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Q2. A reactor converts an organic compound to product P by heating the material in the presence of an additive A (mole fraction = XA). The additive can be injected into the reactor, while steam can be injected into a heating coil inside the reactor to provide heat. Some conversion can be obtained by heating without addition of A, and vice versa. The product P can be sold for $50/lb mol. For 1 lb mol of feed, the cost of the addi- tive (in dollars/lb mol) as a function of x is given by the formula, 2.0 + 10x + 20x2. The cost of the steam (in dollars) as a function of S is 1.0+ 0.003S+ 2.0 × 10-6 S². (S= lb steam/lb mol feed). The yield equation is yp = 0.1 + 0.3x + 0.001S+ 0.0001xA S; y = lb mol product P/lb mol feed. (a) Formulate the profit function (basis of 1.0 lb mol feed) in terms of xд and S. f = Income - Costs The constraints are: 0 ≤ x ≤ 1 S≥ O (b) Determine the amount of additive and steam that maximize the profit.

Q2. A reactor converts an organic compound to product P by heating the material in the presence of an additive A (mole fraction = XA). The additive can be injected into the reactor, while steam can be injected into a heating coil inside the reactor to provide heat. Some conversion can be obtained by heating without addition of A, and vice versa. The product P can be sold for $50/lb mol. For 1 lb mol of feed, the cost of the addi- tive (in dollars/lb mol) as a function of x is given by the formula, 2.0 + 10x + 20x2. The cost of the steam (in dollars) as a function of S is 1.0+ 0.003S+ 2.0 × 10-6 S². (S= lb steam/lb mol feed). The yield equation is yp = 0.1 + 0.3x + 0.001S+ 0.0001xA S; y = lb mol product P/lb mol feed. (a) Formulate the profit function (basis of 1.0 lb mol feed) in terms of xд and S. f = Income - Costs The constraints are: 0 ≤ x ≤ 1 S≥ O (b) Determine the amount of additive and steam that maximize the profit.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Q2. A reactor converts an organic compound to product P by heating the material in the presence of an additive A (mole fraction = XA). The additive can be injected into the reactor, while steam can be injected into a heating coil inside the reactor to provide heat. Some conversion can be obtained by heating without addition of A, and vice versa. The product P can be sold for $50/lb mol. For 1 lb mol of feed, the cost of the addi- tive (in dollars/lb mol) as a function of x is given by the formula, 2.0 + 10x + 20x2. The cost of the steam (in dollars) as a function of S is 1.0+ 0.003S+ 2.0 × 10-6 S². (S= lb steam/lb mol feed). The yield equation is yp = 0.1 + 0.3x + 0.001S+ 0.0001xA S; y = lb mol product P/lb mol feed. (a) Formulate the profit function (basis of 1.0 lb mol feed) in terms of xд and S. f = Income - Costs The constraints are: 0 ≤ x ≤ 1 S≥ O (b) Determine the amount of additive and steam that maximize the profit.
Transcribed Image Text:Q2. A reactor converts an organic compound to product P by heating the material in the presence of an additive A (mole fraction = XA). The additive can be injected into the reactor, while steam can be injected into a heating coil inside the reactor to provide heat. Some conversion can be obtained by heating without addition of A, and vice versa. The product P can be sold for $50/lb mol. For 1 lb mol of feed, the cost of the addi- tive (in dollars/lb mol) as a function of x is given by the formula, 2.0 + 10x + 20x2. The cost of the steam (in dollars) as a function of S is 1.0+ 0.003S+ 2.0 × 10-6 S². (S= lb steam/lb mol feed). The yield equation is yp = 0.1 + 0.3x + 0.001S+ 0.0001xA S; y = lb mol product P/lb mol feed. (a) Formulate the profit function (basis of 1.0 lb mol feed) in terms of xд and S. f = Income - Costs The constraints are: 0 ≤ x ≤ 1 S≥ O (b) Determine the amount of additive and steam that maximize the profit.
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