EMERGY SYNTHESIS 4: Theory and Applications of the Emergy Methodology

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1 EMERGY SYNTHESIS 4: Theory and Applications of the Emergy Methodology Proceedings from the Fourth Biennial Emergy Conference, Gainesville, Florida Edited by Mark T. Brown University of Florida Gainesville, Florida Managing Editor Eliana Bardi Alachua County EPD, Gainesville, Florida Associate Editors Daniel E. Campbell US EPA Narragansett, Rhode Island Shu-Li Haung National Taipei University Taipei, Taiwan Enrique Ortega Centre for Sustainable Agriculture Uppsala, Sweden Torbjorn Rydberg Centre for Sustainable Agriculture Uppsala, Sweden David Tilley University of Maryland College Park, Maryland Sergio Ulgiati University of Siena Siena, Italy ii December 2007 The Center for Environmental Policy Department of Environmental Engineering Sciences University of Florida Gainesville, FL

2 21 Emergy Analysis and the Eigenvalue Method for Solving Transformities Using Microsoft Excel Wade Thompson, Eldon C. Blancher II, and Manish Misra ABSTRACT A popular study in emergy analysis was performed by Odum and Collins (2000), who illustrated the use of mathematical computer programs to calculate the transformities of energy webs or energy flow diagrams, in an effort to standardize the calculation of these ratios. The research work presented here extends the research by Odum and Collins (2000) and uses Microsoft Excel, which is commonly available, to calculate emergy transformities using the eigenvalue method. With the vast amount of research being done in the field of emergy analysis, it seems that it is becoming more accepted by other disciplines and may soon be accepted as a valid method to make economic, ecological, and industrial design decisions. INTRODUCTION The term emergy analysis refers to quantitative methods of accounting for flows of energy through the environment. Emergy is the quantity of energy necessary for the fabrication of a specific material. Since it takes raw materials to make other materials, it is not difficult to suggest that the true measure of the value of a product is the total energy required to make it, instead of the amount of energy that can be extracted from it. Emergy as a concept seeks to measure the true energy cost of an item. When measuring the emergy of a product, all energy inputs, from raw material mining, to transport, manufacturing, assembly, installation and others are considered. Accounting for energy quality is implicit in emergy; all forms of energy are not the same. As an example, one joule of sunlight cannot perform the same amount of a given type of work as one joule of a fossil fuel. The unit of emergy is the emjoule. Most emergy calculations sum the total amount of solar energy required to produce a material. This quantity is known as solar emergy. The unit for solar emergy is the solar emjoule (sej). Another definition of emergy analysis states: Emergy analysis characterizes all products and services in equivalents of solar energy, that is, how much energy would be needed to do a particular task if solar radiation were the only input (Hau and Bakshi 2004). Emergy analysis provides a method to consider ecological and economic effects on the same basis. A fundamental principle of emergy analysis is the maximum empower principle. The maximum empower principle expands on the maximum power principle, introduced in 1922 by the biologist Alfred Lotka. He believed that the maximum power principle was the 4 th law of thermodynamics. It states that systems that will prevail in competition with others, develop the most useful work with inflowing emergy sources by reinforcing productive processes and overcoming limitations through system organization (Brown and Herendeen 1996). This implies that a system that depletes its resources faster than they can be renewed will fail and give way to systems that use resources at a sustainable rate. A useful tool in emergy analysis and in most engineering disciplines is the flow diagram as shown in Figure

3 Figure 1. Emergy systems diagram. (Source: Howard T. Odum, Emergy Evaluation, In Proc: International Workshop on Advances in Energy Studies: Energy flows in ecology and economy, Porto Venere, Italy, May 27, 1998). The solar emergy of a product or service is the energy required to make those products or services in equivalents of solar energy. Emergy assumes the Earth is a closed system with solar energy, tidal energy and deep earth heat as the major energy inputs. All living systems sustain one another by participating in a network of energy flow by converting lower quality energy into higher quality energy and degraded heat energy. Due to the fact that solar energy is the main energy input to Earth, all other energies are scaled to solar equivalents to give a common basis for comparing the different quality energies. The economy can be accounted for as a network flow as wealth directly and indirectly comes form the environmental resources measured by emergy (Odum 1996). Therefore, it is believed that the circulation of money is related to emergy. Solar transformity of a service or product is defined as the solar emergy required to make 1 J of the service or product. Mathematically, the solar transformity of a product is its solar emergy divided by its available energy in the formula: τ=μ/b (1) where, M is solar emergy, τ is solar transformity, and B is available energy or exergy (Hau and Bakshi 2004). Some of the attractive characteristics of emergy analysis (Hau and Bakshi 2004) are as follows. Emergy provides a bridge that connects economic and ecological systems. Since emergy can be quantified for any system, economic and ecological aspects can be compared independent of monetary perception. It compensates for the inability of money to value non-market inputs in an objective manner. Emergy analysis provides an ecocentric valuation method. It is scientifically sound and shares the rigor of thermodynamic methods

4 Its common unit allows all resources to be compared on a fair basis. Emergy analysis recognizes the different qualities of energy or abilities to do work. Emergy theory is sometimes criticized as being too simple, self-contradicting, misleading, and inaccurate. Most of the criticisms probably stem from a lack of details about underlying computations, as well as a lack of formal links with related concepts in other disciplines (Hau and Bhakshi 2004). Another criticism is that emergy analysis does not take into account the uncertainty in many of the numbers used to calculate transformities. Emergy analysis has been used in a wide spectrum of applications. Campbell, Williams, and Meisch (2005) reported research in the field of ecology evaluating ecological impact of practices and policies set by industries or government agencies. Giannetti et al. (2006) reported using emergy analysis to develop ternary diagrams, which can be used as graphic tools to assist environmental accounting and environmental decision-making, based on emergy analysis. Kang and Park (2002) performed an emergy analysis based study to evaluate the effects of environmental policies on the economy and how adding new structures, such as bridges or dams, can change the economy in a positive or negative way. A study by Bastianoni et al. (2005) tested the validity of tabulated values associated with emergy analysis, such as transformities, for analyzing the geochemical process of petroleum formation (naftogenesis) to determine the transformities of oil and natural gas. Towards application of energy analysis for sustainability of industrial processes, an interesting study by Björklund, Geber, and Rydberg (2001) deals with the feasibility of treating wastewater in a way that could produce electricity. Studies have also been conducted to illustrate the use of mathematical computer programs to calculate the transformities of energy webs or energy flow diagrams. The study by Odum and Collins (2000) describes a general procedure of computing solar transformities in ecosystems, and applying the minimum eigenvalue method to previously published sets of data. In that study, the authors describe how to: (1) Create energy systems diagrams, (2) Develop emergy equations for each transformation, (3) Enter energy flow values in a transformity-transformation matrix, (4) Add transformities to connect the data set to global solar energy, and (5) Use MATHEMATICA, a specific computer software program, to calculate transformities. Additionally, the paper by Odum and Collins (2000) provides a template for the program that includes how to input data as a matrix and what commands to give the program to achieve the appropriate mathematical manipulations. After the calculations are complete, transformities are listed as a matrix. Inspired by the successful work of Odum and Collins (2000), this paper presents a formulation for solving transformities by using Microsoft Excel. METHODS The study presented in this paper uses Microsoft Excel, which is a highly popular and commonly available tool for performing statistical functions. Use of the eigenvalue method for solving for transformaties requires the following steps. 1. Determining the transpose of a matrix. 2. Calculating the eigenvectors of a matrix. 3. Calculating the dot product of two matrices. 4. Finding the minimum of a list of numbers. 5. Multiplying all the elements in a matrix with a single number. The standard mathematics package found in Excel will perform all those listed except # 2 to calculate the eigenvectors of a matrix. An Excel Add-in, with capabilities of calculating eigenvectors, is required for performing step #2. The Excel Add-in downloaded from

5 (under the name: MATRIX Matrix and Linear Algebra functions for EXCEL, available as of January, 2007) and has the capability of calculating eigenvectors; this method was used in this study. RESULTS The example from Odum and Collins (2000) was used in this study to illustrate the effectiveness of using the Excel Add-in for solving for transformaties by the eigenvalue method. The following steps illustrate the approach was and should be used. 1. Use the emergy network diagram to write the equations of energy transformations. Figure 2 depicts the emergy network diagram, as provided in Odum and Collins (2000). The related emergy equations, for each of the variables x 1 through x 8, are listed as follows: 2*10 7 *x 1 = 100*x 2 (2) 100*x 2 = 10*x 3 (3) 8*x 3 = 1*x 4 (4) 2*x 3 = 0.2*x 5 (5) 0.2*x *x 6 = 0.01*x 7 (6) 1*x 4 = 0.1*x 6 (7) 8*x 3 = 0.02*x 8 (8) 2. Use the emergy equations to create a Transformity-Transformation matrix. The emergy equations are used to create an N x N transformity matrix, where N is the number of variables in the emergy equation. Individual entries in the matrix contain the coefficient of each variables and the resultant matrix is shown in Table Dot product of the transformation matrix. In order to perform eigenvector analysis, the input data transformation matrix M needs to be multiplied by its transpose. Matrix A is the dot product (M T.M) of matrix M, calculated using the formula: A= mmult(m T.M) (9) where M T is the transpose matrix of M calculated using the Microsoft Excel function transpose (M). 4. Calculation of eigenvectors. Excel Add-in is then used to calculate the eigenvectors of the dot product matrix of the input data transformities. The matrix P contains the eigenvectors of matrix A and it can be calculated using the following formula in Excel: P = MatEigenvector_pow(A) (10) The eigenvectors are shown in Table 3. Figure 2. Emergy transformation systems (Odum and Collins 2000)

6 Table 1. Input data transformation matrix (M). Chapter 21. Emergy Analysis and the Eigenvalue Method x1 x2 x3 x4 x5 x6 x7 x8 Coefficients of xn 2.00E Table 2. Dot product of transformity matrix. 4.0E E E E E E E E-04 Table 3. Eigenvectors of A E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

7 5. Determination of minimum eigenvector. Once the eigenvector matrix is available, u is determined as the minimum of the absolute values in the last column of the eigenvector matrix. It is calculated using the following formula in Excel: u=min(p last column ) (11) Table 4 depicts the determination of u. 6. Calculation of the solar transformity matrix. The solar transformity matrix T is calculated by multiplying the last column of matrix P with 1/u. Table 5 lists the solar transformity matrix for the example under study. Steps 1 through 5 illustrate how the eigenvalue method can estimate transformities of systems, as given in the example in Odum and Collins (2000). Table 4. Determination of the minimum eigenvector. 1 5E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 5. Solar transformity matrix. 1 = x1 2.00E05 = x2 2.00E06 = x3 1.60E07 = x4 2.00E07 = x5 1.60E08 = x6 2.00E09 = x7 8.00E08 = x

8 CONCLUSIONS This study illustrated the use of mathematical computer programs to calculate transformities of energy webs or energy flow diagrams. The detailed, step-by-step formulation presented in this paper calculates transformities by using Microsoft Excel. The work presented in this paper has proven to be consistent with previous research (Odum and Collins 2000). The excel formulation as presented in this paper will help to calculate transformities by using a user-friendly and widely available program. REFERENCES Bastianoni, S., Campbell, D.E., Susani, L., and Tiezzi, E The solar transformity of oil and petroleum natural gas. Ecological Modeling. 186: Björklund, J., Geber, U., and Rydberg, T Emergy analysis of municipal wastewater treatment and generation of electricity. Resources, Conservation and Recycling 31: Brown, M.T. and R.A. Herendeen, Embodied Energy Analysis and Emergy Analysis: A comparative view. Ecological Economics 19: Campbell, D.E., Brandt-Williams, S.L., and Meisch, M. E. A Environmental Accounting Using Emergy: Evaluation of the State of West Virginia. Giannetti, B.F., Barrella F.A., and Almedia, C.M.V.B A combined tool for environmental scientists and decision makers: ternary diagrams and emergy accounting. Almeida Journal of Cleaner Production. 14: Hau, J.L., and Bakshi, B.R Promise and Problems of Emergy Analysis. Ecological Modeling. 178: Kang, D., and Park, S.S Emergy evaluation perspectives of a multipurpose dam proposal in Korea. Journal of Environmental Management. 66: Odum, H.T Emergy Evaluation. International Workshop on Advances in Energy Studies, Porto Venere, Italy. Odum, H.T., and Collins D Transformities from Ecosystem Energy Webs with the Eigenvalue Method. Emergy Synthesis 2: Theory and Application of the Emergy Methodology Wikipedia.com internet encyclopedia, Emergy

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