Carbon and footprint-constrained energy planning using cascade analysis technique
Introduction
Pinch analysis was originally developed based on thermodynamic principles to identify optimal energy utilization strategies for process plants [1], [2], [3], [4]. The basic concept is to match the available internal heat sources with the appropriate heat sinks to maximize energy recovery, and to minimize the need of external utilities such as purchased fuels and cooling agents. Analogies between heat and mass transfer led to the field of mass pinch analysis, which is concerned primarily with the efficient use of industrial solvents [5], [6], [7]. This field has also led to the specialized areas such as water network synthesis [8], [9], [10], [11], [12], [13], [14], [15] and utility gas integration such as hydrogen [16], [17] and oxygen [18]. Some of these important works are worth mentioning.
The seminal work on water network synthesis was reported by Wang and Smith [8] based on the principle of mass pinch analysis [5], which treated the water-using operation as mass transfer operations; such cases are known as fixed load problems. Later works on water network synthesis have been based on the fixed flowrate problem where water-using operations are treated as an allocation problem among the available water sinks and sources. The earliest work on fixed flowrate problem was developed by Dhole et al. [9] that utilized the water-sources and water-sinks composite curves to target the minimum fresh water and wastewater flowrates; however, the approach was proven to lead to sub-optimal solutions for many problems [10]. Hallale [10] then presented the water surplus diagram, which was based on the concept of hydrogen surplus diagram [16] to target the minimum water flowrates. Although the proposed approach is able to identify globally optimal solutions, it involved tedious trial and error plotting of the surplus diagram before the rigorous water targets could be found. In addition, an alternative graphical procedure known as the material recovery pinch diagram was then developed independently by El-Halwagi et al. [11] and Prakash and Shenoy [12]. The main limitation of their approach is the accuracy of the solution which is dependent on the visual resolution or clarity of the graphical displays used. A tabular, algebraic approach was then developed by Foo and co-workers [13], [14], [15], which was particularly useful for finding exact values of the solutions that may not have been possible with purely graphical approach. These methods have subsequently been extended its use for the synthesis of utility gas network [17] through a cascade of processes with progressively lower quality requirements.
More recently, novel applications of pinch analysis for emergy analysis [19], property integration [20], [21], [22] and production planning [23], [24], [25], [26] have been reported in the literature. In all abovementioned cases, the common underlying principle is that pinch analysis makes use of information about stream quantities in conjunction with data about quality. Depending on the application, stream quality can be defined by variables, such as temperature, concentration, emergy, property or time of occurrence.
Emission targeting by pinch analysis has been previously reported by in the framework of total site analysis [27], [28], [29]. Total sites in their work refer to process plants that incorporate several processes which are serviced by a central energy utility system. Although emissions targeting by pinch analysis was introduced in previous studies, the early applications were limited specifically to optimization within industrial facilities, and not to regional or national energy sectors. The latter application covers broader geographic and temporal scales, and also includes different energy demand sectors, such as residential consumption, transportation and industry. Recently, Tan and Foo [30] addressed this latter application by extending the material recovery pinch diagram [11], [12] into the energy planning composite curves to locate the minimum amount of zero-carbon energy source during energy planning. However in this early work, the low-carbon sources are treated as zero-carbon source; hence leading to an approximate target. The accuracy of the graphical targeting approach is further limited by the visual resolution of the displays. From the above description, it is observed that pinch analysis techniques have been widely accepted as a promising tool for solving a specific class of sink–source allocation problems for resource conservation.
In general, the basic source–sink allocation problem can be characterized as follows:
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The system contains m sources (e.g. water, gas, energy, etc.), each producing a stream of fixed quantity (e.g. flowrate) and quality (e.g. concentration).
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In the same system there are n sinks or demands, each requiring a fixed input of quantity (e.g. flowrate) and having a specified minimum quality requirement (e.g. maximum impurity concentration).
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The system is characterized by a single overall measure of stream quality that is inverse in scale (i.e., a value of 0 indicates the highest possible quality and larger numerical values indicate lower grades) and which follows a linear mixing rule (i.e., the quality of a mixed stream is equal to the weighted arithmetic average of the quality indices of its constituent streams prior to mixing). Impurity concentration is one example of such quality indices. Similarly, enthalpy can be said to follow these guidelines if heat losses are negligible and stream mixing generates no heat loss or gain. El-Halwagi and co-workers [6], [20], [21], [22] has also shown that many properties can be made to conform to this kind of behavior when different algebraic transformations are used to linearize the property mixing rules.
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In the system, there exists a valuable external resource of high quality (i.e., whose quality index has a value of 0 or is relatively close to 0 compared to the other streams in the system), and the objective is to determine the minimum quantity of this resource that can be used to sustain the operation of the system. This minimum quantity is known as the target, which serves as a benchmark value prior to detailed allocation network design. The target can be minimized by maximizing the reuse/recycle of available streams from the m internal sources, and by mixing these as appropriate to meet the quality restrictions of the sinks.
The basic source–sink allocation problem can be pictured with the aid of a matching superstructure, as shown in Fig. 1. Note that the stream entering each sink is a mixture of different available sources; and that each source is also able to distribute its discharge to different sinks. For example, the demand of D1 is met by combining an external resource stream, F1, with reuse/recycle streams from the available sources within the network, as shown. On the other hand, the source S4 in Fig. 1 distributes is output into four potential reuse/recycle streams to the different sinks, with any excess of flowrate being discharged as waste stream, W4.
An equivalent linear programming formulation has been suggested by many researchers, such as El-Halwagi et al. [11]. Tan and Foo [30] first recognized how these principles can be extended to energy planning problems, wherein the streams consist of energy flows from sources and into demands, and quality is measured in terms of carbon intensities or emission factors of the different sources. As all the approaches previously mentioned shared the same principle; therefore, such problems can be solved with any of the approaches to yield the same solution, including the graphical technique of energy planning composite curves [30] that is based on the work in material recovery [11], [12]; or the algebraic targeting approach of cascade analysis techniques [13], [14], [15], [17].
In this work, the cascade analysis technique is used to locate the rigorous targets for both low- and zero-carbon energy sources for carbon-constrained energy planning. In the later section, the targeting technique is extended to locate the minimum volume of external ethanol supply for a land-constrained energy planning problem.
Section snippets
Carbon-constrained energy planning
The problem definition of carbon-constrained energy planning is stated as follows:
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Given a set of energy demands (regions), designated as DEMANDS={j|j=1, 2, …, NDEMANDS}. Each demand requires energy consumption of Dj and at the same time, is restricted to a maximum emission limit of ED, j. Dividing the emission limit by the energy consumption yields the emission factor for each demand, CD, j.
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Given a set of energy sources, designated as SOURCES={i|i=1, 2, …, NSOURCES}, to be allocated to energy
Cascade analysis for targeting zero-carbon source
Cascade analysis tool that was developed to determine the minimum flowrate targets for a resource conservation network [13], [14] is extended in this work to set the minimum clean source targets. To demonstrate the approach, Example 1 taken from Tan and Foo [30] will be utilized, with the data tabulated in Table 1. The left side of the table shows the emission factors and availability of different energy sources. It is assumed that the quantities given represent the available resource for the
Cascade analysis for targeting low- and zero-carbon sources
To extend the targeting tool in handling low-carbon sources, the targeting approach for impure fresh water feed in water networks by Foo [15] is adapted. The main assumption of this approach is that the low-carbon energy source may have a much lower cost as compared to the zero-carbon energy source. Hence, the overall strategy is first to utilize the low-carbon source before considering the zero-carbon source. A three-stage approach presented by Foo [15] is readily applied for this case, i.e.
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Cascade analysis for land-constrained energy planning
A new concept was presented recently on integrating waste and renewable energy in energy sector based on the carbon footprint constraint, which is defined as the total emission of CO2 and other greenhouse gases over the full life cycle of a process or product [31]. A similar concept is introduced here, i.e. the bioenergy footprint, which is based on the geographical area requirement as a measure of resource usage in an energy or industrial system. More specifically, bioenergy footprint is a
Conclusion
Algebraic pinch analysis approaches for energy planning have been presented in this work. The first problem involves finding targets for the minimum quantity of zero- and low-carbon energy resource needed to meet a set of energy demands with corresponding emission limits. The second problem involves minimizing the amount of external fuel required in view of agricultural land availability for bioenergy production. The algebraic cascade approach finds precise targets while overcoming many visual
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