Abstract:
A process is described for the production of decomposable soluble products from a slurry of solids in which the slurry is convey axially through the reactor and excess liquid is removed radially through the walls of the reactor. The primary example is the hydrolysis of lignocellulosic biomass to form sugars, usually using an acid catalyst. In one variation of the process liquid and possibly steam are added through the inner wall of the reactor to provide additional flow in the radial direction and to control the temperature. Pressures are maintained such that the product stream is thermally quenched due to partial flashing as it leaves the reactor.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This patent application is not the direct outgrowth of federally sponsored research. 
     BACKGROUND OF THE INVENTION 
     The invention is in the field of chemical reactor design, applied to the conversion of a solid (usually in the form of a slurry) to soluble products, which are subject to decomposition. The objective of the design is to obtain high conversion of the solids while maintaining low decomposition of the soluble product(s). Of particular interest in this application is the hydrolysis of cellulose and hemicellulose in the solid to form sugars. The solid may be a form of biomass, such as wood, or a product derived from biomass, such as paper. The cellulose and hemicellulose in biomass can be hydrolyzed using an acid or base catalyst to form sugars, which are soluble and subject to decomposition. In some cases it is desired to convert the hemicellulose while leaving the cellulose largely untouched, so that the cellulose can be subsequently converted to sugars using enzyme catalysts. This partial hydrolysis is often referred to as pretreatment or prehydrolysis. 
     Many reactor configurations have been considered in the published literature for the hydrolysis of biomass to sugars. The U.S. WWII effort to build a commercial reactor used a percolation reactor (Katzen, ISAF XIII, International Symposium on Alcohol Fuels Stockholm, Sweden, Jul. 3-7, 2000) 1  in which an acid solution was applied to a bed of wood chips, and the sugar containing solution was withdrawn from the bottom of the reactor. Recently this type of reactor has been referred to as a ‘flow-through’ reactor since the liquid flows through a bed of solids. 
       1  These refer to the citation numbers given in the Information Disclosure forms.  
     Grethlein, U.S. Pat. No. 4,237,226 2 , discloses the use of a continuous co-current plug-flow reactor for the pre-hydrolysis of biomass. 
     Converse et al., U.S. Pat. No. 4,556,430 3 , discloses the use of a non-aqueous immiscible carrier fluid in a continuous plug flow reactor in order to convey the solids and, at the same time, increase the sugar concentration in the aqueous phase. 
     Wright et al., U.S. Pat. No. 4,615,742 4  discloses the use of a series of fixed-bed flow-through reactors in which the liquid flow is switched so as to approximate counter-current flow. 
     Converse et al., U.S. Pat. No. 4,818,295 5  discloses the use of a cyclone reactor in order to obtain counter-current flow between the solids and the liquid. 
     None of the above patents, and many others that teach methods of hydrolyzing cellulose and hemicellulose, make use of a cross-flow pattern. The patents referenced in this paragraph do speak of cross-current flow pattern. Torget et al., U.S. Pat. Nos. 5,424,417 6 ; 5,503,996 7 ; and 5,705,369 8  discloses the use of a flow-through reactor for the prehydrolysis if lignocellulosic material. Specific to the current application the patent states. “the lignocellulose solids may be stationary, travel in a counter-current or cross-current fashion. . . . One can perform a solid-liquid separation in the flow-through system by using a screw-like device to cause the separation continuously during or at the end of prehydrolysis. Important to the process is the movement and removal of fluid during the prehydrolysis to separate soluble products as they are released from the solid lignocellulosic residue.” (col. 6, lines 47-57, U.S. Pat. No.  5,503,996)   7 Furthermore it states: “such a reactor would have lignocellulosic material driven through the reactor while fluid is passed through the material, typically in a counter-current or cross-current manner. . . . Alternatively, the lignocellulosic substrate may be driven laterally while fluid is applied on top and allowed to percolate down to be removed at the bottom.” (col. 6, line 66-col. 7, line 10, U.S. Pat. No.  5,503,996)   7  The same statement can be found in the other two patents cited above, as well. O. Bobleter and H. Binder, German Patent No. DE 3225074 14 , include, without comment on implimentation, the crossflow of water to solubilize and remove hemicellulose and portions of the lignin; it does not include the use of an acid catalyst nor the conversion of cellulose. 
     The current application uses these principles but differs from the patents cited above in the following aspects: 1) a unique geometry for effecting cross flow is described, 2) it is not limited to prehydrolysis, and 3) a computer simulation, employing cross-flow reactor 
     Recently the desirability of forcible expression of the liquid in a so-called ‘shrinking-bed’ reactor has been analyzed and demonstrated (Pettersson et al., 22nd Symp. on biotech, for fuels and chemicals, Gatlinburg, Tenn. May 7-11, 2000 Poster 3-48 9 ; Lee et al, Biores. Tech. 71, 29-39, 2000 10 ; Torget et al., Ind. Eng. Chem. Res., 39, 2817-2815, 2000 11 ). 
     Torget et al., U.S. Pat. No. 6,022,419 12 , discloses the use of a continous shrinking-bed flow-through reactor for the hydrolysis and fractionation of lignocellulosic biomass. The patent states that “the invention consists of a series co-current, counter-current or single pass, isolated stages . . . ” No mention is made of cross-current flow or withdrawal of the excess liquid in the radical direction. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention is a reactor system for converting solids to soluble products which are subject to decomposition. An example is the conversion of biomass to such products, and includes the conversion of hemicellulosic, cellulosic and lignocellulosic substances to sugars. The term biomass, as used herein, means substances that are produced by photosynthesis, and includes hemicellulosic, cellulosic and lignocellulosic substances, both natural and processed, as well as natural or manufactured organic materials more broadly. Emphasis in the following discussion is placed on producing sugars for biomass, but the invention is broader, and is applicable to the conversion of any solid to liquid products which themselves are subject to decomposition. 
     The essence of the invention is that liquid, containing products from the reacting solids, is squeezed from the slurry by a compressive force and removed from the reacting zone by passage through an outer porous wall. This is done in order to minimize the residence time of the soluble products in the reactor, and thereby, minimize their decomposition. The liquid product stream may be thermally or chemically quenched as it is withdrawn to prevent further chemical reaction. The direction in which the exiting liquid moves is approximately perpendicular to the direction in which the slurry moves. 
     Liquid, possibly containing acid or base, may, or may not, be admitted into the reactor through the porous wall of the inner tube to aid in the washing of soluble product through the outer wall of the reactor. This liquid may assist in the temperature control of the reacting solids and may be mixed with steam. It may also contain chemicals such as a mineral acid to affect the reaction. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagrammatic representation of one configuration of the reactor. The slurry is fed into annulus A at position  1 . Liquid or steam may be forced into tube C at position  2  and from tube C through a porous wall E into annulus A. The slurry is compressed by an auger, or other means, so a to squeeze water out of the slurry as it proceeds through annulus A. Liquid from the slurry flows through porous wall D into annulus B where the reaction is quenched. Liquid products exit through  3 ; remaining slurry exits through  4 . It may be desirable to add a liquid containing chemicals at  5  in order to chemically quench the reaction. 
     FIG. 2 shows a variation of FIG. 1 in which tube C has been removed, creating tube A and leaving annulus B. Slurry enters A at  1  and is forced through tube A. As it reacts, some of the solids are converted to liquids. The excess liquids are forced through the porous wall D into annulus B. Liquid products exit through  3 ; remaining slurry exits through  4 . It may be desirable to add a liquid containing chemicals at  5  in order to chemically quench the reaction. 
     FIG. 3 shows a variation of FIG. 1 in which wall D has non-porous as well as porous sections, and annulus B has a partition so the various soluble products, such as xylose and glucose, can be separated. One product would be withdrawn through  5  and the other through  3 . It may be desirable to add a liquid containing chemicals at  6  in order to chemically quench the reaction. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In FIG. 1 there is shown a system for producing a product, such as sugars, from a two phase mixture, typically a liquid-solid mixture, which introduced to the system at  1 , at the entrance of Annulus A. This slurry of biomass chips is conveyed horizontally through Annulus A by a auger, or some other means, through a restriction at  4 . The auger, if employed, fits tightly against the inside of Porous Wall D, and scrapes the wall as it turns, thus removing solids from the wall. Liquid is introduced at  2 , at the entrance of Tube C, at a pressure higher than the pressure in Annulus A. Thus, this liquid flows through Porous Wall E into Annulus A. The liquid entering at  2  may be preheated; its temperature may be controlled as it flows through Tub C by heaters or steam injector(s) placed inside Tube C. Thus the temperature of the liquid in C can be caused to increase as it flows through the reactor; since some of this liquid flows through Wall E, the temperature of the slurry in A can also be increased as it flows through the reactor. The liquid entering at  2  may also contain catalysts, e.g., an acid, solvents, or other chemicals, thereby affecting the chemical composition and the reaction(s) in A. 
     The slurry entering at  1  may contain a catalyst, such as sulfuric acid and it may be preheated. As the slurry flows through Annulus A, a portion of the solids is liquefied. Due to the compression of the slurry, some of the liquid in Annulus A is forced into Annulus B. This transfers some of the soluble products from Annulus A to Annulus B. This removal of soluble products, such as sugars, from A to B is furthered by the liquid entering A from C. In addition to temperature control, the introduction of liquid, from C into A, provides a means for quickly removing the soluble products from the slurry, where they are formed, in a radical direction which is much shorter than the axial dimension of the reactor. This is done in order to minimize the decomposition of desirable soluble products formed in the reaction. This movement of the liquid in the radial direction in order to reduce the residence time of the soluble products, is a principal feature of the invention. 
     Annulus B is maintained at a lower pressure than Annulus A; hence, some of the liquid entering Annulus B from A, flashes, reducing the temperature abruptly and quenching the reactions. This flashing also increases the concentration of soluble products in the liquid in B. It may be desirable to feed liquid containing chemicals into B at  5 ; for example, it may be desirable to add a base in this stream in order to neutralize an acid catalyst present in the liquid coming from A. In the application of this system to the hydrolysis of biomass, the liquid in B contains soluble sugars. In the case where it is desirable to separate sugars formed from the hemicellulose from those formed from cellulose, at higher temperatures further down the reactor, partitions are be placed in Annulus B, as shown in FIG. 3, to at least partially separate the two products streams. This is just one example of how the system could be used to separate various products, such as proteins in addition to carbohydrates, in the refining of biomass. 
     A tendency of Porous Wall D to plug up with solids could be partially offset by the scraping action of the auger, if used. It could also be offset by periodically increasing the pressure in Annulus B for a brief period of time which would back-flush the porous wall, D. 
     In order to further the solids washing action of the liquid entering A from C, the auger may be shaped to cause regions where the liquid fraction in the slurry increases, followed by regions where it is again decreased in order to squeeze out the liquid which contains the soluble product. 
     Soluble products exit the reactor at  3 , or, in the case that partitions are installed in Annulus B, at various points from Annulus B. The remaining solids exit from  4 . 
     This reactor system could also be modified to use different liquids at different points in the reactor by installing partitions in Tube C. It would thus be quite generally useful in the refining of wood. If delignifying solvents were used, the remaining solids (e.g., paper pulp) would be a valuable product. 
     Extension I 
     Tube C contains a partition so that at least the initial portion can be filled with steam rather than a liquid. In this case steam flows through the porous wall, E, and condenses in Annulus A. This has the advantage in that the high latent heat of the steam conveys much more heat into A per kg of added fluid; hence, for a given temperature increase, the dilution of the material in A would be much less. Hence the concentration of the soluble product would be greater. In some cases it may be desirable to fill the entire of Tube C with steam. 
     Extension II 
     As shown in FIG. 2 there is only one annular region, B. The liquid that flows into Annulus B is that expressed due to the liquefying reaction and the compression of the solids in A . Unlike in FIG. 1, this liquid is not diluted by liquid being added to C. This would increase the concentration of the soluble product, but at the expense of yield since the soluble product would no longer be washed from the solids that remain in A. The simulated performance of this configuration is presented in Example 5 below. 
     Extension III 
     Combined counter-current and radial flows. By introducing liquid near the outlet of Annulus A and making part of the wall, D, non-porous it would be possible to have counter-current flow in the right and end of Annulus A. This flow could then be withdrawn at the upper portion of the reactor where a porous outer wall would be used in Annulus A. This could be combined with a non-porous section in the upper portion of Annulus A to permit withdrawal of the soluble products at the desired region. As shown in FIG. 3 the use of alternating sections of porous and non-porous sections of the outer wall of Annulus A would allow separate product streams to be withdrawn; hence biomass might be fractionated into a number of products (e.g., lignin, glucose, xylose, proteins). FIG. 3 is drawn to demonstrate the withdrawal of two product streams; the concept could be extended to more than two product streams, or only one, if desired. 
     Extension IV 
     To control the flow rate between Annulus A and B, a second porous pipe section is installed so that it covers the porous section in the outer wall of Annulus A. When rotated so that the pores (holes) match up, the flow is greater; when rotated so that there is a mismatch so that the hole in one is blocked, at least partially, by the solid portion in the other, the flow is reduced. 
     Extension V 
     The fluid fed through tube C into annulus A is immiscible with water. This would still produce a high yield since the sugar is swept from the annulus A into annulus B where the reaction is quenched. However, this modification would also produce a high concentration since the sugars would be extracted into the aqueous portion and would not be diluted. This principle was patented in the context of a co-current plug flow reactor (U.S. Pat. No. 4,556,430). Here it is extended to a cross-current radial flow reactor. 
     EXAMPLES 
     The following is based on computer simulations. The corresponding theory is presented in an unpublished paper, Simulation of a Cross-Flow Shrinking-Bed Reactor for the Hydrolysis of Lignocellulosics by A. O. Converse, which is attached 13 . 
     In all simulations the biomass composition was: 41% glucan, 5% fast glucan (which is converted instantaneously) 24% xylan and 30% inerts, and the values for the ‘kinetic constants’ are computed from the following equations: (C a  is in weight % acid.) 
     Cellulose to glucose (Grethlein and Converse, 1982)                k   c     =                5.39      e22   *     C   a   1.55     *     exp        (       -   47100       1.987   *   T       )            hr     -   1                     =                461                 at                 240      °                   C   .              and                   1      %                 acid                                  
     Glucose to hmf (Grethlein and Converse, 1982)                k   g     =                2.38      e11   *     C   a   0.569     *     exp        (       -   21000       1.987   *   T       )            hr     -   1                     =                268                 at                 240      °                   C   .              and                   1      %                 acid                                  
     Hemicellulose to xylose (Kwarteng, 1983; and Converse et al., 1989)                k   h     =                3.74      e15   *     C   a   1.17     *     exp        (       -   27827       1.987   *   T       )            hr     -   1                     =                5   ,   220                 at                 240      °                   C   .              and                   1      %                 acid                                  
     Xylose to furfural (Kwarteng, 1983; and Converse et al., 1989)                k   x     =                1.40      e14   *     C   a   0.688     *     exp        (       -   27130       1.987   *   T       )            hr     -   1                     =                385                 at                 240      °                   C   .              and                   1      %                 acid                                  
     Dissolution of half of the inserts: 
     k I =300 (a dummy value) 
     Simulation Results 
     Example 1 
     The plug flow results in Table 1 are typical of what has been predicted and obtained. Values close to 60% yield require 1% acid and 260° C. These results are presented here to provide a check on the simulation program, and for comparison with Table 2. The concentrations presented in Table 1 are those that exist when the corresponding yield is maximum. They both could not be obtained in a single plug-flow reactor. 
     Example 2 
     Simulations of an ideal cross flow reactor are presented in Table 2. Through out Table 2 the flow of liquid per unit reactor length from Tube C to Annulus A is given by Rww*(Cg+Cx). Table 2a presents results at 240° C. At this temperature and the indicated flow rate, the reactor is short, 0.1 m. As the cross-flow wash rate, Rww, is increased, the sugar yield increases but the sugar concentration decreases, as expected. The results are sensitive to the ratio of occluded water to solids, Rws. All the runs show reasonably high concentrations and yields in excess of 80%. 
     Example 3 
     Table 2b presents results at 200° C. At this temperature and the indicated flow rate, the reactor is 3 m. In run 8 the yields are good but the concentrations are low because the washing rate per unit reactor length is still high and the reactor is 30 times longer than in Table 2a. As shown in Run 9, the concentrations can be increased but still fall short of what is desired, while the yields fall below what is desired. 
     Example 4 
     Table 2c presents results at 200° C. in a short, 0.3 m, reactor, as might be the case in a pretreatment reactor. Only the xylose results are shown because most of the glucan has been remains unconverted. Comparison with Row 1 in Table 1 indicates that the cross flow reactor can obtain a higher yield than the plug flow reactor but at a lower concentration. 
     Example 5 
     Table 2d presents the results when there is no wash water introduced, but free liquid (i.e. not occluded) is able to escape through the outer porous wall. The yields and concentrations in Table 2d are at the position where the combined yield, of glucose or xylose in the sidestream and in the main axial flow are at their combined maximum values for each of the two sugars. Compared to the plug flow reactor (Table 1) both the yields and concentrations are higher. This comparison clearly demonstrates the advantage of a ‘shrinking-bed’ reactor in which excess liquid is removed as soon as possible 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Simulation Results for Plug Flow - Glucose and Xylose from Mixed Hardwood 
               
               
                 (Rws = ratio of occluded water to solids in the slurry) 
               
             
          
           
               
                   
                 Concentration, g/L 
                   
               
             
          
           
               
                 Length 
                 Temp 
                 Acid 
                   
                 Maximum Yield, % 
                 at Max. Yield 
                   
               
             
          
           
               
                 m 
                 C. 
                 % 
                 Rws 
                 Glucose 
                 Xylose 
                 G 
                 X 
                 Program 
               
               
                   
               
             
          
           
               
                 3 
                 200 
                 1 
                 2 
                 12 
                 77 
                 25 
                 90 
                 CFR28 
               
               
                 3 
                 200 
                 1 
                 10 
                 13 
                 80 
                 6.6 
                 21 
                 ″ 
               
               
                 0.3 
                 240 
                 1 
                 2 
                 44 
                 78 
                 85 
                 89 
                 ″ 
               
               
                 0.3 
                 240 
                 1 
                 10 
                 46 
                 81 
                 22 
                 21 
                 ″ 
               
               
                 0.1 
                 260 
                 1 
                 2 
                 63 
                 79 
                 117 
                 87 
                 ″ 
               
               
                 0.1 
                 260 
                 1 
                 10 
                 65 
                 81 
                 31 
                 21 
                 ″ 
               
               
                   
               
             
          
         
       
     
     Table 2 Simulation Results for Cross Flow—Glucose and Xylose from Mixed Hardwood 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2a 
               
             
             
               
                   
               
               
                 (Reactor length, L = 0.1 m.) 
               
             
          
           
               
                   
                 Rww 
                   
                 T 
                 Yg 
                 Yx 
                 C gss   
                 C xss   
                 C gss  + 
                   
                   
               
               
                 Run # 
                 m 2 h −1   
                 Rws 
                 ° C. 
                 % 
                 % 
                 g/L 
                 g/L 
                 C xss   
                 Program 
                 Date 
               
               
                   
               
             
          
           
               
                 1 
                 3000 
                 2 
                 240 
                 86 
                 89 
                 36 
                 35 
                 71 
                 CFR26 
                 Dec. 27, 2000 
               
               
                 2 
                 ″ 
                 3 
                 ″ 
                 83 
                 87 
                 31 
                 30 
                 61 
                 ″ 
                 ″ 
               
               
                 3 
                 ″ 
                 1 
                 ″ 
                 88 
                 91 
                 47 
                 45 
                 92 
                 ″ 
                 ″ 
               
               
                 4 
                 2000 
                 2 
                 ″ 
                 83 
                 87 
                 43 
                 42 
                 85 
                 ″ 
                 ″ 
               
               
                 5 
                 4000 
                 ″ 
                 ″ 
                 87 
                 90 
                 32 
                 31 
                 62 
                 ″ 
                 ″ 
               
               
                 6 
                 ″ 
                 1 
                 ″ 
                 89 
                 92 
                 41 
                 39 
                 80 
                 ″ 
                 ″ 
               
               
                 7 
                  400 
                 2 
                 ″ 
                 69 
                 73 
                 76 
                 75 
                 151 
                 ″ 
                 ″ 
               
               
                   
               
               
                 (Inlet solids flow, M s (0) = 1000 kg/hr.; Cross-section area, A = 0.1 m 2 ; Density, ρ = 1000 kg/m 3 ; Acid concentration, C a  = 1%)  
               
               
                 (Rww = wash water addition constant, m 2 h −1 (The flow of liquid per unit reactor length from Tube C to Annulus A is given by Rww*(Cg + Cx)); Rws = ratio of occluded water to solids in the slurry; Yg = glucose yield, % ; Yx = xylose yield, %; Cgss = concentration of glucose in the product withdrawn from  
               
               
                 #Annulus B at position 3, g/L; Cxss = concentration of xylose at the same location; Cgss + Cxss = total sugar concentration, g/L.  
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2b 
               
             
             
               
                   
               
               
                 (Reactor length, L = 3.0 m.) 
               
             
          
           
               
                   
                 Rww 
                   
                   
                 Yg 
                 Yx 
                 C gss   
                 C xss   
                 C gss  + 
                   
                   
               
               
                 Run # 
                 m 2 h −1   
                 Rws 
                 T 
                 ° C. 
                 % 
                 % 
                 g/L 
                 C xss   
                 Program 
                 Date 
               
               
                   
               
             
          
           
               
                 8 
                 4000 
                 2 
                 200 
                 83 
                 96 
                 5.7 
                 6.1 
                 12 
                 CFR27 
                 Dec. 29, 2000 
               
               
                 9 
                 400 
                 ″ 
                 ″ 
                 60 
                 87 
                 14.7 
                 19.6 
                 24 
                 ″ 
                 ″ 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2c 
               
             
             
               
                   
               
               
                 (Reactor length, L = 0.3 m.) 
               
             
          
           
               
                   
                 Rww 
                   
                   
                 Yg 
                 Yx 
                 C gss   
                 C xss   
                 C gss  + 
                   
                   
               
               
                 Run # 
                 m 2 h −1   
                 Rws 
                 T 
                 ° C. 
                 % 
                 % 
                 g/L 
                 g/L 
                 Program 
                 Date 
               
               
                   
               
             
          
           
               
                 10 
                 4000 
                 2 
                 200 
                   
                 96 
                   
                 24 
                   
                 CFR27 
                 Dec. 29, 2000 
               
               
                 11 
                 400 
                 ″ 
                 ″ 
                   
                 85 
                   
                 67 
                   
                 ″ 
                 ″ 
               
               
                   
               
               
                 (M s (0) = 1000 kg/hr., A = 0.1 m 2 , L = 0.3 m, T = 200° C., ρ = 1000 kg/m 3 , C a  = 1)  
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2d 
               
             
             
               
                   
               
               
                 (Rww, wash liquid rate = 0) 
               
             
          
           
               
                   
                   
                 T 
                 Ygo 
                 Lgo 
                 Cgo 
                 Yxo 
                 Lxo 
                 Cxo 
                   
                   
               
               
                 Run # 
                 Rws 
                 ° C. 
                 % 
                 m 
                 g/L 
                 % 
                 m 
                 g/L 
                 Program 
                 Date 
               
               
                   
               
             
          
           
               
                 12 
                 2 
                 240 
                 55 
                 0.037 
                 137 
                 79 
                 0.0104 
                 204 
                 CFR30 
                 Jan. 22, 2001 
               
               
                 13 
                 10 
                 240 
                 62 
                 0.148 
                 30 
                 83 
                 0.0412 
                 42 
                 ″ 
                 ″ 
               
               
                 14 
                 2 
                 260 
                 77 
                 0.0087 
                 191 
                 81 
                 0.0036 
                 208 
                 ″ 
                 ″ 
               
               
                 15 
                 10 
                 260 
                 83 
                 0.0343 
                 40 
                 84 
                 0.0142 
                 42 
                 ″ 
                 ″ 
               
               
                   
               
               
                 (Lgo = reactor length at which the sum of glucose in Annulus A and the glucose in Annulus B is maximum; Lxo = reactor length at which the sum of xylose in Annulus A and the xylose in Annulus B is maximum; Cgo = concentration of glucose in the mixture of the two streams at Lgo, g/L; Cxo = concentration of xylose in the  
               
               
                 #mixture of the two streams at Lxo, g/L