Energy and Mass Transfers: Balance Sheet Approach and Basic Concepts
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This is the first book of a series aiming at setting the basics for energy engineering. This book presents the fundamentals of heat and mass transfer with a step-by-step approach, based on material and energy balances.
While the topic of heat and mass transfer is an old subject, the way the book introduces the concepts, linking them strongly to the real world and to the present concerns, is particular. The scope of the different developments keeps in mind a practical energy engineering view.
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Energy and Mass Transfers - Abdelhanine Benallou
Preface
Good things arising from prosperity are desired, but good things stemming from adversity are admired
Seneca, stoic philosopher, 4 BC. - 65 AD.
For several years, I have cherished the wish of devoting enough time to the writing of a series of books on energy engineering. The reason is simple: for having practiced for years teaching as well as consulting in different areas ranging from energy planning to rational use of energy and renewable energies, I have always noted the lack of formal documentation in these fields to constitute a complete and coherent source of reference, both as a tool for teaching to be used by engineering professors and as a source of information summarizing, for engineering students and practicing engineers, the basic principles and the founding mechanisms of energy and mass transfers leading to calculation methods and design techniques.
But between the teaching and research tasks (first as a teaching assistant at the University of California and later as a professor at the École des mines de Rabat, Morocco) and the consulting and management endeavors conducted in the private and in the public sectors, this wish remained for more than twenty years in my long list of priorities, without having the possibility to make its way up to the top. Only providence was able to unleash the constraints and provide enough time to achieve a lifetime objective.
This led to a series consisting of nine volumes:
–Volume 1: Energy and Mass Transfers;
–Volume 2: Energy Transfers by Conduction;
–Volume 3: Energy Transfers by Convection;
–Volume 4: Energy Transfers by Radiation;
–Volume 5: Mass Transfers and Physical Data Estimation;
–Volume 6: Design and Calculation of Heat Exchanges;
–Volume 7: Solar Thermal Engineering;
–Volume 8: Solar Photovoltaic Energy Engineering;
–Volume 9: Rational Energy Use Engineering.
The present book is the first volume of this series. It groups the basic concepts and the fundamental mechanisms governing heat and mass transfers. It aims to meet the requirements of clarity in the presentation of the fundamental theories in the perspective of enabling students to fully understand the basic principles, before moving on to the details of equipment design and sizing.
This book is therefore introductory and simple. It is intended to expose the mechanisms governing heat and matter transfers within the same system or between two or more systems.
As we will see throughout this book, applications of these concepts and principles are multiple: they are considered essential in sizing techniques of industrial equipment of different kinds. They also have become paramount in the design of ‘smart buildings’ and in the development of mathematical models to perform predictions of climate change through the greenhouse effect or the thinning of the ozone layer. In addition, these concepts form the basis of engineering calculation methods of industrial equipment, which must satisfy, from now on, minimum energy consumption constraints.
This introductory book constitutes a clear and solid foundation, on which a robust construction of energy engineering techniques can be undertaken.
We have consequently used simple and practical ways to explain complicated principles. We have also given considerable importance throughout the document to integrating as many practical examples as illustrations, to allow a better visualization of the phenomena and to help make applications of the different equations, student friendly, positive, tangible and concrete.
Abdelhanine BENALLOU
April 2018
Introduction
Transfer Techniques: What Role for the Engineer?
I.1. Energy and mass transfers in industry
Within different industries, products are often elaborated through the transformation of several inputs. In most cases, various manipulations of the inputs are involved before arriving at the desired end products. Through these manipulations, the initial inputs undergo multiple transformations during which they are heated, cooled or even consumed in order to give rise to new components.
It is obvious that heating or cooling will require energy exchange between the components of the process considered. In the same way, generation of new products implies chemical reactions between the inputs.
Thus, during the course of these transformations, several types of transfer take place between the inputs. Energy and mass transfers are the most significant. Whilst mass transfers are mainly conducted to purify or to elaborate products, energy transfers are intended to provide the calories necessary for heating, as well as cooling or air conditioning, delivering the heat for an endothermic chemical reaction, or cooling a nuclear reactor, etc.
I.2. Practical examples
I.2.1. Oil extraction and refining
We already know that in order to manufacture the different fuels that we use for our convenience (gasoline or kerosene, for example), we first have to proceed with the extraction of oil, onshore or offshore.
Figure I.1. Onshore crude oil extraction (https://pixabay.com/fr/gréer-texas-591934/)
Figure I.2. Offshore crude oil extraction (https://cdn.pixabay.com/photo/2017/04/22/16/06/rig-2251648_960_720.jpg)
The crude oil produced in this way is then transferred to refineries, where it will be treated to extract various fuels.
Figure I.3. Oil refinery (https://pixabay.com/fr/industrielle-raffinerie-pétrole-720710/)
Among the products extracted, we find gasoline to keep our car engines running, kerosene to fuel aircraft reactors, fuel oil to power the boilers of thermal powerstations, etc.
These different treatments require multiple mass and heat transfers before resulting in the desired end products.
I.2.2. Air-conditioning a room
Proper operation of data centers or sophisticated electronic devices very often requires an environment whereby temperature and humidity are controlled, in order to ensure optimal operating conditions and avoid any damage to their components.
Figure I.4 shows a typical data center room with an air-conditioning system designed to maintain temperature at T* and humidity at h*, regardless of eventual variations in the surrounding conditions, such as the outside temperature, the sun shining through the windows, the opening and closing of doors, the presence of individuals inside the room, etc.
Figure I.4. Energy and mass transfers in an air-conditioning system
The maintaining of constant temperature and humidity inside the data center requires multiple energy and mass transfers to be operated by the air-conditioning system: Energy transfers aim to maintain the temperature around T* while mass exchange stabilizes the humidity around h*.
I.3. The role of the engineer
Whether for the examples presented in section I.2 or for more general cases of industrial production processes, the engineer’s role will be different depending on the type of task considered: designing a new plant or acting on existing equipment. For the first type of task, the role of the engineer is to design and build the devices that will make it possible to carry out the various transformations and lead to the end products or reach the objectives sought.
If we consider an existing production unit where equipment is already on site, the engineer’s role is to define and ensure optimal operating conditions and parameters, i.e. those which will produce the best results.
In order to do so, it will first be necessary to carry out a detailed analysis of the equipment involved and its operating conditions. This diagnosis will be necessary in order to check whether the different devices are running in the best possible manner or whether their operation can be improved. In the latter case, the role of the engineer is to define possible improvements and to size the equipment or the changes defined by the potential improvement.
Moreover, whether they are designing new production equipment or conducting a diagnosis in the perspective of defining optimal operating conditions of an existing installation, engineers must always keep in mind the cost imperatives. Indeed, the various studies, diagnoses, analyses and calculations must be approached in the most economical manner possible, since the ultimate goal of any industrial operation, beyond product manufacturing, is to make a profit.
Thus, the role of the engineer is often twofold:
– to identify and size the devices needed and define their optimal operating conditions in order to carry out the necessary transformations and thus to manufacture the desired end product;
– to ensure the best economical operation leading to competitive production costs.
The different fields of engineering (electrotechnics, fluid mechanics, electronics, productics, energy, etc.) each respectively define the relevant equipment design and sizing techniques. However, whatever the field of engineering concerned, it will be essential to understand the fundamental mechanisms that govern the different transformations involved, in order to be able to perform optimal design and sizing of the necessary equipment.
Knowledge of the mechanisms underlying the different production processes is especially necessary in order to be able to translate the required transformations into equations. In fact, it is based on these equations that equipment design techniques are developed.
In addition, in order to achieve competitive end product prices, it will be necessary to identify the impacts of the selected processes on production costs. To consider only energy inputs for example, it is readily known that high energy consumption will lead to additional production costs and that, conversely, minimizing energy consumption results in squeezing costs.
An example of this type of optimization is presented when reduction of energy losses through the walls of buildings is considered (see Volume 2, Chapter 4 of this series), or through the envelopes of furnaces or industrial installations (see Volume 2, Chapter 3 of this series).
This type of analysis can also be applied to mass transfer. Indeed, low mass transfer rates will be reflected in high cost prices, while improving the efficiency of a given mass transfer process will lead to higher outputs, and consequently to a reduction in production costs.
I.4. Management requirements
Thus, the engineer is often asked to respond to various requirements of his management which are, in most cases, expressed as follows: how to minimize the operating budget of a manufacturing unit, whilst observing basic safety rules and international regulations in force.
Indeed, the management determines the objectives for the engineer in technical terms (a given production level needs to be ensured), but also in financial (minimal production cost) and regulatory terms (safety and production standards must be adhered to).
An engineer is the refore faced with a multidimensional problem.
I.5. How may these requiremets be met?
At a technical level, the engineer must be in a position to design the equipment that will be capable of ensuring the desired transformation and therefore lead to the end products sought. To achieve this, it will be necessary to translate the sought transform mations into equations. Thus, knowledge of the different mass and energy transfer mechanisms and the establishment of the equations that govern them will be necessary.
Likewise, at the financial and regulatory levels, the production costs and the constraints imposed by safety rule and regulatons (standards) must be taken into consideration.
Figure I.5. Meeting the requirements (https://pixabay.com/fr/ingénieur-caricature-dessin-animé-23810/)
Thus, to satisfactorily respond to management requests, an engineer must firstly be in a position to translate the processes into equations, then incorporate the cost, regulatory and safety considerations into these equations. He/She will then hope to solve the equations thus developed.
I.6. The means at the engineer’s disposal
In order to solve the set of equations that arise from the mathematical translation of his management requests, the engineer can use several means available to him:
– the arsenal constituted by all of the theories learned in the different fields of engineering: fluid mechanics, optimization, applied mathematics, etc. This book deals with one of these theoretical bases of engineering techniques;
– all of the computing means available in order to solve the equations: computers, software packages, etc.
Figure I.6. Solving the equations (http://t0.gstatic.com/images?q=tbn:ANd9GcRy8RuH7MXiGBkSNzuiR2o0hgLAxtCqC6GHLLxeyNMf48a2ZrU7GDi7K56u)
As such, the purpose of this book is to explain the mechanisms that govern mass and energy transfers. The perspective is to establish the equations which govern their underlying processes in a way which will make design and optimization tasks possible.
In addition, many possible practical applications of these equations are presented using concrete examples and, where useful, the resulting economical optimization issues are also discussed.
As we will see in detail in Chapter 1, in order to be able to carry out analyses on manufacturing processes or on physical systems, certain knowledge of the quantities of energy and mass transferred is essential. It will thus be necessary to establish certain rules of accounting for mass and energy exchanges. Indeed, in the same way that an accountant is led to monitor expenditure and revenue in order to draw up a company’s financial balance sheets, the engineer will need to monitor the mass and energy inputs and outputs within a given system in order to draw up the mass and energy balances for the installation concerned. We will see that this notion of ‘balance sheet’ is extremely important in industrial process analysis methodology. We will also see that it is thanks to this balance-sheet approach that we can establish the equations that govern a given transformation.
Chapter 1 also introduces a number of important concepts, such as transfer area and driving potential difference (DPD) that enable a simple formalization of the expressions of mass and energy flows.
Chapter 2 presents the mechanisms of heat transfer, as well as the basic laws governing energy flows in different circumstances. This summary presentation of the various heat transfer laws permits, from the outset, the determination of heat fluxes in the simplest cases, without having to wait for the more elaborated developments detailed in Volumes 2 to 4 of this series.
The mechanisms for mass transfer, meanwhile, are summarized in Chapter 3, where the concepts underlying the flow or the movement of matter are depicted at the microscopic level. This chapter also presents several mass transfer techniques such as reverse osmosis, centrifugation, electrodialysis, distillation or absorption.
In Chapter 4, a formalization of the dimensional analysis technique is presented. The importance of this technique is underlined, first as a powerful tool for verifying the validity of equations or for defining homogeneous unit systems, secondly as a basic technique to be used in Volume 3 of this series to study energy transfer by convection.
Moreover, throughout this series, a database of physical parameters and constants is constructed in order to gather all of the data needed for energy engineering calculations. This volume presents the basic data encountered in the initial developments, as well as a unit conversion table.
It should be noted that the database core presented in the appendix constitutes the seed that will lead, over the course of the different volumes, to the global database. The latter will constitute a quick reference tool for the student to consult in order to resolve the problems posed in the different volumes of the series.
Finally, this book aims to establish, in a clear and solid manner, the fundamental principles and concepts that govern energy and mass transfers in industrial processes. Throughout its various chapters, we have been keen to present and explain the basic theories underlying these transfers, without seeking to introduce the details of the in-depth studies, which are the subject of the subsequent volumes in the series.
We also felt it was important to integrate many practical examples as illustrations, in order to help visualize the phenomena, and to make the applications of the different equations student-friendly, more tangible and concrete.
Moreover, in order to allow the student to implement the new concepts as rapidly as possible, a series of illustrative exercises is presented at the end of each chapter. These exercises have been designed to correspond, as much as possible, to real situations from industrial practise or everyday life. In presenting the solutions retained for each of the exercises, we voluntarily adopted a level of detail that leaves no room for hesitation and encourages full implementation of the solutions; that is, by completing and presenting all of the details of the numerical applications.
Indeed, it is widely known that engineering students are generally reluctant to perform or complete numerical calculations. We have consequently given particular importance to the numerical applications presented in the examples.
We hope that this book will accomplish its initial mission: to provide a simple learning tool that will assist engineering students in their understanding of the basic principles of mass and heat transfer. We voluntarily chose a simple way of presenting the different principles and mechanisms by deferring the more comprehensive and detailed studies to a later stage.
1
Basic Concepts and Balances
1.1. Thermal energy and the first law of thermodynamics
Let us recall that the first law of thermodynamics is a law of energy conservation. It introduces the internal energy
U, which represents the sum of the energies (kinetic and potential) of the system.
Assuming that there is no mass exchange and that we are considering a closed system that is subject to a thermodynamic transformation between two states, initial (1) and final (2), the variation in internal energy, U(2) – U(1), is the sum of the following two terms:
– the macroscopic works performed, W1→2; generally this is the work of the pressure forces;
– the energy exchange between the system and its outside: Q1→2.
This is reflected by:
We can therefore deduce a formal definition of the thermal energy (or heat) that is exchanged by the system between the initial state defined by (1) and the final state defined by (2):
For the thermodynamic systems studied, the work involved is generally due to pressure forces. The work is then given by the integral of these forces:
For the systems encountered in heat transfer analyses, volumes are generally constant (isochoric systems). The pressure forces are therefore not at work.
Consequently:
For such systems, thermal energy is therefore given by the variation in the system’s internal energy: Q1→2 = U(2) − U(1)
This relation between the variation in a system’s internal energy and the heat received (or yielded) by this system is, inter alia, used to determine the specific heats (also known as heat capacities or sensible heats) of different materials,