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CHEMICAL ENGINEERING TRANSACTIONS

VOL. 45, 2015

A publication of

The Italian Association

of Chemical Engineering

www.aidic.it/cet
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu

ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545128

Please cite this article as: Zavíralová L., Šomplák R., Pavlas M., Kropáč J., Popela P., Putna O., Gregor J., 2015,

Computational system for simulation and forecasting in waste management incomplete data problems, Chemical

Engineering Transactions, 45, 763-768 DOI:10.3303/CET1545128

763

Computational System for Simulation and Forecasting in

Waste Management Incomplete Data Problems

Lenka Zavíralová*
,a

, Radovan Šomplák
a
, Martin Pavlas

a
, Jiří Kropáč

a
,

Pavel Popela
b
, Ondřej Putna

a
, Jiří Gregor

a
Institute of Process and Environmental Engineering, Faculty of Mechanical Engineering, Brno University of Technology

Technická 2896/2, Brno, 616 69, Czech Republic
b
Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology,

Technická 2896/2, 616 69

Brno, Czech Republic

zaviralova@upei.fme.vutbr.cz

Nowadays, shift towards an effective waste management is a big issue as well as a necessity for many

countries. Infrastructural projects in waste management (e.g. new waste-to-energy plants, WTE) have

long-term implementation phase (up to 10 y). WTE, processing residual waste, represent keystone

of sustainable concepts. In this context, information on waste availability and incinerated waste properties,

especially calorific value, are vital for successful design and operation of these plants. However, hardly

predictable future changes in these parameters make the design process challenging.

In this contribution, we present a tool for verification and forecasting of current and future production of

residual municipal waste and its lower heating value (LHV) to support WTE design process. Newly

developed tool JUSTINE is introduced. From the principal point of view it is a wait-and-see optimization

model recursively applied to region divided into several sub regions and also their parts.

It processes variety of spatially distributed statistical data bound together through equations and

constraints. This data is supposed to be incomplete (some local information might be unavailable) and

uncertain. The wait-and-see optimization model is used to obtain point estimates of desired parameters

that can be used for waste production and LHV forecasts. In addition, for randomly simulated input data

reflecting real-world uncertainties empirical confidence intervals of input and output values can be

computed. The practical contribution of this tool is presented through a case study.

1. Introduction

All methods of the waste treatment, in line with the waste management hierarchy (Directive 2008/98/EC,

2008), such as WTE, are embodied in the effective waste management. WTE process residual waste with

energy production and thus significantly contributes to minimize the landfilling, which is in the last place of

this hierarchy due to no waste utilization, and therefore, it is the least appropriate option. Based on

examples of European countries with high maturity level of the waste management, such as Germany or

Austria, it can be shown that there is still about 50 % of waste that must be diverted from landfill by using

another way of treatment, even when using the potential of the first three levels of the waste management

hierarchy and high usage level of recycling and composting. This amount of waste is designated as

residual solid waste (RSW) and WTE is a suitable technology for its processing (Eurostat, 2014). In many

countries, both in Europe (Šomplák et al., 2013) and outside of Europe (Santibañez-Aguilar et al., 2014),

the effective waste management becomes very current topic. Therefore there is an increasing motivation

for construction of new WTE units. However, there is a necessity to know the amount of available RSW

and its LHV, both in the present and with respect to future trend, in order to be able to plan operations and

economy of WTE (Touš et al., 2013).

This article builds on a study Putna et al. (2014), where the concept for a new computational system

designed to predict waste production and LHV based on a realistic assumption of differences in availability

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of spatially heterogeneous and hierarchical input data, was introduced. In this paper, the model and

implementation of the above mentioned concept and the case study will be presented (see Section 4).

2. Principal modeling ideas

Generally, available data on the production of RSW and its LHV are variable both in time and within

territorial location, which makes the process of planning of new WTE processing capacities more

complicated. Furthermore, countries with less developed waste management generally suffer from poor

data base regarding the RSW production. The LHV is known only sporadically because the systematic

surveys on the waste composition are very rare. Usually, there are available only non-complex data

sources, such as public databases, operating data or local waste studies. An important feature of data

sources is and inaccuracy of provided values. The aim is then to design a comprehensive, predictive tool

to estimate waste production LHV at several levels of territorial arrangement.

Theoretical concept of the tool is based on the assumption that searched RSW weight and LHV, required

as inputs for further calculations (see motivation above), are not available in ideal quality. There are only

measurement results or expert estimates, where they are expected to be burdened by the random error.

Therefore, the aim will be to obtain relevant forecasts, as complete as possible, which are close to ideal

values of the unknown parameters. Estimated representative amounts of the randomly fluctuating RSW

(denoted m) and LHV are marked with an asterisk (m*, LHV*) and inaccuracy of this estimate to real value

is denoted by ε. Superscripts then specify to which variable the error refers and subscripts denote

territorial units.

The estimated values are then obtained by minimizing a suitable criterion – the objective function. The

objective function is then formed by the sum of the absolute values of inaccuracies ε, and therefore, the

emphasis is placed on the robustness of the estimation of unknown parameters (i.e. the weights of large

deviations, which are frequently present in heterogeneous data, are not accentuated). Like in regression

models, the theoretical (wait-and-see) model is considering the minimization of random errors, but for

computational purposes their observed values are used. The above mentioned objective function related

ideas are further utilized to obtain constraints taking into account both input data and hierarchical structure

of territorial units. They also guarantee that the data for higher territorial unit is not contradictory with the

aggregated data of sub-units involved in the higher unit. Specifically, the set of constraints is formed by

energy balances for each type of territorial units and equipment. Total energy in a given area is determined

as a product of the weight of the waste produced in this area and the corresponding LHV value. Due to

these energy balances, the computational system becomes nonlinear and it is necessary to use the

nonlinear programming techniques for minimization of the objective function subject to discussed

constraints. Due to incomplete data, alternative optimal solutions can be expected. In addition, considering

nonlinearities included in the equations, the problem is non-convex, and thus, the possible existence of the

local extremes must be taken into account for the choice of a suitable solution algorithm. The model also

envisages the possibility of the use of operational data and data inputs include both amounts of RSW

generated or processed, as well as, information on LHV.

3. Mathematical model

The resultant calculation of m and LHV for the particular territorial area or facility is given by Eq(1)-(2). The

equations together with related weighting of input data sets using parameters ν are described in detail in

Section 4. Due to the approach of minimizing the sum of the absolute values of the inaccuracies, the

individual errors were divided into positive and negative component, denoted by signs (+) or (-) in the

indices, see Eq(3)-(4). Both of those components are defined as non-negative, and so, the negative

deviation can be described by their difference. Then, the sums of these components represent the

absolute values of inaccuracies and are denoted by ̂ - see Eq(5)-(6). Eq(7) describe hierarchical relations

for energy balances. For this purpose we denote territorial units by indices . If unit with index j

immediately belongs to higher unit indexed by i, we say that i is an ancestor of j and write . We

also identify for any index i a set of all successors j satisfying the same equality as above and denote it

as . Then, set collects indices i, which is empty. Eq(8) represents the objective function

involving standardized weight parameters for different groups of territorial units. Notation used in

mathematical model (Eq(1)-(8)) is summarized in Table 1.

Input data related constraints

∑

(

)
, (1)

∑

(

)
, (2)

765

where
,

are variables and weight coefficients satisfy the conditions

〈 〉 ∑

∑

, (3)

, , (4)

, (5)

, , (6)

where ̂
̂

and

are variables.

Constraints reflecting the hierarchy of territorial units

∑ {∑

(

)
∑

(

)

} ∑

(

)
∑

(

)

; .
(7)

The objective function

∑ (∑ ̂

∑ ̂

) , (8)

where weight coefficients are standardized as follows 〈 〉 ∑ .

Table 1: Mathematical model related notation

Symbol Description Unit

i
p P
q Q
mi
mi,p*
LHVi
LHVi,q*

indices of territorial units

index determining data set for amount of waste generated

index determining data set for lower heating value

real amount of waste generated (result of calculation) for
estimated amount of waste generated (available data) for
real lower heating value (result of calculation) for
estimated lower heating value (available data) for
inaccuracy of amount of waste generated for
positive part of inaccuracy of amount of waste generated for
negative part of inaccuracy of amount of waste generated for
absolute value of inaccuracy of amount of waste generated for
inaccuracy of lower heating value for

positive part of inaccuracy of lower heating value for

negative part of inaccuracy of lower heating value for

absolute value of inaccuracy of lower heating value for

simulated error of the repeated measurements for RSW production
simulated error of the repeated measurements for LHV,

standardized weight for the data set p for estimated RSW production for

standardized weight for the data set q for estimated LHV for

standardized weight of territorial unit
set of indices of territorial units immediately belonging to unit

index i identifies territorial unit j that includes unit j i.e.

set of indices i such that is a nonempty set

[-]

[t/y]

[t/ y]

[GJ/t]

[%]

[-]

4. Case study

Application of the model is focused on the calculations within the Czech Republic, and therefore assumes

the inputs of four levels with respect to the territorial units Czech Republic, that is the state - CR (NUTS 0,

Nomenclature of Units for Territorial Statistics), regions (NUTS 3), districts (LAU 1, Local Administrative

Units) and municipalities with extended powers (MWEP, without NUTS/LAU classification). In total there

are 206 territorial units on the MWEP level.

The data base available for the Czech Republic was used in the test calculation and results are presented

in this paper. In this case study, there were considered two models for LHV and one data source for the

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production m (see Figure 1). Publicly accessible database ISOH (Waste Management Information System)

contains data on production, waste management and information concerning facilities for waste treatment,

recovery and disposal in the Czech Republic since 2002. For the purposes of this case study, the historical

data only from 2008 to 2012 were used as models for m, because just for this period the consistency of

data processing was kept. Unlike data on production, no database collecting the data on LHV is available

for given territory. In professional practice there is often an assumption that LHV is of value about 10 GJ/t,

i.e. simply and rounded LHV = 10 GJ/t, which reflects current LHV values reported by Reimann (2012) for

Europe. It should be emphasized that this value is not good estimate for each the territorial area and also

that it does not reflect the trends in the waste management, such as the waste separation increase

affecting the LHV. Another LHV model (on the MWEP level) used in the study case is a model taking into

account correlation between type of heating and waste composition reported in three particular MWEPs.

Complex composition analyses were performed in these MWEPs in 2009 and 2010. Generally, the LHV

determination is an important problem. Good example might be a study, Lin et al. (2013), which presented

a description of solutions for calorific value of RSW calculation from several aspects, along with a

comparison of different methods of determining the caloric content with respect to the composition and

humidity of the waste.

Figure 1: Data base available for the Czech Republic

As explained above, there is no sufficient data base on LHV currently available in the Czech Republic and

additionally the input data is only an estimate of the real value. Also the real values are seasonable

dependent. Therefore, the stochastic approach employing the Monte Carlo methodology was used in the

model for testing and for pilot calculations. The artificial "blurring" of the input data (denoted by δ) was

implemented, wherein the optimization model can be solved repeatedly for different sets of input data set.

This blurring is realized by randomly generated value from a pre-selected probability distribution where the

probability distribution parameters are determined based on the expert analysis of the credibility of the

original data. Implemented options for the probability distributions are for now as follows: a) Fixed value: δ

= 0; b) normal distribution: δ ~ N(μ,ζ
2
); c) uniform distribution: δ ~ U(a,b).

Practically, different scenarios are created when for the certain model value (e.g. LHV*=10) one scenario

is generated with the value of LHV** = 10 + δ, where δ is a random number generated from the selected

distribution, e.g. from normal with μ = 0 and ζ = 0.08LHV*. If the entry value is very reliable, the possibility

of fixed data, i.e. no blurring, is selected. If the input data is quite reliable, the blurring value is generated

from the normal distribution. If the entry value is more of general type of information (e.g. frequently used

LHV = 10 GJ/t), it is preferable to use a value generated from a uniform distribution.

In the future, it can be assumed that the m and LHV data base will increase, most likely in the form of local

studies, or from waste treatment facilities. Therefore, it will be necessary to suitably combine these data

sets into a single optimization calculation. Then, it is convenient to consider the different weights for each

input data (see Eq(1)-(2)), due to a variety of meaningful values for different data sources. Alongside it is

possible to detect errors of the individual models employing the detailed analysis and to further develop

proposed model.

By using ca. hundreds of Monte Carlo simulations, the variability of m and LHV in the respective areas can

be observed, and thus, the sensitivity of inaccuracies on the resulting estimates can be detected. The

average value, or the interval, for both of the parameters in the area can be determined. Figure 2 shows

the results for the case of MWEP#2. Graph on the left side of the figure presents the variability of the

results together with the estimate of the mean value and 95 % interval for point results for 500 simulations.

The graph on the right side of the figure then provides another perspective of the results using the

histogram of generated data. The input models values for this particular case of MWEP#2 were LHV1=10

767

GJ/t and LHV2=9,176 GJ/t. From the graph it can be concluded that in the range of the LHV value in

MWEP#2 is 9,339±1.0875 GJ/t. Analogous information for the m in MWEP#2 is presented on Figure 3.

Presentation of the results using a histogram, instead of a single value, is an important benefit of this tool,

since in the reality it is not possible to achieve the constant value of m and homogeneous LHV, as already

mentioned by Putna et al. (2014). Production and LHV also change during the year, and therefore, it is

necessary to calculate the predictions with the variability of both parameters. Therefore, another possible

extension of this tool is calculation performed on a monthly basis.

Figure 2: Simulations output – LHV estimation for MWEP#2

Figure 3: Simulations output – RSW mass production estimation for MWEP#2

Figure 4: Comparison of credibility of the models for input data for RSW production and LHV in MWEP#2

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Finally, the implementation offers also the possibility to compare the credibility of the models that provide

the input data for m and LHV in terms of the sum of inaccuracies (see Eq(5)-(6)). The top graph in Figure 4

presents the evolution of the sum of inaccuracies ( ̂) in dependence on the weights reflecting the credibility

of individual models (v), for combinations including production models and LHV models within MWEP#2.

The bottom graph in Figure 4 presents the models (v) weights ratio (the weights are standardized - see

assumptions for Eq(1)-(2)). For the sake of clarity the weights for RSW production models and LHV

models were put into the same graph separated by the line.

Apart from the total error we can also observe the proportion of individual models to a total error (Figure 4

– top). By detailed analysis, it is possible to detect errors among different models from the perspective of a

specific locality. These outputs can serve to improve the estimation of weights for each model.

5. Conclusions

This article, building on a study Putna et al. (2014), introduced current computational model and its results

of the practical implementation of tool for predicting RSW production and LHV in the Czech Republic.

Despite of a limited number of input data, the results provide information about the likely state of the RSW

production and LHV in relevant territorial units. This information represents the valuable inputs for the

design process of new waste management facilities. The knowledge of the RSW quantity and LHV are

required already in the design and concept phase of WTE design, which is the leading technology in

effective waste management. The concept described in the study Putna et al. (2014) was further extended

with practical solutions to the implementation and with respect to the quantity of currently available data.

Further development of the tool is connected to the growing data base that will contribute to more accurate

results. Other possible extensions of the tool are the calculations on a monthly basis. Input models can be

extended to the socio-economic factors and their influence on the parameters of RSW in relevant area.

Acknowledgement

The authors gratefully acknowledge financial support provided by Technology Agency of the Czech

Republic within the research project No. TE02000236 “Waste-to-Energy (WtE) Competence Centre”. At

the same time, financial support provided by the Ministry of Education, Youth and Sports within the under

National Sustainability Programme I (Project LO1202).

References

Directive 2008/98/EC of the European Parliament and of the Council on waste and repealing certain

Directives (Directive 2008/98/EC), 2008, Official Journal of the European Communities 22.11.2008, L

312, 3-30.

Eurostat, 2014, Statistical Office of the European Communities, Municipal waste statistics

<ec.europa.eu/eurostat/statistics-explained/index.php/Municipal_waste_statistics> accessed

13.12.2014.

Lin C.-J., Chyan J.-M., Chen I.-M., Wang Y.-T., 2013, Swift model for a lower heating value prediction

based on wet-based physical components of municipal solid waste, Waste Management, 33(2), 268-

276.

Ministry of the Environment of the Czech Republic, 2002-2014, Public information system of waste

management, Ministerstva životního prostředí (VISOH, ISOH) <isoh.cenia.cz/groupisoh/> accessed

14.08.2014 (in Czech)

Putna O., Kropáč J., Frýba L., Pavlas M., 2014, Prediction of heating value of waste and its importance for

conceptual development of new waste-to-energy plants, Chemical Engineering Transactions, 39, 1273-

1278.

Reimann D.O., 2012, CEWEP Energy Report III (Status 2007-2010) Results of Specific Data for Energy,

R1 Plant Efficiency Factor and NCV of 314 European Waste-to-Energy (WtE) Plants, Bamberg,

Germany, <cewep.eu/m_1069> accessed 28.2.2015.

Santibañez-Aguilar J.E., Ponce-Ortega J.M., González-Campos J.B., Serna-Gonzaléz M., El-Halwagi

M.M., 2014, Optimal planning of supply chains for multi-product generation from municipal solid waste,

Chemical Engineering Transactions, 42, 55-60.

Šomplák R., Procházka V., Pavlas M., Popela P., 2013, The logistic model for decision making in waste

management, Chemical Engineering Transactions, 35, 817-822.

Touš M., Frýba L., Pavlas M., 2013, Improving Calculation of Lower Heating Value of Waste by Data

Reconciliation – Analysis and Evaluation, Chemical Engineering Transactions, 35, 877-882.

http://isoh.cenia.cz/groupisoh/