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Graphical Pinch Analysis for Planning Biochar-Based Carbon Management Networks

  • Raymond R. TanEmail author
  • Santanu Bandyopadhyay
  • Dominic C. Y. Foo
Original Research Paper

Abstract

Biochar is a potentially scalable negative emission technology (NET). The negative net flow of carbon is achieved sequentially via photosynthesis which fixes atmospheric carbon into biomass, followed by thermochemical processing of biomass into biochar which converts the bulk of the fixed carbon into stable or recalcitrant form, and finally by the application of the resulting biochar to soil. In addition, this process can result in additional carbon offsets through favorable modification of soil by reducing fertilizer requirement, as well as other secondary benefits. On the other hand, biochar is typically contaminated with traces of organic (e.g., dioxins) and inorganic impurities (e.g., salts) that are detrimental to soil quality. The presence of such impurities and the capacity of the receiving soil to tolerate their presence put an upper limit on the amount of biochar that can be added without causing adverse environmental effects. Thus, scaling up biochar-based systems requires the planning of a carbon management network (CMN) consisting of biochar sources (i.e., production facilities) and biochar sinks (i.e., receiving tracts of land). In general, such CMNs need to be operated so as to maximize system-wide carbon sequestration without exceeding the tolerance limits of the biochar sinks. This paper proposes a graphical pinch analysis approach to planning such biochar-based CMNs. The applicability of the methodology is illustrated using a hypothetical case study.

Keywords

Biochar Negative emission technology (NET) Process integration (PI) Pinch analysis Carbon management network (CMN) 

Introduction

Climate change is widely regarded as a critical global environmental issue, with atmospheric carbon dioxide (CO2) levels of over 400 ppm and exceeding safe limits as a result of escalating emissions from anthropogenic activities (Rockström et al. 2009). The problem has progressed to the extent that negative emission technologies (NETs) will need to be used to keep atmospheric CO2 concentration to a safe level in the coming decades. Such rapid net removal of atmospheric CO2 into a “carbon bank” within a relatively short time frame can provide an important interim measure while long-term solutions to climate change are being developed (Dyson 1977). Such NETs can offset carbon emissions from human activities by achieving net removal of CO2 from the atmosphere via techniques such as direct air capture (DAC), ocean fertilization, bioenergy combined with CO2 capture and storage (BECCS), and biochar application to soil; these prospective NETs are available at different levels of technological maturity and scalability (McLaren 2012; McGlashan et al. 2012). Biochar application, which is well-recognized as a soil amendment strategy, is now also seen as a scalable carbon management strategy for climate change mitigation (Woolf et al. 2010; Lehmann et al. 2011).

Biochar is the carbon-rich solid product of the pyrolysis of biomass. It is normally generated along with gaseous (syngas) and liquid (bio-oil) co-products, whose proportions are functions of feedstock properties and process conditions. The negative emissions from biochar systems result from three sequential steps of (a) photosynthetic carbon fixation into plant biomass, (b) thermochemical carbonization of plant biomass to form biochar, and, finally, (c) the application of biochar into soil. Much of the carbon content of biochar is recalcitrant (i.e., unreactive), so that applying biochar to soil results in long-term carbon sequestration over a time scale of multiple centuries (Lehmann et al. 2011). Typically, a smaller portion of the carbon in biochar is labile (i.e., reactive). After application to soil, this labile fraction of carbon returns to the natural carbon cycle through decomposition. The website of the International Biochar Initiative contains plenty of information on current developments pertaining to research and demonstration projects on biochar systems (International Biochar Initiative 2017).

Other than direct sequestration of recalcitrant carbon in biochar, additional secondary climatic benefits may result from its application to soil, which can result in improvements in fertility, pH, porosity, water retention, and microbial profile (Lehmann et al. 2011). These benefits may result from reduction of carbon footprint resulting from lower demand for fertilizer and irrigation water, credits from co-production of biofuels (e.g., biogas and bio-oil) in biochar plants, and the reduction of emissions of greenhouse gases (GHGs) such as methane (CH4) and nitrous oxide (N2O) from soil bacteria (Roberts et al. 2010). The maximum sustainable technical potential of biochar was estimated at 130 Gt CO2-C equivalent until the end of the century, taking into account both direct and indirect effects (Woolf et al. 2010). On the other hand, McLaren (2012) estimates the global reduction potential of biochar at 0.9–3.0 Gt CO2/y. However, critics have pointed out that these benefits may be partly offset by albedo effects resulting from increased radiation absorption from soil darkened by adding biochar (Kuppusamy et al. 2016). Biochar-based carbon sequestration has been rated as being of intermediate technological maturity (McGlashan et al. 2012). Because of many site-specific considerations, abatement cost estimates can vary over two orders of magnitude, ranging from US$8 – 300/t CO2 (McLaren 2012). Furthermore, the price of biochar for alternative markets, such as activated carbon production, may hinder its use for carbon sequestration purposes (Vochozka et al. 2016).

By far, the most critical issue in the large-scale application of biochar to soil is the potential to introduce various potentially harmful contaminants, such as salts, dioxins, polycyclic aromatic hydrocarbons (PAHs), and heavy metals (Kuppusamy et al. 2016). The impacts of such contaminants can range from reduction in soil quality, to various adverse environmental or health impacts. Determining the levels of such trace contaminants in biochar can be done via laboratory assays (Amin et al. 2016). On the other hand, determining how much contaminant can be tolerated by soil at any given site is not as straightforward (Tan 2016). Thus, systematic decision support tools need to be used to plan large-scale biochar-based CMNs so as to account for the trade-offs between benefits and risks (Belmonte et al. 2017a). For example, models have been developed to optimize the co-production of biochar and bioenergy (Field et al. 2013; Ubando et al. 2014).

Process integration (PI), which was originally developed for minimizing energy use in process plants, has diversified over the course of four decades of evolution to cover a broad range of applications (Klemeš et al. 2013; Tan et al. 2015). In particular, pinch analysis methodology that allows for system-wide targeting and facilitates subsequent detailed network design is regarded as the core concept in PI (Linnhoff et al. 1982). The application of pinch analysis to carbon-constrained energy planning was first proposed by Tan and Foo (2007). The methodology has also been extended to other systems for managing carbon emissions, such as CO2 capture and storage (CCS) networks (Tan et al. 2012). Key developments in this area are described in a review paper by Foo and Tan (2016). Furthermore, the term “carbon management network” (CMN) was recently proposed to describe various systems intended to reduce emissions of CO2 and other GHGs (Tan et al. 2017a). Future systems where biochar production facilities are linked to sequestration sites can be regarded as a special type of CMN. A recent work proposed a mixed integer linear programming (MILP) model for planning such biochar-based CMNs (Tan 2016). A two-stage optimization approach was subsequently proposed to account for sequestration cost (Belmonte et al. 2017b).

A graphical pinch analysis approach to planning biochar-based CMNs is developed in this work. Similar assumptions are used as in the previous MILP model of Tan (2016). This paper is organized as follows. First, a formal problem statement is given in the next section. The stepwise procedure of the graphical methodology is described next. Then, an illustrative case study is solved to demonstrate the graphical pinch technique. Finally, conclusions are given and some prospects for further work are discussed.

Formal Problem Statement

The problem addressed here can be formally stated as follows. Given the following information:

  • A biochar-based CMN (as shown schematically in Fig. 1) where biochar quality is defined in terms of the concentration of one major impurity

  • A set of M biochar sources, designated as SOURCES = {i | i = 1, 2, …, M}, each being a pyrolysis plant that produces a biochar stream at a maximum carbon equivalent flowrate SRi and with an impurity concentration level of Qi. It is assumed here that the plants are yet to be built, and the flowrates given represent upper limits of capacity, based on considerations such as biomass feedstock availability in the vicinity of the plant. In practice, the carbon equivalent flowrate can be determined from the gross biochar flowrate and the corresponding mass fraction of recalcitrant carbon.

  • A set of N biochar sinks, designated as SINKS = {j | j = 1, 2, …, N}, each being a tract of land (agricultural or non-agricultural) that can accept biochar at a carbon equivalent rate of SKj and at an impurity limit of up to QjMAX. In practice, this limit can be estimated from background levels of the contaminant, as well as from health and environmental considerations related to the use of the land. For example, in the case of agricultural lands meant for growing crops for human consumption, the potential for contamination of produce should be considered when setting the limiting values.

Fig. 1

Superstructure for a biochar-based CMN with two sources and two sinks

The objective is to determine the allocation of biochar in the system from the sources to the corresponding sinks, so as to maximize carbon sequestration, without violating any of the sink impurity limits of the receiving soils.

The formal mathematical optimization formulation of the problem is presented next. Let fij denote the biochar transferred from source i to sink j. Biochar balances for the sources, and the sinks may be expressed as follows:
$$ \sum \limits_{j=1}^N{f}_{ij}\le {SR}_i\kern1.08em \forall i\in \mathrm{SOURCES} $$
(1)
$$ \sum \limits_{i=1}^M{f}_{ij}\le {SK}_j\kern1.08em \forall j\in \mathrm{SINKS} $$
(2)
The sink impurity limits of the receiving soils are expressed as follows.
$$ \sum \limits_{i=1}^M{f}_{ij}{Q}_i\le {SK}_j{Q}_j^{MAX}\kern1.08em \forall j\in \mathrm{SINKS} $$
(3)
The overall objective is to maximize the overall carbon sequestration, expressed in Eq. (4), subject to constraints given by Eqs. (1)–(3).
$$ \operatorname{maximize}\ \mathrm{CS}=\sum \limits_{i=1}^M\sum \limits_{j=1}^N{f}_{ij}\kern0.24em $$
(4)

It should be noted that this is a linear programming problem with M × N variables and (2 M + N) inequality constraints. In this paper, a graphical procedure is proposed, based on the principles of pinch analysis, to solve the above optimization problem.

It may be noted that the above formulation is different from the standard optimization problems solved using pinch analysis (Bandyopadhyay 2015). However, this formulation can be transformed into a standard optimization problem by introducing slack variables. By introducing slack variables fiw, Eq. (1) can be written as an equality equation. Physically, fiw represents excess biochar from source i that cannot be stored.
$$ \sum \limits_{j=1}^N{f}_{ij}+{f}_{iw}={SR}_i\kern1.08em \forall i\in \mathrm{SOURCES} $$
(5)
Similarly, Eq. (2) can be written as an equality equation through introduction of slack variables f0j. Physically, f0j represents unutilized storage capacity for the jth sink. In terms of pinch analysis, f0j may be viewed as external resource requirement for sink j.
$$ \sum \limits_{i=1}^M{f}_{ij}+{f}_{0j}={SK}_j\kern1.08em \forall j\in \mathrm{SINKS} $$
(6)
As the external resource does not add any additional impurity to the system (Q0 = 0), introduction of external resource in Eq. (3) does not change it mathematically.
$$ \sum \limits_{i=1}^M{f}_{ij}{Q}_i+{f}_{oj}{Q}_0\le {SK}_j{Q}_j^{MAX}\kern1.08em \forall j\in \mathrm{SINKS} $$
(7)
Using Eq. (6), the overall carbon sequestration (CS) can be expressed as follows:
$$ \mathrm{CS}=\sum \limits_{i=1}^M\sum \limits_{j=1}^N{f}_{ij}=\sum \limits_{j=1}^N\left(\sum \limits_{i=1}^M{f}_{ij}\right)=\sum \limits_{j=1}^N\left({SK}_j-{f}_{0j}\right)=\sum \limits_{j=1}^N{SK}_j-\sum \limits_{j=1}^N{f}_{0j} $$
(8)
For a given problem, total demand over all the sinks are known. Hence, the objective function, Eq. (4), can be modified as
$$ \operatorname{minimize}\ \mathrm{R}=\sum \limits_{j=1}^N{f}_{0j}\kern0.24em $$
(9)

Therefore, the transformed problem is to minimize the unutilized storage capacity, expressed in Eq. (9), subject to constraints given by Eqs. (5)–(7). It may be noted that this transformed linear programming formulation is equivalent to a standard optimization problem solved using pinch analysis. The graphical procedure to solve this problem is discussed next.

Graphical Pinch Analysis Methodology

A graphical technique known as the biochar pinch diagram is proposed, which is extended from the pinch diagram used for a wide range of resource conservation network (RCN) problems described in key textbooks (El-Halwagi 2011; Foo 2012). The main steps for generating the biochar pinch diagram are given as follows:
  1. Step 1.

    Arrange the biochar sources in order of ascending values of Qi.

     
  2. Step 2.

    Generate the source composite curve by sequentially plotting each source, with the cumulative equivalent carbon flowrate as the x-axis and the cumulative impurity load (i.e., the product of SRi and Qi) as the y-axis (see Fig. 2a). Using these coordinates, the geometry of the source composite curve is such that the slope of each segment is equal to the Qi of the corresponding source.

     
  3. Step 3.

    Arrange sinks in order of ascending values of QjMAX.

     
  4. Step 4.

    Generate the sink composite curve by sequentially plotting each sink. As with the source composite curve in the previous steps, the cumulative equivalent carbon flowrate is the x-axis, and the cumulative impurity load (i.e., the product of SKj and QjMAX) is the y-axis (see Fig. 2b). The slope of each segment is hence equal to the QjMAX of the corresponding sink.

     
  5. Step 5.

    Superimpose the two composite curves to form the biochar pinch diagram, and take note of their relative orientation. The source composite curve may lie completely below the sink composite curve, in which case a feasible and optimal solution is immediately indicated by the pinch diagram. On the other hand, the part (or all) of the source composite curve may be above the sink composite curve, which results in an infeasible biochar pinch diagram (see Fig. 2c).

     
  6. Step 6.

    In the case of infeasible initial orientation, the source composite curve must then be translated (shifted) horizontally to the right, until it lies just below and to the right of the sink composite curve. This final orientation then indicates an optimal biochar pinch diagram. A mathematical discussion of the optimality condition of this method is discussed by Bandyopadhyay (2015). Under this condition, the two composite curves will be tangent to each other at a pinch point, (see Fig. 2d). The horizontal overlap of the two composite curves is the target of the system (Eq. 4) and the maximum carbon sequestration rate of the CMN.

     
  7. Step 7.

    At the optimal geometric position of the biochar pinch diagram, the following key features can be used for decision support. Firstly, the overhang of the sink composite curve on the left hand side of the pinch diagram gives the unutilized biochar storage capacity. This excess is because of the contaminants present in the biochar. Next, the aforementioned system target represents the storable carbon in the biochar system, where both carbon and impurity mass balances are satisfied. In this work, only the effect of direct sequestration of carbon in biochar is considered, while the secondary effects previously discussed are neglected. Finally, if the source composite curve extends to the right hand side of the pinch diagram (beyond the source composite curve), the horizontal distance of the extension gives the amount of excess biochar that cannot be stored. This excess biochar results from the combination of excess carbon flowrate and excess contaminant load.

     
  8. Step 8.

    The existence of the pinch point also signifies that the system can be decomposed into two regions or sub-problems. Below and to the left of the pinch point, the system has excess storage capacity; above and to the right of the pinch point, there is excess biochar. The significance of this information for planning the biochar-based CMN is as follows. First, the so-called golden rule of pinch analysis can be applied. According to this rule, biochar cannot be transferred from a source to a sink that are on opposite sides of the pinch point (with the exception of the source that forms the pinch point). In addition, from the pinch diagram the optimal allocation of biochar within the CMN can be determined. For simple systems, this can often be done by inspection. In the more general case, a rigorous network generation procedure known as the nearest neighbor algorithm (NNA) (Shenoy, 2010) can be used.

     
Fig. 2

Features of a generic pinch diagram

For a detailed description of the methodology, the reader may refer to discussions found in a textbook (Foo 2012) and book chapters (Tan and Foo 2013, 2017b).

Illustrative Case Study

This case study is adapted from the illustrative example of Tan (2016). The biochar CMN has three sources and four sinks. The relevant impurity is PAH, which is formed through minor side reactions during pyrolysis. These persistent organic pollutants may have potential adverse effects on health and the environmental impacts, especially if the sink is agricultural land for producing edible crops (Kuppusamy et al. 2016). This case study first delves into basic targeting and network synthesis, as described in the previous section. Additionally, it also explores the exploration of alternative optimal networks, as well as pinch-based sensitivity analysis resulting from changing the characteristics of the sources and sinks.

Data on the biochar sources are given in Table 1, while data on the sinks are given in Table 2. Note that sources and sinks are already arranged in order of ascending PAH concentration, which makes steps 1 and 3 in the methodology described above unnecessary. Analysis of this case study proceeds as follows. The source composite curve can be generated from Table 1 based on step 2 in the previous section. Likewise, the sink composite curve can be generated from the data in Table 2 via step 4. Next, these two composite curves are superimposed to form the biochar pinch diagram (step 5), however giving an infeasible orientation. The source composite curve should then be translated horizontally by 1.5 kt/y of carbon (step 6), until the optimal orientation is determined as shown in Fig. 3. Note that the pinch point occurs at the coordinates of 3 kt/y of carbon and 1.5 kg/y of PAH; this solution also indicates that the target for the optimal amount of carbon sequestration, as indicated by the overlap of the composite curves, is 4.5 kt/y (= 6.0–1.5 kt/y). The corresponding allocation of the biochar in this CMN can be determined (by inspection or using NNA) as shown in Table 3. The excess carbon storage capacity below the pinch point is 1.5 kt/y, while the excess biochar from the sources is 1.7 kt/y (= 7.7–6.0 kt/y). The latter excess originates from source 3, and accounts for 85% of the total flowrate available from that biochar production plant. Two possible interpretations are possible. First, this excess may be exported from the system if there are sinks in neighboring regions that can tolerate the PAH level in the biochar. Alternatively, the production from source 3 can be reduced from its original flowrate (2.0 kt/y) to 0.3 kt/y (= 2.0–1.7 kt/y) because of the limited storage capacity within the system. This initial solution will be the basis for variants discussed below.
Table 1

Case study biochar source data

Source

Biochar flowrate (kt/y C equivalent)

PAH concentration (ppm)

1

3.00

1

2

1.20

2

3

2.00

12

Table 2

Case study biochar sink data

Sink

Biochar flowrate limit (kt/y C equivalent)

PAH concentration limit (ppm)

1

3.00

0.5

2

1.00

5

3

1.00

10

4

1.00

15

Fig. 3

Feasible biochar pinch diagram showing optimal solution

Table 3

Optimal source/sink matrix with flowrates in kt/y of carbon

 

Sink 1

Sink 2

Sink 3

Sink 4

Excess biochar

Source 1

1.50

1.00

0.50

  

Source 2

  

0.50

0.70

 

Source 3

   

0.30

1.70

Excess storage capacity

1.50

    

Alternative Optimal Networks

There will typically be excess degrees of freedom above the pinch point, which allows for alternative optimal solutions to be explored. This feature can allow minor advantages not formally reflected in the model to be gained. For example, since both sources 2 and 3 are above the pinch point, they can be interchanged to generate an alternative solution without changing the system target (see the feasible biochar pinch diagram in Fig. 4). In other words, the excess carbon storage capacity and the excess biochar capacity remain identical as in the earlier case.
Fig. 4

Modified composite curves showing alternative optimal solution

The allocation within this alternative CMN is shown in Table 4. In this case, none of the biochar from source 2 is used within the system. Thus, this biochar plant can be eliminated entirely from the system (i.e., the plant can be shut down or not built in the first place) without altering the solution. In this case, the engineering advantage gained from the alternative solution is the relative simplicity of the network, which in practice can lead to smoother, more economical operations.
Table 4

Alternative optimal source/sink matrix with flowrates in kt/y of carbon

 

Sink 1

Sink 2

Sink 3

Sink 4

Excess biochar

Source 1

1.50

1.00

0.50

  

Source 2

    

1.20

Source 3

  

0.50

1.00

0.50

Excess storage capacity

1.50

    

Changes in Source and Sink Characteristics

Next, the solution in Fig. 4 can be revisited to explore the effect of changing the quality of the biochar generated by source 3. Such changes can result during the operating life of a biochar plant due to changes in biomass feedstock quality, changes in processing conditions, aging of process equipment, and other such pragmatic factors. Above the pinch point, there is excess capacity to absorb contaminant, as the sinks in this region are not saturated with PAH. Thus, if process modifications in source 3 result in a 25% increase in PAH concentration from 12 to 15 ppm, it can be seen in Fig. 5 that the source composite curve changes, but that there still remains a safe margin of PAH load into the system sinks. Thus, the network given in Table 4 remains a valid solution even with the higher contaminant load.
Fig. 5

Modified biochar pinch diagram showing optimal solution with low-grade biochar (source 3)

Finally, we consider the case of a conservative decision-maker who seeks to have a large margin of safety with respect to the PAH limit of the sinks. Such margins can be accounted for using a risk aversion parameter (ψ), whose value represents the fraction of the contamination limit that is deemed to be acceptable (Tan 2016). In this case, if ψ = 0.5, the sink composite curve of the biochar pinch diagram in Fig. 3 takes a revised version in Fig. 6, where an infeasible result can be seen (i.e., the level of PAH entering sinks 1 and 2 exceed the acceptable limits). A feasible and optimal solution can then be determined by further shifting the source composite curve to the right by 0.75 kt/y of carbon, as shown in the feasible biochar pinch diagram Fig. 7. This results in a reduced sequestration target of 3.75 kt/y (= 4.5 − 0.75 kt/y) of carbon. On the other hand, the excess storage capacity increases to 2.25 kt/y of carbon, while the excess biochar also increases to 2.45 kt/y (= 8.45–6.0 kt/y). Note that none of the biochar from source 3 can be stored within the system, so the option exists to either export the stream, or to eliminate the source altogether. The latter interpretation also leads to the advantage of network simplification, as previously discussed. Table 5 shows the resulting optimal CMN.
Fig. 6

Modified biochar pinch diagram showing infeasible solution for risk-averse decision-makers

Fig. 7

Revised biochar pinch diagram showing optimal solution for risk-averse decision-makers

Table 5

Revised optimal source/sink matrix with flowrates in kt/y of carbon

 

Sink 1

Sink 2

Sink 3

Sink 4

Excess biochar

Source 1

0.75

1.00

1.00

0.25

0

Source 2

   

0.75

0.45

Source 3

    

2.00

Excess storage capacity

2.25

    

Conclusion

In this work, a graphical pinch analysis approach has been developed for planning the large-scale deployment of biochar-based CMNs. Such systems can be an effective means for achieving negative carbon emissions by using soil as a “carbon bank”; along with other NETs, biochar may thus prove to be an important strategy for stabilizing atmospheric CO2 concentration to a safe level. The methodology allows system-wide carbon management benefits to be maximized by matching biochar sources with compatible biochar sinks, while ensuring that the adverse effects of the impurities in biochar are kept under control. This graphical technique can be used as a tool for preliminary, high-level planning of large-scale biochar projects; it can facilitate or complement the use of more detailed approaches based on mathematical programming or other PSE tools (e.g., P-graph). By focusing just on key, high-level features of the system, the graphical pinch-based methodology can provide insights that are easily interpreted and communicated for effective decision support (Geoffrion 1976). Future work can focus on developing an enhanced methodology that is able to account for indirect reductions in carbon emissions (e.g., from fertilizer and fuel offsets), as well as extensions for multi-objective and multi-region problems. Data uncertainties with respect to the capacity of soils to tolerate contaminants are also a critical issue that should be addressed.

Notes

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Raymond R. Tan
    • 1
    Email author
  • Santanu Bandyopadhyay
    • 2
  • Dominic C. Y. Foo
    • 3
  1. 1.Chemical Engineering DepartmentDe La Salle UniversityManilaPhilippines
  2. 2.Department of Energy Science and EngineeringIndian Institute of Technology BombayMumbaiIndia
  3. 3.Department of Chemical and Environmental Engineering/Centre of Excellence for Green TechnologiesThe University of NottinghamSemenyihMalaysia

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