# ch21 - 21-1 CHAPTER 21 SOLUTIONS21.1 The RGA is completed...

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Unformatted text preview: 21-1 CHAPTER 21 SOLUTIONS21.1 The RGA is completed using the property that rows and columns must add to unity: −−−=Λ6.44.12.47.3.4.49.47.48.Based on the RGA coefficients, the most promising pairings are: y1u1, y2u3and y3u2;i.e.,Option c. 21-2 21.2a. Mass and component balances for the mixer are: Fmm=+21(1)( )11211211xmmmmmm=+=+−(2)Linearization in the vicinity of the desired operating point, {x1}*, gives: ( )( )+−+=21*221122121ˆˆ11ˆˆmmmmmmmmxF(3)The RGA is computed based on the linear model: *21111mmm+=λ(4)If {x1}*= 0.8, {m1}*= 0.8 and {m2}*= 0.2, and from Eqn. (4), λ11= 0.8. Thus, diagonal pairing is recommended in this case, with pairings: F m1and x1m2. On the other hand, when {x1}*= 0.3, {m1}*= 0.3 and {m2}*= 0.7, and from Eqn. (4), λ11= 0.3. Thus off-diagonal pairing is recommended in this case, with pairings: F m2and x1m1. b. Mass and component balances for the mixer give: Fmmm=++321(5)( )1132113211xmmmmmmmm=++=++−(6)( )2132123212xmmmmmmmm=++=++−(7)Linearization in the vicinity of the desired operating point, {x1,x2}*, gives: ( )( )( )( )( )( )++−+++++−++−++−+++=321*2321223213223212232112321123213221ˆˆˆ111ˆˆˆmmmmmmmmmmmmmmmmmmmmmmmmmmmmmxxF(8)Eqn. (8) is computed at the desired operating point: F= 1, x1= 0.1, and x2= 0.2: 21-3 −−−−=321*21ˆˆˆ2.8.2.1.1.9.111ˆˆˆmmmxxF(9)Hence: =Λ2.8.1.9.7.2.1.(10)Thus, the recommended pairings are: F m3, x1m1and x2m2. 21-4 21.3The process is described by the linear model: −−−=...
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ch21 - 21-1 CHAPTER 21 SOLUTIONS21.1 The RGA is completed...

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