EP1 Mass balance PDF

Preview

Summary

Mass balance handout...

Description

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-1

Unit 2 Mass Balances & Modeling

2.1 Utilization: Mass balances are essential to both the technical and financial operation of food processing operations. For technical operation, the mass balances generate the flow rates for each step in the process. They are needed in order to correctly size each piece of equipment in the plant. From the financial point of view, mass balances determine the amount of each ingredient or raw material used in the process, and is used to calculate the yield based on finished product. This in turn leads to the gross margin and eventually the net profit for the operation.

Conservation of Mass: The Law of Conservation of Mass states that, except for atomic reactions, matter is neither created nor destroyed. No atomic reactions occur in food processing, so we can deal with mass as an unvarying quantity. The common engineering statement of this law is in the form: Input = output + accumulation A less elegant way of stating the same thing is: What goes in must stay in or come out In most cases, we can simplify the calculations by defining the process in such a way that accumulation is eliminated. This will become clearer as we look at examples. With this, the equation becomes Input = output. In addition, unless chemical changes take place, we can state that each component of the process stream also follows the same law. For example, salt input as an ingredient must equal salt in the finished product plus salt in any waste product. In batch processing, the inputs and outputs are easily seen as those quantities in and out of each batch. For continuous processes, time is added as a variable. In this case we can deal with quantities input during a unit of time and quantities out of the process during the same time interval.

FS - 341

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-2

Defining the System: In order to talk about “in” and “out”, we must set a boundary for the process or system. In a batch operation, this might be a single processing tank. In a continuous process, this might be certain sequential steps in the process. An appropriate boundary must be one where we can determine the inputs and outputs, except for those unknowns for which we wish to solve. This requirement may help to determine the location of the boundary. One common way to visualize the process is in the form of a schematic drawing. This will be the method used in this chapter. This often makes the selection of the boundary easier.

Method of Solving Mass balances: A systematic method of solving mass balance problems is usually helpful. One can then apply the same method to a wide variety of problems. The steps recommended for mass balance solutions are given below. 1.

Draw a box

Draw a schematic or diagram of the process. This does not have to be representational (realistic looking). For calculation purposes rectangles (boxes) can represent process steps and arrows can represent flows of materials. (Engineers call flows of materials “streams”). 2.

Label streams

Assign a letter as the identifier of each stream (arrow). This letter will be the name of the stream (stream B) and also represent algebraically the mass of that stream (Stream B has a mass of B pounds). This way there is no need of two letters for each stream. On the arrow list all of the pertinent information about that stream. This can include type of material, mass, composition, etc. As calculations are made it is helpful to put intermediate answers on the arrows also. State any assumptions made in solving the problem. 3.

Draw boundaries.

A dotted line encompassing the rectangle is appropriate. Arrows should cross the boundary to indicate inputs and outputs. A complex process with more than one step may have two or more boundaries 4.

Write mass balances

Select a basis for solving the problem. Next, a variety of balances can be written as algebraic equations. These include a total mass balance, and individual component balances. Experience has shown that writing a total mass balance first is helpful much of the time.

FS - 341

Engineering Principles Unit 2: Mass balances and modeling

5.

01/24/2008 PAGE 2-3

Solve for the answer

This is just the algebraic solution of the one or more equations developed in step 4. This may involve solving simultaneous equations. The order of solution is usually not critical, although experience may lead to more efficient solutions. While solving, it is important to remember to solve for both the total stream flow rate (that is the total mass flow rate of the ingredient or product) and the individual component (like water content of the ingredient or product or the salt content etc). The composition can be written in the form of percentages or on a mass basis. For example, if the problem states that the flow rate of orange juice is 200 kg/hr and the water content of the orange juice is 90%, then the total mass of water flowing in the stream is (90/100) x 200 = 180 kg/hr. If the mass flow rate of the ingredient or product (here orange juice) is known, then using percentages is often easier when solving for the individual component (here water). However, if the flow rate of the ingredient or product is not given, then considering the mass flow rate of the component is often more useful that the percentages. Example 2.1 A relish is prepared by the following recipe: pickles 1000 pounds onions 500 pounds sugar 90 pounds salt brine 75 pounds spices 5 pounds The onions are 85% water, the pickles are 92% water and 1.1% salt, and the salt brine is 88% water. During processing, 18% of the water originally in the mixture is evaporated out. What is the salt content (percent) of the final relish?

FS - 341

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-4

FS - 341

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-5

Basis: 1000 pounds of pickles (A) Assumptions: There is no water in the sugar or in the spices. There is no salt in the onions or in the spices. Data good to 2 significant figures Part of the given information is: F = 0.18 x (water input) Water input

= 0.092A + 0.85B + 0C + 0.88D + 0E = 920 + 425 + 0 + 66 + 0 = 1411

∴ F = 0.18 (1411) = 253.98 Total Mass Balance: A+B+C+D+E=F+G

(writing each balance initially in algebraic form is desirable)

1000 + 500 + 900 + 75 + 5 = 253.98 + G G = 2480 – 253.98 = 2222.06 Salt Balance: 0.011A + 0B + 0C + 0.12D + 0E = 0F + X

(Convert percents to decimal fractions. Calculating in percents often leads to errors.)

11 + 0 + 0 + 9 + 0 = 0 + X X = 20

⎡ 20 ⎤ Percent salt in final relish = ⎢ ⎥ X 100 = 0.9000657% ⎣ 2222.06 ⎦ ≈ 0.90%

(round final answer to 2 significant figures)

Example 2.2

A slurry (a mixture of solid and liquid which will flow) is 21% soy protein solids. This slurry is diluted with 1 part water for each 4 parts slurry. After dilution, this diluted slurry is heated, and formed into soy protein fibers. During the process of forming the fibers, 20% of the water in the diluted slurry evaporates. What is the moisture content of the finished soy protein fibers? FS - 341

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-6

Basis: 400 pounds of slurry (A) Assumptions: Slurry consists of only soy protein solids and water. Data good to 2 significant figures. Boundary 3 Boundary 1

A

Slurry 0.21 solids

Dilute

B

Boundary 2

Dilute slurry X kg water

C

Heat & Form

Water 0 solids

Water 0 solids

D

Fiber Y kg water

E

Boundary 1 WATER BALANCE:

0.79A + B = X 0.79(400) + 100 = X = 416

From the statement of the problem: D = 0.20X = 0.20(416) = 83.2 Boundary 3 TOTAL BALANCE:

A + B = D + E 400 + 100 = 83.2 + E E = 416.8

Boundary 2 WATER BALANCE:

X = D + Y ∴ Y = X - D = 416 - 83.2 = 332.8

⎡ 332.8 ⎤ % water in E = ⎢ ⎥ x 100 = 79.846% ≈ 80% ⎣ 416.8 ⎦

FS - 341

Engineering Principles Unit 2: Mass balances and modeling

01/24/2008 PAGE 2-7

Example 2.3 TomAgro food products makes tomato sauce for various restaurants. The process for manufacture of tomato sauce is as follows. 1 metric tonne (1000kg) per hour containing 6% solids are washed and sorted. During sorting 3% tomatoes are removed. The tomatoes are then chopped and immediately immersed in a externally heated tank with 100 kg/hr of steam to rapidly raise the temperature of the tomatoes to 100°C. The steam condenses and adds to the stream as water. After 15 mins of heating for inactivation of all enzymes, the tomatoes are strained to remove 5% seeds and pulp containing 80% moisture. A spice mix (2% moisture) is then added to the juice at a level of 3% of the juice weight. The mixture is then boiled to evaporate moisture and get a sauce with 20% solids.

a) Draw the flow sheet for the tomato sauce processing. At each mark and label all incoming and outgoing streams and the total mass of the stream and the percentage solids in it. b) What is the weight of the tomato sauce that you get. c) If tomatoes cost $1/kg and the spice mix costs $10/kg, what is the cost of ingredients required to make 1 kg of tomato sauce

Symbols and Abbreviations Appropriate to This Chapter

A ⎫ through ⎬ names and mass of input/output streams G ⎭ kg kilogram lbm pounds mass X unknown quantity Y unknown quantity

FS - 341

Engineering Principles: Mass balance and Modeling (Unit 2) Homework 2A (5 points)

Due: 01/24/2008

Name: _______________________ Show calculations where necessary. 1) For the lab on canning of green beans a. Draw a process flow diagram including steps of washing beans, cutting the ends off, blanching, filling and canning (1 point)

b. Show the mass balance for the whole process, considering it as one step. Note the mass of the fresh beans, the waste, the mass of water filled in the can and the total mass of the product after canning. (1 point)

c. Does this obey the law of conservation of mass? How did you get to this conclusion? (0.5 points)

FS - 341

Engineering Principles: Mass balance and Modeling (Unit 2) Homework 2A (5 points)

Due: 01/24/2008

2) Based on Dr. Morgan’s lecture on the 22nd of January (modeling), give the equation for which you would use a linear model, a semi logarithmic linearized model and a logarithmic linearized model. Give the linearized form of each of the equations. (2.5 points)

FS - 341...