Mass Balances for Chemical Engineers

Gumersindo Feijoo, Juan Manuel Lema, Maria Teresa Moreira

• Publisher: De Gruyter
• Year: 2020
• ISBN:
  9783110624311
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Industrial & Technical Chemistry

The fundamentals of mass balances, relevant for chemical engineers summarized in an easy comprehensible manner. Plenty of example calculations, schemes and flow diagrams facilitate the understanding. Case studies from relevant topics such as sustainable chemistry illustrate the theory behind current applications.

1 Conservation principles

1.1 The law of conservation of mass

Conservation laws define the fundamentals of science and engineering. The most common statements of these laws express that “mass (or energy) cannot be created or destroyed,” “the mass (or energy) of the universe is constant,” “the mass (or energy) of an isolated system is constant” and so forth. That is, there are certain characteristics of matter that remain constant when a physical or chemical change takes place in a system. The constancy of these properties, that is, their conservation, is the main object of the study of the so-called principles of conservation.

Although the ancient Greeks first proposed the idea that the total amount of matter in the universe is constant, the French chemist Lavoisier¹ enunciated the law of conservation of mass based on countless experiments where he measured the mass of all the components of a wide range of chemical reactions. This law states that, despite chemical reactions or physical transformations, mass is conserved – that is, it cannot be created or destroyed – within an isolated system. In other words, in a chemical reaction, the mass of the products will always be equal to the mass of the reagents.

Therefore, chemical reactions can be visualized as a rearrangement of atoms and bonds, while the number of atoms involved in a reaction remains unchanged. This assumption allows us to represent a chemical reaction as a balanced equation, in which the number of moles of any element involved is the same on both sides of the equation.

A more general statement of this law consists in pointing out that matter is neither created nor destroyed, it is only transformed. This fact is valid for practically all physical and chemical changes, with the exception of nuclear reactions, where part of the matter is transformed into energy.

1.2 General balance equation

The calculation and design of industrial unitary equipment requires the resolution of equations that describe the systems under study and relate the variables involved to each other (flow rate, T, P, composition, energy, etc.).

Using the conservation principle of matter, a series of equations (=balances) can be formulated between the various units, systems and flows of the processes. Accordingly, it is possible to:

1. Calculate mass flows by reducing in situ measurements.
2. Close the mass flows (=close the mass balances) to describe the system comprehensively or compare the actual (measured) values with the target values.

These balances give an idea of “how much” the change in a given system meant. Now, we cannot solve these equations without some knowledge and interpretation of the transport mechanism. That is, in addition to “how much,” we need to know “at which rate” the change occurs. This value is given by kinetic laws:

• Physical kinetics: friction (motion), conduction–convection and radiation (energy), and diffusion (matter).
• Chemical kinetics: for systems where a chemical reaction occurs.

A third important element to take into account is the information about natural and/or nonnatural restrictions. These restrictions can take the form of the following:

• physical equilibrium,
• chemical equilibrium,
• boundary conditions,
• other (economic, safety, legislation, etc.).

The knowledge of all this information is the first step for the definition of a mathematical model from which it is possible to analyze, simulate, design a system and/or process.

The basic principle used in modeling of chemical engineering process is based on the concept of balances (momentum, mass and energy). The application of balances must refer to a system defined by a control volume, perfectly delimited in space by a control surface. Generally speaking, any balance can be expressed in a general form as follows (Figure 1.1):

Figure 1.1: Mass balance scheme.

$Input+Generation=Output+Accumulation$

• Input/Output: This corresponds to the flow of property (mass and/or energy) that crosses the limits of the system in a given time.
• Accumulation: This corresponds to the amount of property within the system after a time t, so it can be both positive and negative.
• Generation: This corresponds to the amount of property that appears or disappears within the system without initially being present or having been transferred across the system boundaries.

The extent of description of the balances can be defined at various scales:

• Macroscopic balance (also called integral): It is applied to a volume element and allows to know what happens between two instants of time. It is characterized by the knowledge of only one value of each variable, which will be the mean value of the whole system.
• Microscopic balance (also called differential): A differential element of volume is applied and allows to know what happens in an instant of time; therefore, there is a variation of the property (mass/energy) with space (x, y, z) and time (t).

At the same time, the existence of chemical reaction (generation term) or nonstationary state (accumulation term) implies notorious differences in the type of equation of the balances and, therefore, in their resolution. Appendices C, D and E show the basic mathematical aspects and their application in Excel for solving systems of linear and nonlinear equations.

The synoptic description of a process is usually represented through flow diagrams, which help to understand how the flow of materials or energy is carried out in a process or in an equipment. Different representation options are considered: block diagram, process flow diagram and piping and instrumentation diagram (P&ID).

The block diagram is represented by means of boxes or rectangles in which the input and output flows are identified (usually with an identifying number in a rhombus over each process line). Process flow diagrams include symbols representing major equipment items and process lines (including bypass and recycle streams). The physical properties, quantities, temperatures and pressures of the materials can be indicated for each process line in the stream table that typically compiles an inventory of the different flows. More exhaustive information is included in the P&ID such as instrumentation and control details, vents and drains and relief and safety valves.

2 Balances in systems without chemical reaction

2.1 Formulation of the general equation of macroscopic mass balance

2.1.1 Overall balance

The rigorous formulation of the mass balance for a control volume (V) delimited by a control surface (A) (Figure 2.1...

Table of contents

• Title Page
• Copyright
• Contents
• 1 Conservation principles
• 2 Balances in systems without chemical reaction
• 3 Balances in systems with chemical reaction
• 4 Balances in multiple systems
• Nomenclature
• Glossary
• Index