The chapter on membrane processes deals with liquid food concentration but provides the basis for other applications of membranes in food processing. As demands for safe, high-quality, nutritious, and convenient foods continue to increase, the need for the concepts presented will become more critical.
In the near future, the applications of new technologies such as nanotechnology in food manufacturing will increase, and the role of engineering in process design and scale-up will be even more visible. Finally, the use of engineering concepts should lead to the highest quality of food products at the lowest possible cost. The editors wish to acknowledge the authors and their significant contributions to this edition of the handbook. Zogzas Mass and energy balances are powerful tools for the design and optimization of food manufacturing plants. They are based on the application of mass and energy conser- vation laws to an individual part or the whole food process.
The aim is to determine the mass flow rate and composition of any stream of raw material, intermediate or the final product, by-product, waste, or effluent encountered in the process along with the amounts of energy mainly heat that must be supplied or rejected. The basic steps that are followed are the construction of the process flow diagram along with any available information, the consideration of the suitable system boundaries, and the establishment and solving of the set of independent equations resulting from the suitable mass and energy balance application. The above mentioned will be discussed in detail in the following sections along with comprehensive examples and problems collected from a variety of existing food process applications.
The law can be applied for the total amount of mass entering, leaving, or accumulating within the system, as well as, for any individual component. Typical examples of mass bal- ance applications in food processing can be found in mixing, blending, separation, dilution, concentration, drying, evaporation, and crystallization.
The boundary can be real or imaginary and separates the system from its surroundings. Let us consider a can in atmospheric air that contains concentrated milk. The outer surface of the can could be considered as the boundary between milk and the atmospheric air. We could also draw an imaginary boundary around the can Figure 2. Whatever be the case, the system consists of milk and the can walls.
A typical example is that of a heat exchanger shown in Figure 2. If we draw a boundary around the body of the exchanger, we can easily notice that there are hot and cold fluid streams entering or leaving the system. In the majority of food engineering operations, the systems that we deal with are actually open systems, since continuous and semibatch processes are of common practice. Closed systems are rare and can be met mainly in batch processes i. The definition does not exclude any component transforma- tion within the system and in the case of a chemical or a biochemical reaction the total mass of the reactants equals the total mass of the products at any time point.
Note that in the case of mass depletion the second part of Equation 2. A continuous process is by definition an open system in which the total mass of the feed entering is continuously removed by the form of products and wastes. In this case, there is no accumulation or depletion of mass within the system and Equation 2. The above equation also holds for a batch process in terms of a total mass balance at the beginning and at the end of the process.
That is, the total mass of the feed entering the system at the beginning of the process equals the total mass of the products at the end. In general, the total mass flow rate that enters or leaves a system may consist of several streams. Equation 2. Under this condition Equation 2.
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Physical properties of fluids such as water, steam, air, and other liquid foods are provided. For an incompressible fluid, that is, for a fluid that does not change its density under the processing conditions, Equation 2. However, this equation is rarely applied to food processing practices since systems are complex involving solid, liq- uid, and gas mixtures, phase transitions, and material transformations with density change.
Constructing the flow diagram of the process 2. Defining the suitable boundaries 3. Collecting all available data for the streams of materials entering or leaving the boundaries 4. Selecting a basis for calculations 5. Applying of mass balance Equations 2.
Solving the system of equations to estimate the unknowns There are four types of flow diagrams used in food process design and optimiza- tion. The first is the simplest and shows all streams of raw materials, products, side products, and wastes. It is made of blocks that symbolize all individual unit opera- tions needed to complete the process. Conventional international symbols are used to depict the vari- ous types of equipments along with process parameters such as temperature, pres- sure, composition, flow rate, level, and any other property necessary to describe the process.
The third is a layout of the machinery arrangement on the floor or in space [3D] of the plant showing the dimensions of equipment. This type of diagram is use- ful in estimating the necessary surface and space of the food plant. The fourth dia- gram is focused on the details of connections and control of process equipment such as piping including pumps, fans, ducts, regulating and safety valves, steam traps, and other fittings and instrumentation such as gauges, sensors of temperature, pres- sure, level, flow, moisture and others, signal transducers, controllers, and wiring.
Of the above diagrams, the first two types are useful for applying mass and or energy bal- ances. In fact, the PBD is used for overall mass and energy balances across each unit operation and PFD is used for more detailed calculations within a specific operation, for example, estimating the operating conditions, flows, and composition in a triple effect evaporator.
Boundaries can be drawn around the whole or an individual part of the process. Usually, an overall mass balance along with some selected individual parts is ade- quate. The choice of the suitable boundaries, as well as, the set of mass balance equa- tions depends on the number of unknowns, the available data, and the easiness of calculations. Collecting the suitable data such as material compositions, mass or volumetric flow rates, process conditions pressure and temperature , and any other information provided by the flow diagram is essential for solving the set of mass balance equa- tions.
Process conditions can be used to estimate thermophysical properties of food materials including water and air. For example, the pressure of saturated steam is necessary to estimate its temperature, specific volume, and other thermodynamic properties from the available literature steam tables. In a generalized approach, food materials can be said to consist of water and total solids, with the latter comprising soluble and insoluble matter. In this way, composi- tion can be expressed in a wet or a dry basis. That is, Xi,w. Obviously, Equation 2. The basis of calculations is kg of oranges.
Reprinted with permission from Maroulis, B. For example, the total fat in cheese is expressed as a percentage in dry matter, as well as, the moisture content of dried foods. In the latter, the dry matter of the feed materials entering a dryer remains constant throughout the drying process. Conversion between dry and wet basis moisture content can be done by using the relation X X Xd b w b w b.
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Rearranging and solving for Xw. Another important parameter in applying mass balances is the basis for calcula- tions. An obvious choice that has an economic importance would be the quantity of the final product produced during a specified time period e. However, this might not be easy, since calculations are facilitated when done concurrently with the flow of the process. An alternative would be the consideration of arbitrary quantities of raw materials resulting through mass balance calculations to specific quantities of the final product and then scaling up or down to the real situation.
Whatever be the case, the basis of calculations must not be changed throughout the process. Generally, there is more than one choice in establishing the set of mass balance equations. It depends on the specific boundaries considered throughout the flow- sheet and on the ease of calculations. However, the number of independent equations has to be equal to the number of unknowns, excluding equations that are identical.
Moreover, the mass balances for all intermediate streams must be in accordance with the overall mass balance of the process. In the following sections typical examples of mass balance applications in food engineering are provided to familiarize with, while at the end of the chapter some unsolved problems are provided for further practice.
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If the feed of the concentrated liquor is 1. The densities of concentrated liquor and product are given as 1. A flow diagram of the batch-type process is shown in Figure 2. A boundary dotted line is chosen around the mass of the product accumulated within the tank. Let the mass of concentrate that enters the boundary be mc, the mass of water mw, and the mass of the product mp.
Thus, the mass flow rate of pure water is 6. Air enters with 0. A flow diagram is shown in Figure 2. In drying systems the usual basis of calculations is the dry matter of the feed or the product. As it has been said this dry matter remains constant throughout the drying process. The same happens with air, since air can be con- sidered as a mixture of dry air and water vapor see chapter 9 Psychrometrics , and during drying the water removed from the feed material is absorbed by the air.
Applying Equation 2. Note that the specific or absolute humidity of air is its moisture content in dry basis and psychrometric properties of air are estimated using psychrometric charts. From the above relation the mass flow rate of dry air is calculated as m md a d a. In the above example, this ratio can be easily found as m m d a d s.
Air out, 0. In the first stage, a juice extractor is fed with oranges containing Figure 2. The results of calculations for mass and total solids composition of every stream are shown in Table 2. If this table is constructed as a spreadsheet i. This is especially useful in food process design and optimization where we are interested in scaling up, as well as, in the influence of specific process variables to the opera- tion cost.
The light cream is produced by mixing a portion of the full fat cream that is exiting from the centrifuge, with a suitable portion of the milk feed. Assuming that mf is the mass of milk entering the centrifuge, mc is the mass of full fat cream that is mixed with a suitable mass ms of the feed milk and X is the mass fraction of fat in skim milk, we may apply the mass balance Equations 2. Orange feed 2.
Again making all calculations on a spreadsheet, it is easy to scale up the results and to observe the influence of changing the amounts of cream products, or their fat composition, to the rest of process parameters. Since a small amount of mother liquor is transported along with the crystals, the removal of the excess of water is continued into the rotary drier to produce the final dried crystals.
Let mf be the mass of feed solution, ms the mass of steam evaporated in crystal- lizer, mm the mass of magma, mc the mass of crystals separated in centrifuge, mR the mass of recycled liquor, mp the mass of the final product, and md. Applying a total mass balance around the rotary drier boundary A in Figure 2. Applying a mass balance for solute around the same boundary 0.
Air in, 0. This is a common practice in food engineering design since recycles are used for raw material and energy conservation increasing the overall efficiency of the process. However, in real situations, the feed solution includes impurities or inert solids and recycling favors accumulation of these sub- stances within the process, thus leading to poor-quality final products.
A means to partially overcome this problem is to provide a suitable purge stream, or to separate, or to eliminate e. Inevitably, all this has to go through the mass and energy balances, with the latter to be discussed in the following sections. The main types of energy involved in food process operations are heat, mechani- cal work, potential, kinetic, chemical, and electromagnetic. It should also be noted that significant amounts of heat are lost through the walls of food process equipment, piping, and effluents.
Mechanical work appears when a system moves its boundaries i. Potential is the energy occupied by an object because of its position in respect to a datum level, while the kinetic energy appears in any moving object due to its veloc- ity. Chemical energy is the energy that is evolved or absorbed by a chemical or a bio- chemical reaction i. From the above types of energy, heat is the most important and it would not be exaggerating to say that it is involved in almost any food processing. Therefore, it will be discussed separately.
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When ther- mal equilibrium is reached, that is the temperatures of the two bodies are equal, there is no heat transmission between them. This means that there must be a temperature difference between the two bodies in order to observe heat flowing and that heat like mechanical work is a transitory type of energy i. As a consequence of heat flowing from or to a body there is a temperature or a phase change.
For example, if water is heated, it primarily raises its temperature until it reaches its boiling point and then it is evaporated under constant temperature provided that its pressure remains constant. If the temperature difference is negative In general, the specific heat capacity of a substance depends on its temperature and process type. For gases, there are two specific heat capacities, cp for a constant pressure and cv for a constant volume process.
The specific heat capacity of solids and liquids does not depend on process type. Values for specific heat capacities of food materials are very useful in food engineering calculations and are given in literature as functions of temperature and composition Choi and Okos , while the composition of foods may be obtained from the USDA database. Note that the latent heat of vaporization of a liquid is a func- tion of its saturation pressure or temperature.
Values for the latent heat of vaporiza- tion of water can be found in many handbooks or in saturated water and steam tables as that provided in Haywood, R. Applying this principle it leads to the conclusion that the total energy that enters a system equals the total energy that leaves, plus any energy change within it. Or in terms of an equation, Etot. Thus, Equation 2. By convention, the heat supplied to the system and the work done by the system are positive, while the heat rejected and the work consumed by the system are negative.
For a constant volume process, the work done by the system is zero and Equation 2. Note that both specific internal energy and enthalpy are properties of the components of a system and are related to its pressure and temperature. Values for specific enthalpy, specific internal energy, and other thermodynamic properties are given for water and steam in various food engineer- ing textbooks, for various ranges of pressure and temperature.
However, they must be used with care, since they are referred to specific food compositions and based on reference values of enthalpy that are not the same in any case. For example, in thermodynamic water and steam tables the reference value of the specific enthalpy of liquid water is 0 at its triple point 0.
In fact, we are not interested in the absolute values of specific enthalpy but in the changes of it that can be calculated combin- ing Equations 2. In the case of phase change, the change of enthalpy in Equation 2. For example, the latent heat of vaporization of water equals the difference of its specific enthalpy from saturated liquid to dry saturated vapor.
The latter represents the specific enthalpy of an ideal gas at temperature T, as water vapor is superheated and considered ideal at atmospheric conditions.
The above approximation facilitates energy balance calculations when values of specific enthalpy for water and steam are going to be used along with the ones for moist air, as for example, in the case of air drying of foods. Work W is produced while heat Q is supplied to the system. The fluid enters with a pressure P1, a velocity c1, an internal energy U1, a volume V1 corresponding to mass m, and at a height z1 from a datum level and exits with the respective values of P2, c2, U2, V2, and z2.
The total energy of the fluid entering or leaving the system consists of kinetic, potential, internal, and an amount of energy that causes the fluid to flow. The last is the work necessary to push the volume V of the fluid of mass m into or out of the duct and is easily proved to be the product of pressure P and volume V. Since the system is at steady state there is no energy change within it and applying the energy conservation law Equation 2. Considering Equation 2.
However, in food engineering applications, the amounts of potential and kinetic energy can be considered negligible compared to heat and mechanical work. Thus, they can be eliminated without considerable error and Equation 2. In these situations, the enthalpy change of the system is zero and thus, the total enthalpy of the streams entering the system equals the total enthalpy of the streams leaving it H H H Htot in tot out i in i k j out j n.
In the event of such interactions the enthalpy of products formation should be taken into account. On the contrary, there are some food process operations where the work term of Equation 2. These pro- cesses involve milling or grinding, mixing or emulsification, and transportation or circulation of highly viscous materials.
In these situations the amounts of mechani- cal energy are significant and are consumed to overcome frictional losses that are finally converted to heat absorbed by the process materials. Extrusion cooking could be referred as an example of severe mechanical work consumption along with heat. The critical steps are the process flow diagram construction, the selection of the suitable boundaries, and the establishment of the set of equations. In general, a mass balance should precede an energy balance to account for the quantities of the materials that enter or leave the system.
However, there are situations where mass and energy balances cannot be carried out independently. Roelen, and Henk P. Montero Coffee, Solange I. Teixeira Beer, Solange I. Mussatto, Nuno G. We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.
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