Lb-mol/hr H2 75000289403219372191.18 .1947.15214403 25000934207006569925 140 150568420 Argon 10004259542595425.10 0.85 9541595 Ammonia 0.00 462471.7 4.721 467.00 0.10462 Total mol/hr1010042587937916933202547145|7145324879 Mol per H2 7426%67.95%5785%6599%0.47%65996599 2475%21.94%1848%21.06%0.30%21.06%21.06% Ar 099%10.00%11.23%1280%0.18%12.80%12.80% Ammonia 00001]12424014%9906%014%014 10000%10000%10000%10000%10000%10000%1000% verage mw 11.53 12.37 17.04 12.37 Total lb/hr 89164491017849101784106919803259883814018538 Table l-1. Stream Summary for Ammonia Synthesis Loop There are many ways of characterizing reactors. In general, what we want to know is the extent of reaction△ for each component i We define the extent of reaction of compo- nent i as the mols of i STin STout that are made or used up in the reactor. For out. L a continuous steady- state reaction. the extent of reaction is really a rate, namely the mols of i formed ou z f质n or consumed per unit time Figure Reactor The extent of reaction can be determined in various ways. Regardless of how determined, the Ai must satisfy the reaction stoichiometry. Let us consider a simple example. Let us suppose that methane(CH4)is being oxidized using air to a mixture of Co and CO2 according to the following chemistry CH4+3/202->CO+2H2O 2)CH4+202->CO2+2H20
-23- f out,i f in i f f outi = in, i + Di STin STout Lb-mol/hr H2 750.00 2894.03 2193.37 2191.18 2.19 47.15 2144.03 N2 250.00 934.20 700.65 699.25 1.40 15.05 684.20 Argon 10.00 425.95 425.95 425.10 0.85 9.15 415.95 Ammonia 0.00 4.62 471.72 4.72 467.00 0.10 4.62 Total mol/hr 1010.00 4258.79 3791.69 3320.25 471.45 71.45 3248.79 Mol percent H2 74.26% 67.95% 57.85% 65.99% 0.47% 65.99% 65.99% N2 24.75% 21.94% 18.48% 21.06% 0.30% 21.06% 21.06% Argon 0.99% 10.00% 11.23% 12.80% 0.18% 12.80% 12.80% Ammonia 0.00% 0.11% 12.44% 0.14% 99.06% 0.14% 0.14% Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% Average MW 8.83 11.53 12.95 12.37 17.04 12.37 12.37 Total lb/hr 8916.4 49101.78 49101.78 41069.19 8032.59 883.81 40185.38 Table III-1. Stream Summary for Ammonia Synthesis Loop There are many ways of characterizing reactors. In general, what we want to know is the extent of reaction Di for each component i. We define the extent of reaction of component i as the mols of i that are made or used up in the reactor. For a continuous steadystate reaction, the extent of reaction is really a rate, namely, the mols of i formed or consumed per unit time. Figure III-1. Reactor The extent of reaction can be determined in various ways. Regardless of how determined, the Di must satisfy the reaction stoichiometry. Let us consider a simple example. Let us suppose that methane (CH4) is being oxidized using air to a mixture of CO and CO2 according to the following chemistry: 1) CH4 + 3/2 O2 ---> CO + 2 H2O 2) CH4 + 2 O2 ---> CO2 + 2 H2O
This reaction system involves two reactions. There are five components involved the reactions as well as one inert- the nitrogen that comes with the air. Let us assume that for present purposes the small amount of argon also present in the air can be lumped with the nitrogen. Let r;=the rate of the jth reaction in, say, lb-mol/hr and 1- the mols of component i that are formed or consumed by one mol of reaction j. ai j is known as the stoichiometric coefficient of component i with respect to reaction j Then if there are nr reactions in the system, (团-1)△ For the ch4 oxidation reactions the stoichiometric coefficient matrix is Stoichiometric Coefficient for Reaction CH4 2 CO CO2 H20 N2 0 Note that the stoichiometric coefficients for reactants are negative, those for products, positive Let us suppose that ri=20 lb-mol/hr and r2=10 lb-mol/hr Then AcH4=(-1)(20)+(-1)(10)=-30 lb-mol/hr △o2=(-3/2)(20)+(-2(10) -50 lb-mol/hr △co=(1)(20)+(0)(10) 20 Ib-mol/hr (0)(20)+(1)(10 0 lb-mol/hr △Ho=(2)20)+(2)(10) 60 lb-mol/hr (0)(20)+(0(10) 0 lb-mol/hr Note: For a reactor to operate at these reaction rates, the feed will have to contain at least 30 lb- mol/hr of CH4 and 50 lb-mol/hr of O2. If this is not the case, the reactant that is in short supply is termed the limiting reactant. For instance, suppose that the feed contains 60 lb-mol/hr of 02 but only 15 lb-mol/hr of CH4. CH4 will then the limiting reactant. The best we can expect to do is 50% of the assumed reaction rates
-24- This reaction system involves two reactions. There are five components involved the reactions as well as one inert - the nitrogen that comes with the air. (Let us assume that for present purposes, the small amount of argon also present in the air can be lumped with the nitrogen.) Let rj = the rate of the jth reaction in, say, lb-mol/hr and ai,j = the mols of component i that are formed or consumed by one mol of reaction j. ai,j is known as the stoichiometric coefficient of component i with respect to reaction j. Then if there are nr reactions in the system, For the CH4 oxidation reactions, the stoichiometric coefficient matrix is: Stoichiometric Coefficient for: Reaction CH4 O2 CO CO2 H2O N2 1 -1 -3/2 1 0 2 0 2 -1 -2 0 1 2 0 Note that the stoichiometric coefficients for reactants are negative; those for products, positive. Let us suppose that r1 = 20 lb-mol/hr and r2 = 10 lb-mol/hr. Then DCH4 = (-1)(20) + (-1)(10) = -30 lb-mol/hr DO2 = (-3/2)(20) + (-2)(10) = -50 lb-mol/hr DCO = (1)(20) + (0)(10) = 20 lb-mol/hr DCO2 = (0)(20) + (1)(10) = 10 lb-mol/hr D H2O = (2)(20) + (2)(10) = 60 lb-mol/hr DN2 = (0)(20) + (0)(10) = 0 lb-mol/hr Note: For a reactor to operate at these reaction rates, the feed will have to contain at least 30 lbmol/hr of CH4 and 50 lb-mol/hr of O2. If this is not the case, the reactant that is in short supply is termed the limiting reactant. For instance, suppose that the feed contains 60 lb-mol/hr of O2 but only 15 lb-mol/hr of CH4. CH4 will then the limiting reactant. The best we can expect to do is 50% of the assumed reaction rates. ( ) , III a r i i j j j nr - = = 1 å 1 D
Often, the overall reactor performance is characterized in terms of conversion and selectivity. We pick a key component, usually either the more valuable reactant or the limiting reactant We define the conversion Ck with respect to the key component k as follows Ck=Mols ofkey component converted by all reactions Total mols ofkey component in the reactor feed) For our reaction system above, suppose we feed 50 mols/hr of CH4 to the reactor. The conversion of cH4 is then CH4 =30/50=0.6or60% We define the selectivity Sk of the key component with respect to the jth reaction as follows Ski=ols ofkey component converted by reaction i2 (Mols of key component converted by all reactions) For our reaction system above, the selectivity of CH4 to CO(Reaction 1)is ScH4=20/30=0.667or667%, and the selectivity to Co2 (Reaction 2)is ScH42=10/30=0.3330r33.3% Note that the selectivities over all reactions must sum to unity, i.e m1-2)∑Sk One should be aware that there are other definitions of selectivity that are used in the literature However, the one given above is the most commonly used and the only one that has the property d in Eqn. III-2 Let f in= the feed rate of the key component to the reactor Then 2-3) r,=CK Skj fi, in,j=1,.r
-25- Often, the overall reactor performance is characterized in terms of conversion and selectivity. We pick a key component, usually either the more valuable reactant or the limiting reactant. We define the conversion Ck with respect to the key component k as follows: Ck = (Mols of key component converted by all reactions) (Total mols of key component in the reactor feed) For our reaction system above, suppose we feed 50 mols/hr of CH4 to the reactor. The conversion of CH4 is then CCH4 = 30/50 = 0.6 or 60% We define the selectivity Sk,j of the key component with respect to the jth reaction as follows: Sk,j = (Mols of key component converted by reaction j) (Mols of key component converted by all reactions) For our reaction system above, the selectivity of CH4 to CO (Reaction 1) is SCH4,1 = 20/30 = 0.667 or 66.7%, and the selectivity to CO2 (Reaction 2) is SCH4,2 = 10/30 = 0.333 or 33.3%. Note that the selectivities over all reactions must sum to unity, i.e., One should be aware that there are other definitions of selectivity that are used in the literature. However, the one given above is the most commonly used and the only one that has the property expressed in Eqn. III-2. Let fk,in = the feed rate of the key component to the reactor. Then, (III-3) rj = Ck Sk,j fk,in, j = 1,...,nr. ( ) , III Sj k j nr - = = 2 å 1 1
The extents of reaction i can be calculated using Eqn. Il-1 Separators to any chemical process. A simple separator is shown in Figure Ill-2. It has one input stream,STin, and two output streams, STlout and STzout. This separator can be used to represent flash drums, simple distillation columns and other separators that do not require a mass separating More complex separators are shown in Figure IIl-3. Separator A is typical of gas absorbers and liquid-liq SToutI uid extractors where sTlin is the input out iI stream which is to be separated and ST2in is the lean mass separating agent STlout corresponds to STlin from which the components of interest have been removed. ST2out is a mass sepa- ra STin compone f interest that were to be 1, separated from STI Separator B is typical of a complex distillation column with side stream(ST2out) as well as the distillate STout or overhead(ST2out and the bottoms (STout) out L, Si fin There are two indices of how well a separator does its job. The first S is the fraction of a given component that is recovered from a specified feed stream. The second is the purity of one Figure Ill-2. Simple Separator or more output streams from the separator The fractional recovery is important from an economic point of view. Purity specifications have output stream is a final product, the sales purity specificationg down-stream equipment or, if the to be met in order to satisfy the feed purity requirements of
-26- f in i, f s f f s f out i i in i out i i in i , , , ( ) , 1 = 2 = 1- f out i,1 f out i,2 STin STout1 STout2 The extents of reaction i can be calculated using Eqn. II-1. 2. Separators to any chemical process. A simple separator is shown in Figure III-2. It has one input stream, STin, and two output streams, ST1out and ST2out. This separator can be used to represent flash drums, simple distillation columns and other separators that do not require a mass separating agent. More complex separators are shown in Figure III-3. Separator A is typical of gas absorbers and liquid-liquid extractors where ST1in is the input stream which is to be separated and ST2in is the lean mass separating agent. ST1out corresponds to ST1in from which the components of interest have been removed. ST2out is a mass separating agent enriched with the components of interest that were to be separated from ST1in. Separator B is typical of a complex distillation column with side stream (ST2out) as well as the distillate or overhead (ST2out) and the bottoms (ST3out). There are two indices of how well a separator does its job. The first is the fraction of a given component that is recovered from a specified feed stream. The second is the purity of one Figure III-2. Simple Separator or more output streams from the separator. The fractional recovery is important from an economic point of view. Purity specifications have to be met in order to satisfy the feed purity requirements of down-stream equipment or, if the output stream is a final product, the sales purity specifications
SToutI SToutI STin2 STin2 STink Tinl STout STout Fig. 11-3. Complex separators Simple separators can be characterized at the simplest level in terms of a separation coefficient This is defined in Chapter Evaluation of equipment model finit STinT parameters such as the STin2 separation coefficient covered in Appendix B STin3 STout Complex separators can be in i. 3 out.I characterized using the basic material balance models as is described in STain Appendix c ln l.h Mixers out I a mixer is a device that brings together two or more Input streams of different compositions and produces an Fig. 1-4. Mixer
-27- f out,i f in i,1 f in i,2 f in i,3 f in i,nin f out i f j in i,j nin = å =1 STin1 STin2 STin3 STnin STout Fig. III-3. Complex Separators Simple separators can be characterized at the simplest level in terms of a separation coefficient. This is defined in Chapter IV. Evaluation of equipment model parameters such as the separation coefficient is covered in Appendix B. Complex separators can be characterized using the basic material balance models as is described in Appendix C. 3. Mixers A mixer is a device that brings together two or more input streams of different compositions and produces an Fig. III-4. Mixer A STout1 STin1 STin1 STin2 STin2 STout1 STout2 STout2 STout3 B