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A General Process Model of Sustainability Michael Neuman* Department of Landscape Architecture and Urban Planning, Texas A & M University, MS 3137 College Station, Texas 77843-3137, United States
Stuart W. Churchill* Department of Chemical and Biomolecular Engineering, University of Pennsylvania, 311A Towne Building, 220 South 34th Street, Philadelphia, Pennsylvania 19104, United States ABSTRACT: Sustainability is high on many research and policy agendas, and a number of specific models to measure sustainability have been developed. However, most models are based only on the first law of thermodynamics and, thereby, are incomplete and approximate. Sustainable processes are those whose rates are maintained over time without exceeding the innate ability of their surroundings to support the process. We present a model for measuring the sustainability of processes that adapts and integrates the first and second laws of thermodynamics and the concept of rate processes, thereby forming a new synthesis. The degree of sustainability of a process, whether ecological, economic, social, chemical, or biological, is expressed quantitatively in terms of algebraic equations. It is a dynamic approach that applies at any scale and takes into consideration the spatial and temporal factors of processes, thus permitting empirical applications that correspond to real world conditions (dynamic, complex, and evolving). These characteristics make it especially suitable for applications in the fields of chemistry, chemical engineering, and ecology.
’ A GENERAL MODEL FOR SUSTAINABLE PROCESSES Measures and models of sustainability have been proposed by researchers in numerous disciplines. These range from models for climate change, metabolic flow, and ecosystem services to biodiversity indicators, intactness indices, and assessments of ecosystems and cities.1-8 Increasingly, they address complex and dynamic phenomena such as climates, cities, and biological habitats as well as the functions and services that these systems perform. The rates of change (e.g., extinction of species, loss of habitat, and rise of sea level), the processes on which these changes are based, and the multiple scales or levels of the activities have now become of concern. Yet there is only a limited consensus across these disparate disciplines, and even within individual ones.9-11 When there is agreement, it is constrained or vague.9,12 These limits are echoed in policy fora and arenas. While each discipline has its own theories, methods, and vocabulary, there is general agreement about fundamental precepts such as balancing development and the environment while at the same time mediating social, economic, and ecological concerns, with an eye toward future generations.13,14 What has been missing in science, engineering, and public policy is a rigorous definition of sustainability and a theory to conceptualize and measure it quantitatively. That is our objective here. Our model is presented in the context of the emerging discourse on sustainability that is providing normative and scientific frameworks for a variety of disciplines and organizations. The noun sustainability refers to the degree to which an entity exists in a coevolutionary process with its environment whose inherent condition (essence) enables it to continue evolving and developing without jeopardizing its own life and livelihood, or the lives and livelihoods of those it affects, including the larger systems and r 2011 American Chemical Society
networks in which the entity finds itself situated, now and in the foreseeable future. An entity may be an object (building), process (industrial production), place (city), organization, or other living or territorial system. Sustainability refers to the ecology of human presence from a normative perspective: can humans inhabit a city, region, ecosystem, etc. sustainably, without damage and ill effects to others? The intellectual roots of sustainability and some of its theoretical consequences for sustainable development have been reviewed, and need not be here.15,16 The measurement of sustainability should incorporate the rateprocess concept. That is, a sustainable process is one whose rate can be maintained over time without exceeding the innate ability of its surroundings to support it, including the ability of the surroundings to absorb the associated impacts. Sustainable processes have rates of production and regeneration that equal or exceed rates of consumption and byproduct absorption. Just as material processes are governed by the first and second laws of thermodynamics and the theory of rate processes, the general theory of sustainability is based on these three concepts as applied to dynamic as well as steady-state processes. Sustainability has often been examined only in terms of the first law of thermodynamics, that is, in terms of the conservation of mass and energy. This approach is inadequate in two senses. First, the environment cannot be defined in terms of mass and energy only. Other qualities more difficult to quantify are essential to the survival Special Issue: Churchill Issue Received: October 4, 2010 Accepted: December 20, 2010 Revised: December 14, 2010 Published: January 18, 2011 8901
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Industrial & Engineering Chemistry Research of humankind, as well as other species and habitats. The addition of the second law of thermodynamics to the analysis of sustainability has revealed that full sustainability is not possible and can only be considered a goal to be approached, and never fully attained. This is because the entropy of any system increases with time due to irreversibilities, and because the exergy (or availability of energy), which is a quantitative measure of the ability to do work in a thermodynamic sense, decreases with time. These irreversibilities are the unavoidable consequence of any chemical or biological reaction or process. The practical aim for sustainability, therefore, is to minimize rather than eliminate these effects. In order to apply thermodynamics to a closed or open system it is necessary to define the boundaries of the system very carefully. Different choices of a boundary are a major source of disagreement over the sustainability of various processes. Another source of disagreement is the failure to account for all of the inputs and outputs through the boundary. To compare the sustainability of two processes, their boundaries, all of the inputs and outputs through these boundaries, and all net changes within the boundaries must be identified. Thermodynamics indicates the limits of what can be done within any system or framework of space. On the other hand, the rate processes such as fluid flow, heat transfer, mass transfer, chemical reactions, and bulk transport determine the time and/or space required to carry out the transformations both within and through any system or spatial framework. Basing the theory on the twin pillars of thermodynamics and rate processes enables it to be generalized across physical-metabolic and social-economic phenomena. Sustainability as a Process. Given that societies have become consumption oriented, and thus production oriented to satisfy consumer demand, then the processes of consumption and production are at the heart of a sustainable society or policy. However, classical and neoclassical modes of economics are insufficient to understand and explain the new relation of production and consumption in a framework of sustainability. The general theory of sustainability provides a new basis to conceptualize consumption and production as sustainable processes. In this framework, sustainable processes are ones that replenish the flows of matter, energy, information, capital, and other evolutionary factors through a system at levels in which the outputs are at least equal to the inputs, in terms of quality and in quantity. This concept incorporates the rate processes in which the rates of regeneration (replenishment) equal or exceed the rates of depletion plus extraction plus consumption; and the rates of production of wastes or byproduct are less than the rate at which the environs can absorb them and remain healthy and viable over the long term. These rates of replenishment also should lessen the rates of difference in equity among social groups. Sustainable processes give back in a circular way, with the outputs of one process continuously forming the inputs of others. Waste disappears in a truly sustainable process. This dynamic and scale-independent basis for the general theory of sustainability overcomes limitations of steady-state approaches that measure values at one point in time and/or one place in space. Moreover, some current conceptions of sustainability assume a completely closed system, which does not correspond to reality from a thermodynamic point of view. We envision that the rate-process concept for sustainability can apply to five general categories. These five categories are rates of consumption, rates of production, rates of accumulation, rates of depletion, and rates of assimilation. The theory can be applied to any factor within these categories. For example, for rates of consumption we can use energy and materials. For rates of
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production, we can use goods, services, and wastes. For rates of accumulation we can use wealth and poverty, and debt and profit, whether personal, corporate, or governmental. Examples of rates of accumulation also include nitrogen fixation, atmospheric carbon dioxide, and global climate change. For rates of depletion we can use atmospheric ozone, aquifer recharge, desertification, biological diversity, and habitat, language, and cultural loss. For rates of assimilation we can use water quality, atmospheric fluorocarbons, and the introduction of invasive and exotic species into an environment. A Mathematical Model for Sustainable Rates of Change. Two laws underlie the rate-process concept. The first law of thermodynamics states that matter and energy are conserved. The second law of thermodynamics, the entropy law, rephrased, states that matter and energy consumed and then rejected into the environment are of equal or poorer quality than that acquired from the environment. The first law reveals that all resources are finite and that their exploitation invokes inexorable trade-offs. The second law reveals limitations and consequences of the possible trade-offs. Both laws require the careful choice and scale of an envelope for the system, whether a single processing unit, an entire industrial plant, a city, an ecosystem, or the entire earth and its atmosphere. All choices for the exploitation of resources invoke, in addition to the first and second laws of thermodynamics, the rates at which they can be carried out, and thereby introduce restrictions in terms of space and/or time. (It should be noted that the value of information and knowledge added to a product in a manufacturing process is one of a number of quantities that have not been considered in this preliminary exposition.) The first and second laws of thermodynamics, as generalized for open as well as closed systems and for dynamic (time-dependent) as well as stationary conditions, constitute a necessary constraint for a mathematical model of sustainability. The rate-process concept provides a necessary complement; expressions for the rate of change of energy, mass, and chemical species can be derived from the first law but not for rate processes in general.17 The first and second laws and rate theory comprise a necessary but insufficient basis for sustainability because of the difficulty in quantifying such factors as the quality of life and diversity, and of system-wide phenomena. The first and second laws of thermodynamics and the concepts of entropy and exergy (availability) are well-known and therefore not elaborated here. The generalized treatment of rates is less wellknown and therefore is described briefly. The rate-process concept was developed by Churchill in the context of process design and was generalized with respect to chemical reactions, fluid flow, heat transfer, mass transfer, and bulk transport.17 For example, for a batch (confined, unsteady-state) process X 1 dx ¼ ri L dt
ð1Þ
Here, x represents some extensive quantity such as mass, t time, and L a measure of the extent of the system, while ri represents various rate mechanisms, which may be positive (inputs) or negative (outputs). A positive value for the left-hand side of eq 1, namely, (dx/dt)/L, represents the rate of accumulation of the quantity x and a negative value its rate of depletion, in both cases by the sum of the rate mechanisms ri. In either event a finite value of (dx/dt)/L indicates a deviation from sustainability that must be compensated for by some other rate mechanisms. Thus, eq 1 is only one component of an expression for sustainability. 8902
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As a simple example of a rate of change in a closed system consider the decrease in the number of moles of species A in a batch reactor due to first-order forward and reverse reactions. Equation 1 then becomes -
1 dNA ¼ k1 CA - kCB V dt
ð2Þ
Here, NA is the number of moles of species A, V is the volume of the reactor, CA and CB are molar concentrations, and k1 and k2 are forward and reverse rate constants, respectively, for the disappearance of species A. As an aside, chemists usually postulate implicitly an invariant density and replace -(1/V)(dNA/dt) with -dCA/dt. The analogue of eq 1 for a process carried out in continuous flow through a tube of cross-sectional area A is X w dX ¼ ri A dz
ð3Þ
Here z is the distance along the tube, w is the mass rate of flow through the tube, and X is the extensive quantity of concern per unit mass. The Eulerian equivalent of eq 2 may be expressed as -
dðnXA Þ ¼ kf CA - kr CB dV
ð4Þ
Here n represents the rate of flow in moles per unit time, XA the mole fraction of species A, and V the volume swept out by the flow. The term on the left-hand side represents the deviation from sustainability resulting from this process when considered in isolation. Changes that occur outside the boundaries of the chosen system(s), including the net flows through the boundaries into or out of that portion of the environment not encompassed by these systems, must also be considered in these calculations. One of the contributions of the rate-process concept was the distinction between rates of change (as represented by the lefthand side of eqs 1 and 3) from process rates (as represented by the terms on the right-hand side of eqs 2 and 4).18,19 Equations 2 and 4 may also be derived by reducing the general partial differential equation for the conservation of a species, in accordance with the imposed restrictions.20 That is, eqs 2 and 4 are special cases of the first law of thermodynamics. Our theory has the advantage of being applicable to a wide range of factors that make a place or process sustainable. Moreover, it is a scale-independent theory that answers what until now has been the most intractable barrier in the search for a general theory of sustainability: what are we trying to sustain, where are we trying to sustain it, and over what time span? The planet? An ecosystem? A city? A business? A way of life? Life itself? This decade, this century, this millennium, or indefinitely? Rate process theory combined with thermodynamics applies to dynamic, nonlinear, nonequilibrium systems as well as equilibrium systems, and is therefore applicable to complex urban, social, and ecological phenomena such as cities, organizations, and ecosystems as well as to single, simple processes such as a chemical reactor. Rate processes form an essential component of sustainability because it must be possible to maintain the rate of any process over time without exceeding the innate and “natural” ability of its surroundings to support it. This goes beyond existing carryingcapacity formulations in urban and environmental planning pioneered in the 1960s and 1970s by Ian McHarg, and by Donella Meadows and her colleagues in The Club of Rome report.21,22
These traditional views of carrying capacity dealt with a specific place at a specific point in time. Neither was process oriented, and consequently they did not account fully for the dynamic nature of the systems they modeled. They did not consider the coevolutionary character of human interaction with ecosystems. Another limitation in applying these two carrying-capacity approaches and their derivatives is that they did not pay close attention to the environs and the definition of the boundary between the activity system under study and its surroundings. The rate-process theory adds the dimension of time to the dimensions of space that the carrying-capacity approaches employed. For a straightforward exposition of our proposed method, consider the battery-powered electric car. It is a striking example of the loss of exergy as compared to the loss of energy. For example, losses of exergy include (1) the irreversible conversion of the chemical energy of the fuel to thermal energy during combustion of fuel in the power plant, (2) the irreversible transfer of thermal energy from the hot burned gases to the water in the boiler, (3) the nearly reversible transfer of thermal energy to inertial energy and then the irreversible transfer of that inertial energy to mechanical energy in the turbine, (4) the irreversible conversion of mechanical energy to electrical energy in the dynamo, (5) the irreversible ohmic loss in the up-voltage and down-voltage transformers, (6) the irreversible ohmic loss of electrical energy to thermal energy in the transmission lines, (7) the irreversible ohmic loss and other irreversibilities in the conversion of electrical to chemical energy in the battery of the car, and (8) the irreversible loss of exergy in the conversion of electrical energy to mechanical energy in the electric motor. (The exergy losses in the power train of the car are relatively unchanged from that of a gasoline engine.) Imagine what a small fraction of the exergy of the fuel reaches the wheels! Furthermore most of these losses in exergy cannot be greatly reduced in a practical sense. For example, decreasing the exergy loss in the process of combustion is almost impossible except at the cost of burning with oxygen instead of with air. Despite their pervasive use, no one has succeeded in increasing the overall efficiency of the turbine and dynamo much above 40%. The most obvious way is to raise the temperature in the boiler by increasing the pressure or by using a fluid such as mercury rather than water, but the cost and the hazards in terms of safety are obvious. The use of natural gas instead of coal as a fuel allows elimination of the boiler and offers the possibility of a related increase in efficiency, but most electricity will be generated using coal in the foreseeable future. Significant reduction in transmission losses including that in the transformers is unlikely, considering the maturity of that technology. Many schemes to increase the efficiency of batteries are currently being pursued, but they are also counterbalanced by costs and hazards. Most of these second-law losses have a more widely recognized first-law counterpart, for example, the loss of energy to the surroundings in the hot gases entering the stack, and the heat losses to the surroundings from each element in the overall process from fuel to wheels. The first-law losses from the combustor, boiler, and dynamo can be reduced somewhat by heat exchange and thermal insulation with some associated decrease in second-law losses. The thermal losses from the transmission lines to the surroundings can be reduced by using higher voltages but at the expense of second-law and first-law losses in the transformers. The second-law and first-law losses do not necessarily have the same importance. For example, the heat loss from the battery to the surroundings during charging due to ohmic heating is trivial in magnitude, whereas the corresponding loss of exergy is critical and may in itself defeat the whole scheme. 8903
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Industrial & Engineering Chemistry Research A limitation in rate exists in most of these steps. Two examples are the rate of transmission of electricity through the high-voltage lines as restricted by thermal heating, and the rate at which the battery can be charged as restricted by the internal electrical resistance. All the steps in this example are processes that occur over time and vary with time, and have corresponding process rates. These rates of exergy losses over time can be calculated, and differing technologies such as standard fuel, all electric, and fuelelectric hybrids can be compared over their life cycle (energy source to wheel) to determine which is more sustainable using our model. Implications. The general theory of sustainable processes has implications for sustainable development, including environmental impact assessments, urban design, the design of industrial processes, and the design and management of infrastructural and social-service delivery systems. Consider for example calibration of a model for one aspect of a social system, income distribution (equity) in an economy. One can specify the rate in terms of the rate of increase or decrease of income inequality (differences in per capita income between rich and poor) over time. One can also specify the boundary of the economy (say, metropolitan or national), recognizing that in a global economy these boundaries are fluid. The general nature of the theory enables it to be applied to the life cycle of all these processes, that is, for their assessment, planning, design, construction, management, maintenance, operations, repair, replacement, recycling, and disposal. In summary, thermodynamics and rate-process concepts have been adapted to develop a general theory of sustainability. The model permits the calculation of the sustainability of any process, whether chemical, biological, ecological, economic, or social. It is a dynamic and scale-independent theory that takes into consideration the spatial and temporal factors of processes, thus permitting empirical applications that correspond to actual (dynamic, complex, evolving) conditions. This theory of sustainability reflects a new manifestation of human will that does not merely shape and subjugate nature and ourselves along with it. Instead, sustainability embodies the will to work with nature, respecting it, and adhering to its capacities and limitations while still realizing our own hopes and dreams.
’ THE CONTRIBUTIONS OF A RATE PROCESS THEORY OF SUSTAINABILITY 1. Enables the mathematical calculation of the degree to which any process is sustainable over the long term, using the theories and methods of thermodynamics and rate processes. 2. Enables a comprehensive consideration of the relevant factors that impinge upon sustainability: economic, ecological, technological, and social. 3. Facilitates the determination of where in geographic space to draw the system boundary lines in the calculation of the degree of the long-term sustainability. 4. Enables a quantitative comparison of several processes to determine their relative degrees of sustainability and thereby inform technology and policy choices. 5. Places long-term sustainability alongside short-term efficiency in the cost-benefit calculus of choosing processes, technologies, and materials.
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’ ACKNOWLEDGMENT The authors thank Theresa Good of the University of Maryland for her insights and contributions to parts of this manuscript. ’ REFERENCES (1) Wigley, T. M. The Climate Change Commitment. Science 2005, 307, 1766. (2) Meehl, G. A.; et al. How Much More Global Warming and Sea Level Rise? Science 2005, 307, 1769. (3) Wang, G.; Schimel, D. Climate Change, Climate Modes, and Climate Impacts. Annu. Rev. Environ. Resour. 2003, 28, 1. (4) Luck, G. W.; Daily, G. C.; Ehrlich, P. R. Population Diversity and Ecosystem Services. Trends Ecol. Evol. 2003, 18, 331. (5) Scholes, R. J.; Biggs, R. A Biodiversity Intactness Index. Nature 2005, 434, 45. (6) Reiners, W. A.; Driese, K. L. Transport of Energy, Information, and Material through the Biosphere. Annu. Rev. Environ. Resour. 2003, 28, 107. (7) Millenium Ecosystem Assessment. Millenium Ecosystem Assessment Synthesis Report; Millenium Ecosystem Assessment: New York, 2005. (8) Pickett, S. T.; et al. Urban Ecological Systems: Linking Terrestrial Ecological, Physical, and Socioeconomic Components of Metropolitan Areas. Annu. Rev. Ecol. Syst. 2001, 32, 127. (9) The Royal Society. Measuring Biodiversity for Conservation; The Royal Society: London, 2003. (10) Balmford, A.; et al. The Convention on Biological Diversity’s 2010 Target. Science 2005, 307, 212. (11) Houghton, J. T. et al. , Eds. Climate Change 2001: The Scientific Basis; Cambridge Univ. Press: Cambridge, 2001. (12) Mace, G. M. An Index of Intactness. Nature 2005, 434, 32. (13) United Nations World Commission on Environment and Development. Our Common Future; Oxford Univ. Press: Oxford, 1987. (14) United Nations World Summit on Sustainable Development. Johannesburg Plan of Implementation; United Nations: New York, 2002. (15) Neuman, M. The Compact City Fallacy. J. Plann. Educ. Res. 2005, 25, 11. (16) Owens, S., Cowell, R. Land and Limits: Sustainability in the Planning Process; Routledge: London, 2002. (17) Churchill, S. W. The Interpretation and Use of Rate Data: The Rate Concept; Hemisphere Publishing: Washington, DC, 1974. (18) Kabel, R. L. Rates. Chem. Eng. Commun. 1981, 9, 15. (19) Kabel, R. L. Reflections on Rates. Ind. Eng. Chem. Res. 1992, 31, 641. (20) Bird, R. B., Stewart, W. E., Lightfoot, E. N. Transport Phenomena, 2nd ed.; Wiley and Sons: New York, 2002. (21) McHarg, I. Design With Nature; Natural History Press: New York, 1969. (22) Meadows, D. et al. Limits to Growth; Universe Books: New York, 1972.
’ AUTHOR INFORMATION Corresponding Author
*M.N. E-mail:
[email protected]. Tel: 979 845 7062. Fax: 979 862 1784. S.W.C. E-mail:
[email protected]. Tel: 215-898-5579. Fax: 215-573-2093. 8904
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