in this discussion, only the qualitative aspects of these models will be presented.

Assume the changes in pj and uj due to reaction depend only on the starting composition, cY Thus, in general

Arpj =fi(cj)t (29)

A,uj = f2(cj). (30)

Assume the changes in pj and uj due to mechanical effects depend on carbon content, cj, gas mass flux, V,, and average solids residence time, T. Thus, in general

Aztij =_f~(cj,Pg/grr), (31)

Azuj = J+(C) Fgvr)* (32)

The changes due to chemical reaction and mechan- ical attrition are superimposed to give the outlet distribution parameters

@J” = py’ + Arpj + AzMj, (33)

8’ = uy) + A,uj + AZuj I (34)

M@’ is transformed into M$) by substituting II,!” and uj” into Eqs. (23)-(26).

The second step in the transformation is to mimic the effect of a change in composition by transforming M$’ into M$) keeping I$‘) invariant. The effect of reaction is to reduce the fraction of solids at one concentration and increase it at another. In general notation, the change is represented by a linear trans- formation of the vector gj” into gy’ as shown

#’ = f(gJ”, cj, T), (35)

Changing particle characteristics in solids processing 335

where a general functional dependence on Q’), cj, and mean solids residence time, 7, is assumed. By mass balance

t gy) = 1 (j - 1,m). (36)

The outlet matrix is constructed from the vectors F$‘) and g(12) based on the invariance of Fi”. Thus

and

F!2’ = F!” I I 9 (37)

J/f’;) = F$*’ #)/F(2),

where by total material balance

(38)

F(2) _ F(l) = F’O’ (39)

It should be pointed out again that the reactions taking place are not strictly related to the material balance kinetics but are convenient algorithms for the transformation of Iti which mimic the effects of reac- tion.

For isothermal, first order reaction,fin Eq. (35) is independent of cj and g(,” and depends only on the temperature (rate constant) and residence time, T. In this case

f=l-3; (40)

and the overall conversion constant, {, is computed from an external rigorous_kinetics model. Assuming that the first column of M represents inert material (zero concentration)

gy) = (1 - {)&” (j = 2, m), (41)

and by Eq. (36)

g\‘) = 1 - 2 gy) (j = 2, m). (42)

For nonisothermal and/or higher order reactions, f is a nonlinear function and the transformation is some- what more complicated.

2.4. Application to oil shale processing In a hypothetical surface process for extraction of

oil from shale, shown in Fig. 1, raw shale is combined with a hot recycle shale in a mixer for internal heat recovery. In the retort (reactor 1) kerogen in the shale decomposes liberating product vapor which leaves the process and depositing carbon residue in or on the shale (retorted shale). The product vapor entrains fine solid particles which are removed downstream by cyclones and scrubbers. In the combustor (reactor 2) retorted shale is combined with air and burned.

In the combustion stage the shale breaks up by removal of the carbon matrix and by mechanical

interaction between particles. The flue gas entrains fine particles as it leaves the system. The remaining solids fall out of the vapor stream in the disengage- ment zone. A portion of the hot solids needed to heat the feed shale to retorting temperature is then recy- cled.

The particle breakup model described previously indicated that the degree of particle breakup depended on composition, residence time, and flow characteris- tics. If particle breakup were severe, solids entrain- ment in the flue and product gases may be excessive increasing the load on the solids removal systems. Under severe processing conditions, particles may break up and leave the system causing the particle inventory to fall below the level required to sustain heat balance. Thus the substream matrix models would provide useful information on the maximum shale richness and process severity consistent with maintaining a stable process.

The details of the flowsheet of this process are beyond the scope of this paper. The present discussion will focus on the results of typical operating conditions on the substream attribute matrix as it undergoes change around the loop.

For a practical process, conditions in the retort and burner are such that kerogen and carbon conversions are complete in the retort and combustor, respectively. Thus, regardless of the reaction order, by Eq. (40), { = 1 and f = 0. For complete reaction in each of the reactor blocks in Fig. 1, the solids substreams have three possible carbon levels corresponding to raw, retorted, and burned shale. The specific values will depend on the raw shale grade and the detailed processing conditions. For convenience, the particle size distribution is approximated by a discrete distri- bution, Di, having 11 elements with values shown

Di (Mm) - [ 10,20,61,210,297,420,

595,841, 1190,1680,2380]. (43)

Thus, the matrix fi is an 11 x 3 array of values in which column 1 represents burned shale having no carbon, column 2 retorted shale, and column 3 raw shale.

A feed is chosen with a log-mean diameter ~1 = 3 and standard deviation u - 0.32_as defined by Eqs. (27) and (28). The elements of M for raw shale are shown in Table 1. Raw shale, introduced at 0.0347 kg s-’ (275 lb h-‘) and 297K (75OF), is mixed with recycle shale at 0.1554 kg s-’ (1232 lb h-‘) (recycle ratio of 4.48) to achieve a final retorting temperature of 755K (zOOoF) in the stream exiting Reactor 1. The effect on M of mixing the shale is shown by comparing @I), i%(*) and l$@ in Table 1.

In the retort (Reactor 1) kerogen decomposition removes some of the hydrocarbon matrix contributing to some degree of particle decrepitation. The shift in the distribution parameters are computed by means of f, and f2, Eqs. (29) and (30) which depend on hydro-

336 G. L. JONES

Table 1. Example of substream attribute matrix to quantify changes in particle size and composition in shale processing with recycle

-0 0 0.005. 0.005 0.005 0.020 0.035 0.030 0.100 0.160 0.240 0.250

-0 0 0.150.

Raw shale Go)

0.0105 0.0009 0.0248 0.0009 0.1192 0.0009 0.2718 0.0143 0.0852 0.0134 0.0797 0.0200 0.0703 0.0263 0.0574 0.0300 0.0444 0.0303 0.0321 0.0267 0.0222 0.0209

Retorted shale before elutriation of fines

fl3,

0-

O_

-0.0307 0 07 0.0129 0 0.0496 0.0304 0.1786 0.1458 0.3227 0.3325 0.0926 0.1042 0.0848 0.0975 0.0740 0.0859 0.0604 0.0702 0.0472 0.0544 0.0347 0.0392

,0.0246 0 0 0.0271 0

RS’ R6’ Combusted shale Recycle shale

0.296 0.001 o- 0.702 0.001

0 0

b 0 0,

Fine particles entrained in product vapor

fl”

- 0.0883 0.1219 0.3451 0.3306 0.0659 0.0330 0.0120 0.0029

0 0

_ 0

Fine particles entrained in

$&!)a

‘0.0105 0.0009 0.0248 0.0009 0.1192 0.0009 0.2718 0.0036 0.0852 0.0064 0.0797 0.0055 0.0703 0.0182 0.0574 0.0292 0.0444 0.0438 0.0321 0.0456 0.0222 0.0274,

Mixed shale IIP

0 0 0 0

0.1236 0.0009 0.2818 0.0149 0.0883 0.0139 0.0826 0.0207 0.0728 0.0272 0.0592 0.03 11 0.046 1 0.0314 0.0330 0.0276 0.0230 0.0217

Retorted shale after elutriation of fines

AP

0-

O_

0-

O_

carbon

Elutriation from Reactor 1 occurs when the super- ficial vapor velocity, us, exceeds the particle terminal velocity, U,, which depends on particle diameter, Di, density difference, ps - pgr gas viscosity, p, and particle Reynolds number, Re,, defined by the follow- ing correlations for spherical particles [ 121

Changing particle characteristics in solids processing 331

where L, lift-pipe length, is 21.3 m, t, average void fraction is 0.99894, F,, inlet solids flow rate is 0.1778 kg s-‘, A, superficial area of flow is 2.04 x lo-’ m*, ps, solids density is 2900 kg mm3 and r = 0.75 s.

The extent of particle breakup depends on an estimation of the average particle residence time in the loop. Proper determination of particle residence time is quite complex in general. However, it can be shown that by lumping the selective and nonselective split- ting, performing an “age” balance over each block in the loop and combining this with a material balance, the average particle residence time, T, in the process depends on the one-pass residence time, t, divided by the ratio of feed rate to feed plus recycle rates

u, = g (P, - P,> #/(lfb) We, c 0.4), (47)

u, = [(Ps - P,)” g/w~P,d”1

DJO.4 < Re,, c MO), (48)

U = i3.1 g(p, - PJ Dil~,l”*

(500 < Re, -c 2 x lo’), (49)

where g is the acceleration due to gravity and

Rep 5 DiPgurlp. (50)

Purge gas added for stripping combined with sig- nificant product vapor flow from the rich shale leads to a relatively high superficial gas velocity, 0.155 m s-‘, causing elutriation of the 10 and 20 pm particles as shown by comparing M (‘) fic4) and Mi(‘) in Table 1. , Particle terminal velocities are 0.0056, 0.0224 and 0.208 m s-’ for the 10, 20 and 61 pm particles, respectively. Particle Reynolds numbers are 0.0014, 0.0112, and 0.3 164 for these three particles, indicating that Eq. (48) applies in each case. For particles 4-9 Eq. (49) applies and Fq. (50) applies for particles 10 and 11. A considerable quantity of solids (0.0065 kg SK’) (51.6 lb h-‘) is entrained with the product and purge gas stream (0.014 kg s-‘) (112.7 lb h-‘, 2569 ft-’ h-l). A large fraction of these solids are separated by passage through a high-efficiency cyclone. However, the remaining solids represent a substantial problem in separating oil and fine particles.

T = t/(FcR/(FcF’ + fiRI)). (54)

Determining the mean residence time when a size selective block is present requires simultaneous solu- tion of both age and particle size balances which are generally nonlinear and highly coupled.

For the shale flow stated previously by Eq. (54), 7 is 4.1 s. Complete combustion (1 = 1) is reached by achieving particle ignition conditions within the com- bustor.

The combined effects of combustion and mechani- cal attrition are shown by comparing fic4) and fi@). Note that the elements of columns 1 and 2 in Gic4) were combined and the distribution of column 1 in Go) were shifted downward substantially. Almost 60% of the combusted shale is less than 210 pm.

Elutriation of fine particles in the selective splitter with disengagement zone is handled empirically through a correlation relating the fraction of each particle size entrained, ran, depending on gas Reynolds number, Re, particle Reynolds number, Re,, and a geometric ratio, p equal to an adjustable slot width, B, divided by particle diameter, Di

The more severe reaction and mechanical condi- tions of the combustor (Reactor 2) result in more significant particle breakup and a substantial change in the elements of R. For chemical reaction Eqs. (44) and (45) apply.f, andf, are evaluated with Cj = C2 = 7.4. The mechanical contributions determined fromf, andf, are based on correlations of data by Carley [2]

where

I)~ = 0.02193 6 (vi 5 1) (55)

$, = O.O00395Re, - O.O003536Re,

-I- 1.338 x 1O-5 8, (56)

f, = -2.3 x 1O-4 Cj (1 + 2.79 x lo-* C,) V; t, (51)

h=7.73 x lo-4cj(l - 1.0 x 10-*Cj)V;~‘t, (52)

where V, is the gas mass flux, 0.92 kg m-* SK’. The one-pass residence time, t, is based on the

weighted average solids residence time in the combus- tor. The void fraction, t, is computed from two-phase flow hydrodynamic correlations based on data by 2,:” [ 131. For dilute phase transport (plug flow) of

t = L (1 - c) Ap,/F,,

Re, = u~BP~IcL. (57)

Re, = &J,P,I~~ (58)

/3 = BIDi. (59)

The gas superficial velocity, v~, is 0.1877 m s-’ and Re, = 1506. For the 10 I.crn particles, Re, = 134, j3 = 6.69 x 104, Gi = 1.44 and rri = 0.0927,

The methodology for computing M for this elutria- tion step is handled by the procedure outlined for selective splitting, Eqs. (8)-( 15). As with the elutria- tion from Reactor 1, the component mass balances are

(53) also influenced by the overall solids split fraction. The

338 G. L.

vapor is assumed to be completely carried out with the fine solids stream. The effects of the selective splitting are shown by comparing l%“, I%@ and fi@) in Table 1. The conditions are such that a wide range of particle sizes are elutriated. The solids flow rate of the com- busted shale is 0.1765 kg SC’ (1400 lb he’) of which 0.0105 kg SC’ (83.6 lb h-‘) of solids are elutriated. The contributions to the vapor velocity include combustion air, combustion product, and substantial carbon diox- ide from mineral reactions.

Although the relative quantity of residual solids is quite small, i.e. the split fraction is high, 0.9365, there are sufficient hot solids for recycling. The quantity of solids lost from the process and the heat requirements

JONES

Greek symbols { conversion or extent of reaction (fraction) 7, elutriation fraction p, meanof I, fi gas viscosity p, solids density pa gasdensity cj standard deviation off, about the mean

Subscripts = i, j indices of M or one of the associated vectors

Superscripts

(0) (1)

(01). (02) (111% (12)

inlet outlet

are such that the process is close to the point where steady-state recycling could not be sustained. The model has been successfully applied to define pre- ferred operating conditions and process improvements to avoid these problems. 1.

Instead of using a single average residence time, %

(2)

first and second inlet streams, respectively first and second outlet streams, respectively second outlet stream in a two-step process.

could be expanded to a three-dimensional matrix where the third dimension represents discrete values of particle residence time. This approach would have the added advantage that each particle size would be associated with a residence time as well as a composi- tion distribution. However, rarely are data available on a process in sufficient detail to justify such a detailed analysis.

NOMENCLATURE

element of the row vector of the composition variable, Z element of the column vector of particle sizes, D split fraction total mass flow rate, mass flow rate for each particle siz& and mass flow rate for each element of M, respectively acceleration due to gravity r_o vector representing the sums of the rows of M indices log,, Di upper limits to indices j and i, respectively column vec&r representing the sums of the columns of M substream attribute matrix elements of a two-dimensional substream attribute matrix discrete distribution function for particle size discrete cumulative distribution function for particle size particle Reynolds number functional operators terminal velocity gas velocity gas mass flux normalized log-normal distribution function parameter

5.

9.

10.

11.

12.

13.

REFERENCES

Synthetic Fuels Data Handbook (2nd ed.). Cameron Engineers, Denver, Colorado (1978). J. F. Carley, Attrition of spent oil shales during pneu- matic conveying and cyclone separating, Lawrence Liv- ermore National Laboratory. UCRL-88505 Preprint, April (1983). H. I. Britt, Multiphase Stream Structurs in the ASPEN process simulator, Foundations of Computer Aided Pro- cess Design (Edited by R.S.H. Mah and W.D. Seider), Vol. 1, pp. 471-509. Engineering Foundation, New York (1981). L. B. Evans, B. Joseph & W. D. Seider, System struc- tures for process simulation. A.1.Ch.E. J 23 (5). 658-666 (1977). .

. ,.

L. B. Evans, J. F. Boston, H. I. Britt, P. W. Gallier, P. K. Gupta, B. Joseph, V. Mahalec, E. Ng, W. D. Seider & H. Yagi, ASPEN: an advanced system for process engi- neering. Comput. Chem. Engng 3,3 19-327 (1979). ASPEN PLUS The Process Simulator. Aspen Technol- ogy, 251 Vassar Street, Cambridge, Massachusetts (1983). L. B. Evans & W. D. Seider, Requirements of an advanced computing system. Chem. Eigng Prog. 72, (6), 8&83 (1976). L. B. Evans, Advances in process flowsheeting systems. Foundations of Commuter Aided Process Design (Edited by R.S.H. Mah and- W.D. Seider), pp. 425469. Engi- neering Foundation, New York (1981). ASPEN Project, ASPEN User Manual. ASPEN Pro- ject, Room 20A-023, Massachusetts Institute of Tech- nology, Cambridge, Massachusetts (1980). ChemShare Corporation, Guide to solving process engi- neering problems by simulation, User Manual. Chem- Share Corporation, Houston, Texas (1979). E. M. Rosen, Steady state chemical process simulation- a state-of-the-art review, Presented at the Symposium on Computer Applications to Chemical Engineering Pro cess Design and Simulation, 178th National ACS Meet- ing, Washington, D.C., September (1979). Kunii, Daizo & Octave Levenspiel, Fluidization Engi- neering. p. 76. Robert E. Krieger, Huntington, New York (1977). R. Quong, Verticle pneumatic conveying of mixed- particle-sized oil shale. UCRL-88524 Revision 1 Pre- print, Lawrence Livermore Laboratories, March (1983).