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Volume 5, Issue 1 2010 Article 6
Chemical Product and Process
Modeling
Simulation and Control of a Commercial
Double Effect Evaporator: Tomato Juice
Praveen Yadav, Indian Institute of Technology, Kharagpur
Amiya K. Jana, Indian Institute of Technology, Kharagpur
Recommended Citation:
Yadav, Praveen and Jana, Amiya K. (2010) "Simulation and Control of a Commercial Double
Effect Evaporator: Tomato Juice," Chemical Product and Process Modeling : Vol. 5: Iss. 1,
Article 6.
DOI: 10.2202/1934-2659.1443
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Simulation and Control of a Commercial
Double Effect Evaporator: Tomato Juice
Praveen Yadav and Amiya K. Jana
Abstract
This work aims to present a detailed study on a commercial double-effect tomato paste
evaporation system. The modeling equations formulated for process simulation belong to
backward feeding arrangement. Open-loop process dynamics has been studied by rigorous
simulation of the model structure. In the next, three multi-loop control schemes, namelyconventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have
been synthesized for the sample process. Finally, several simulation experiments have been
conducted to investigate the comparative closed-loop performance based on set point tracking and
disturbance rejection.
KEYWORDS: evaporator, double-effect, tomato paste, modeling, dynamics, control
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1 INTRODUCTION
An evaporator is commonly used to concentrate a solution by removing a part of
the solvent in the form of vapor. It has various areas of application. In most of theindustrial and commercial applications, the multiple effect evaporator is used due
to its advantages over the single effect system. The first and most importantadvantage is the economy. Multiple effect scheme evaporates more water per kg
of steam fed to the unit by reusing the vapor from one effect as the heating
medium for the next. Secondly, the heat transfer gets improved due to the viscous
effects of the products as they become more concentrated. The invention of themultiple effect evaporators is the result of the demand of sugar industry. A
revolution in the sector of sugar industry was brought by Norbert Rillieux by the
development of multiple pan evaporation system for use in sugar refinery.Literature reviews revealed that in the beginning, the study on the multi-
effect evaporators was based on steady state analysis. Subsequently, the researchattention was paid to develop the dynamic model of the evaporation system. In the1960s, the mathematical model for a single effect evaporator was proposed by
Andersen et al. (1961) and the simulation was carried out after reduction and
linearization of that model to study the closed-loop control performance using an
analog computer. An empirical input-output model of a single concentrationevaporator with PID control application was described by Kropholler and Spikins
(1965). Andre and Ritter (1968) formulated the nonlinear model of a double-
effect evaporator.During 1970s, it was realized through the development of several process
models that the important behaviors of the evaporator system can easily be
described by its dynamic nature. Linear and nonlinear models of a genericevaporator were discussed in detail by Newell and Fisher (1972). The simulation
study became easier with the development of a computer code which is capable ofsimulating the steady state condition of a multiple effect evaporator. This
computing technique was brought by Bolmstedt and Jernquist (1976) which was
further supported by their publication in 1977 showing a dynamic simulatorthrough blocks which is capable of simulating more complex plants.
A mathematical model with a wide variety of its extension for plants of
different configurations, including the death-time arising due to circulation in
each effect and through the pipe within effects, was developed by Tonelli (1987).In the past, the mathematical models were constructed for open-loop simulations
and for application of conventional control laws. But in the last decade, the statespace models suitable for designing the multivariable controllers and stateestimations (Newell and Lee, 1989) were reported. Cadet et al. (1999) formulated
a detailed evaporator model based on energy and mass balance with considering
semi-empirical equilibrium functions. This model was implemented in a sugar
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plant and showed satisfactory results. Recently, a phenomenological, stationary
and dynamic model of a multi-effect evaporator was presented by Miranda and
Simpson (2005) for simulation and control purposes.
In the recent years, energy conservation is a big issue for the research andindustrial organizations. Thus the latest research efforts by the scientists and
engineers working in industrial organizations are towards more efficient use ofenergy. Balkan et al. (2005) did the performance evaluation of a triple-effect
evaporator with forward feeding using exergy analysis. Kaya and Sarac (2007)
developed a model for a multiple effect evaporator and performed energy
analysis. There are several types of feeding patterns for the evaporator systemssuch as forward feeding, backward feeding, mixed feeding and parallel feeding.
Each operation was investigated by the authors with and without pre-heating
arrangements. The effect of pre-heating on evaporation process was investigatedfrom the point of energy economy. Mohanty and Khanam (2007) developed a
simplified model based on the principles of process integration for the analysis ofmultiple effect evaporator systems taking into account the variation in physico-thermal properties as well as boiling point rise. It included new concepts of stream
analysis, temperature path and internal heat exchange for the formulation of the
model equations.
Modeling and online control is very relevant for food concentrates, mainly because of its influence on product quality and also on energy consumption
(Cadet et al., 1999). Although, a significant progress has been made on modeling,
there are limited papers dealt with the control of multi-effect evaporation systems(e.g., Runyon et al., 1991; Kam and Tadé, 2000). It is with this intention that the
present work has been undertaken.
In this paper, a systematic study is conducted on a commercial double-effect tomato paste evaporator. The dynamic process model, consisting of mass
balance, energy balance and empirical correlations, is presented by thedifferential-algebraic equations. The simulation of the model structure is
performed for open-loop process dynamics. For closed-loop study, three multi-
loop control strategies, namely conventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have been synthesized. Finally, a
comparative control performance is addressed on the sample process. The
contribution of this paper is the comparison of the three control schemes.
2 THE PROCESS
The example process as shown in Figure 1 is a double-effect evaporator with backward feeding arrangement used for tomato concentrate. The two effects are
numbered from left to right as Tank1 and Tank2, respectively. The raw juice
having flow rate F , concentration X f and temperature T f enters Tank2, and the
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steam with flow rate S and temperature T S enters Tank1. The mass holdup in the
two tanks are defined as M 1 and M 2 . V 1 and V 2 are the vapor flow rates from
the overhead of two tanks with temperature T 1 and T 2 , respectively. P 1 and P 2 are the product flow rates from the two effects with product concentration X p
and X 2 , and temperature T 1 and T 2 , respectively. The steady state and parameter
values are listed in Table 1 (Runyon et al., 1991).
Figure 1 Schematic of a double-effect evaporator.
Process model
The dynamic model for the sample process is derived for tomato concentrate based on the study of Runyon et al. (1991), and Miranda and Simpson (2005).
This model is also validated (Runyon et al., 1991) for a different set of design and
parametric variables. An evaporation process involves mass and heat transfer. Thetomato juice is assumed as a binary solution of water and soluble solids, both
considered inert in a chemical sense. The macroscopical evaporator model
consisted of a set of differential-algebraic equations (DAEs) has been constructed
based on conservative laws and empirical relationships. It should be noted that
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only the juice phase is considered for modeling. The assumptions involved in the
formulation of model are listed below.
● Negligible heat losses to the surroundings● Homogeneous composition and temperature inside each evaporator
● Variable liquid holdup and negligible vapor holdup
● Overhead vapors considered as pure steam
● Latent heat of vaporization or condensation varied with temperature
● No boiling point elevation of the solution
Table 1 Steady state and parameter values.
Term Abbreviation (unit) Value
Tank1 mass holdup M 10 (kg) 2268
Tank2 mass holdup M 20 (kg) 2268
Input feed flow rate F 0 (kg/hr) 26103
Input steam flow rate S 0 (kg/hr) 11023
Tank1 liquid product flow rate P 10 (kg/hr) 5006
Tank2 liquid product flow rate P 20 (kg/hr) 14887
Vapor flow rate from Tank1 V 10 (kg/hr) 9932
Vapor flow rate from Tank2 V 20 (kg/hr) 11165
Feed composition X f0 (kg/kg) 0.05
Tank1 composition X p0 (kg/kg) 0.2607 Tank2 composition X 20 (kg/kg) 0.0874
Steam temperature T s0 (0C) 115.7
Feed temperature T f0 (0C) 85.0
Temperature in Tank1 T 10 (0C) 74.7
Temperature in Tank2 T 20 (0C) 52.0
Heat transfer area of Tank1 A1 (m2) 102
Heat transfer area of Tank2 A2 (m2) 412
Overall heat transfer coefficient for Tank1 U 1 (kJ/hr.m
2.0C) 5826
Overall heat transfer coefficient for Tank2 U 2 (kJ/hr.m2.0C) 2453
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Total mass balance
First effect: V P P dt
dM 112
1
−−= (1)
Second effect: V P F dt
dM 22
2 −−= (2)
Component (solids) mass balance
First effect: X P X P dt
X M d p
p
122
1 )(−= (3)
⇒ X P X P dt
dM X
dt
dX M p p
p
1221
1 −=+ (4)
⇒ dt
dM X X P X P
dt
dX M p p
p 11221 −−= (5)
Substituting equation (1),
)( 1121221 V P P X X P X P dt
dX M p p
p−−−−= (6)
⇒ V X P X P X X P X P dt
dX M p p p p
p
1121221 ++−−= (7)
⇒ M
V X X X P
dt
dX p p p
1
122 )( +−= (8)
Second effect: X P X F dt
X M d f 22
22 )( −= (9)
Simplifying and rearranging, finally we get
M
V X X X F
dt
dX f
2
2222 )( +−= (10)
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Energy balance
The steam flow rate to the first effect is obtained through energy balance on the
first effect heat exchanger as:
)()( 111 T T AU T S S S −=λ (11)
where, λ is the latent heat. That means,
)(
)( 111
T
T T AU S
S
S
λ
−= (12)
Similarly, the vapor flow rate to the second effect is derived from the energy
balance on the second effect heat exchanger as:
)()( 212211 T T AU T V −=λ (13)
⇒ )(
)(
1
21221
T
T T AU V
λ
−= (14)
In the following, the energy balance equations are derived.
First effect: )(),()(),()],([
1111222
11
T H V X T h P T S X T h P dt
X T h M d pS
p−−+= λ (15)
⇒ (16) )(),(
)(),(),(),(
1111
2221
1
1
1
T H V X T h P
T S X T h P dt
dM X T h
dt
X T dh M
p
S P
p
−
−+=+ λ
⇒(17) ),()(
),()(),(),(
1111
11222
1
1
dt
dM X T hT H V
X T h P T S X T h P
dt
X T dh M
p
pS
p
−
−−+= λ
Substituting equation (1),
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)],()([)()],(),([
),(1111222
1
1 X T hT H V T S X T h X T h P dt
X T dh
M pS p p
−−+−= λ (18)
Using equation (11),
)],()([)()],(),([),(
1111111222
1
1 X T hT H V T T AU X T h X T h P dt
X T dh M pS p
p −−−+−=
------------(19)
This gives,
M
X T hT H V T T AU X T h X T h P dt
X T dh pS p p
1
11111112221 )],()([)()],(),([),( −−−+−=
-----------(20)
Second effect:
)(),()(),()],([
22222112 22
T H V X T h P T V X T Fhdt
X T h M d f f −−+= λ (21)
Simplifying and rearranging, finally we have
M
X T hT H V T T AU X T h X T h F
dt
X T dh f f
2
22222122222 2)],()([)()],(),([),( −−−+−
=
-----------(22)
Empirical correlations
The enthalpy of the product (tomato juice) is represented as (Heldman and Singh,
1981):
T X X T h )506.2177.4(),( −= (23)
The pure solvent vapor (steam) enthalpy is obtained using a polynomialregression equation of values from the steam tables as:
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T T T H 002128.0958.10.2495)(2−+= (24)
For the condensate streams, the pure solvent liquid enthalpy is also found from
the steam tables as:
T T h 177.4)( = (25)
The latent heat of vaporization can be computed as:
T T T hT H T 2002128.0219.20.2495)()()( −−=−=λ (26)
Using the above correlations, the energy balance equations ((20) and (22)) have
the following final forms:
)506.2177.4(
)()())(506.2177.4(
1
111212212221
X M
T T AU T T AU T T X P
dt
dT
p
S
−
−+−−−−= (27)
)506.2177.4(
)](177.4[)())(506.2177.4(
22
222212222
X M
T H T V T T AU T T X F
dt
dT f f
−
−+−+−−= (28)
Therefore, the final form of the model includes equations (1), (2), (8), (10), (12),
(14) and (25)-(28).
3 APPLICATION OF CONTROL THEORY
3.1 Control objectives
The control objectives for an evaporation system are selected taking into account
the product specifications, operational constraints and cost considerations. For theconcerned process, the primary objective is to maintain the product solids
concentration (or product viscosity) at its desired value. In order to achieve the
desired product quality in presence of disturbance and uncertainty, severaladditional control schemes, as mentioned below, need to employ with the
evaporator.
● To prevent the overflow or drying out of evaporator tubes, liquid mass holdupshould be controlled.
● To avoid the product degradation or damage, temperature must bemaintained at the desired value.
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● To reduce the steam consumption, steam economy should be maximized.
3.2 Degrees of freedom analysis
The evaporator model presented earlier includes fifteen independent variables
X X V V S T T T T M M P P F p f S f ,,,,,,,,, ,,,,[ 21212121 and ]2 X and eight
independent equations ((1), (2), (8), (10), (12), (14), (27) and (28)). Among these
variables, the inputs, namely f T , S T
, f X , S and F are specified by the external
world. Obviously, the degrees of freedom is seven. In order to have a completely
determined process, the number of its degrees of freedom should be zero. For this
purpose and to meet the control objectives, five control pairs have been selected
and two input variables, f X and f T , can be treated as known disturbances.
3.3 Selection of control pairs
For the example tomato paste evaporator, the followings are selected as controlled
variables: (i) final product concentration ( X p ), (ii) temperature of the inlet steam
( S T ), (iii) temperature of the second effect (T 2 ), (iv) liquid mass holdup in first
effect ( 1 M ), and (v) liquid mass holdup in second effect ( 2 M ). In order to
regulate the process variables, the corresponding manipulated variables are
chosen as the product flow rate from first effect ( P 1 ), the steam flow rate ( S ), the
vapor flow rate from second effect (V 2 ), the product flow rate from second effect
( P 2 ), and the feed flow rate ( F ). Figure 1 as well as Table 2 includes all these
control configurations.
Table 2 Control pairings and controllers used.
Controlled variable Manipulated variable Controller type
X p P 1 PI, NLPI and GSPI
S T S PI, NLPI and GSPI
T 2 V 2 PI, NLPI and GSPI
1 M P 2 P-only
2 M F P-only
3.4 Control equations
In this paper, a comparative control study is presented. For this, three types of
multi-loop controllers, namely PI, NLPI and GSPI, have been designed in this
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section for the example evaporator. The ISE performance criterion has been used
in selecting the controller tuning parameter values and they are reported in Table
3.
3.4.1 Proportional integral (PI) controller
The general form of a single-loop PI control law is given by the following
expression:
])1
()[(0 ∫ −+−+= dt Y Y Y Y K U U sp spτ
(29)
Here, K is the proportional gain, τ the integral time constant, U 0 the bias signal
and Y sp the set point value of Y .
Table 3 Tuning parameters values.
Parameter P or PI NLPI GSPI
a = 3.0
K f 1000 hr-1
− −
K V2 , K V20 1250 kg/hr.0C 1250 kg/hr.
0C 1550 kg/hr.
0C
K S , K S0 15 kg/hr.0C 15 kg/hr.
0C 15 kg/hr.
0C
K P1, K P10 30000 kg/hr 20000 kg/hr 20000 kg/hr
K P2 800 hr-1
− − 2V τ 0.03 hr 0.01 hr 0.01 hr
S τ 0.35 hr 0.52 hr 0.52 hr
1 P τ 0.05 hr 0.01 hr 0.01 hr
3.4.2 Nonlinear proportional integral (NLPI) controller
Different forms of nonlinear PI (and PID) controller are available in scientific
literature. It can be developed by adding higher-order terms of the error signal andintegral of the error to the control law. Also, there is a way to make the controller
parameters functions of the error (Cheung and Luyben, 1980) or parameterscheduling (Rugh, 1987) or both (Jutan, 1989). Actually, there is no particularcontrol scheme that has become standard in the literature.
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Here, the following nonlinear PI control scheme is applied on the
evaporator. The proportional gain of the NLPI is a function of the absolute value
of the error.
])1
()[(0 ∫ −+−+= dt Y Y Y Y K U U sp spτ
(29)
with )1(0 Y Y a K K sp −+= (30)
where, K 0 is the initial fixed gain. It is obvious that if there is no integral term,
the controller output is effectively proportional to the square of the error.
3.4.3 Gain-scheduled proportional integral (GSPI) controller
A gain-scheduled PI law (Bequette, 2003) has been designed for the
representative process. The GSPI has the following form:
])1
())[((0 ∫ −+−+= dt Y Y Y Y Y K U U sp spτ
(31)
The controller gain, K , is varied aiming to keep K K P constant, which then
keeps the stability margin constant. When the process gain is characterized as a
function of the scheduling variable, ( )Y K P , then the controller gain can be
scheduled as:
)(
)()()(
00
Y K
Y K Y K Y K
P
P = (32)
The gain of the GSPI scheme used has the following forms:
(i) When Y > 0Y ,
Y
Y K Y K
−
−=
1
1)( 00 (33)
where, Y Y K P −=1)( and 00)( K Y K = .
(ii) When Y < 0Y
0)( K Y K = (34)
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Here, Y 0 represents the nominal operating value of Y (=Y sp ). It is worthy to
mention that this is a one-way approach. Since the process gain increases with
lower purity, maintaining a constant controller gain speeds up the response when
the product is less pure.
4 RESULTS AND DISCUSSION
Matlab codes have been developed to generate simulation results. The 4th order
Runge-Kutta method is used to solve the differential equations contained in the
model. In the subsequent discussion, the open-loop followed by the closed-loopevaporator performance is presented.
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Figure 2 Effect of a pulse input change in Tank2 product flow rate (changed from14887 to 15200 kg/hr at time = 5 hr and then from 15200 to 14887 kg/hr at time
=10 hr).
4.1 Open-loop performance
Figure 2 illustrates the effect of Tank2 product flow rate on the main product
composition. Two consecutive step changes have been introduced in the product
flow rate (step increase: 14887→ 15200 kg/hr at time =5 hr; step decrease: 15200
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→ 14887 kg/hr at time =10 hr). As a consequence, the final product purity gets
disturbed and the process attains a new steady state against a change. This result
shows the interactive behavior of the process variables and it confirms that the
sample evaporator is open-loop stable.
4.2 Comparative closed-loop performance
4.2.1 Disturbance rejection
The comparative regulatory performances are depicted in Figures 3 and 4introducing a pulse input change in feed concentration (step increase: 0.05 →
0.0525 kg/kg at time = 5 hr; step decrease: 0.0525 → 0.05 kg/kg at time = 15 hr)
and feed temperature (step increase: 85 → 900C at time = 5 hr; step decrease: 90
→ 850C at time = 15 hr), respectively. Both the figures include the control
performance in terms of final product composition and liquid mass holdup inTank1. However, Tables 4 and 5 record the integral square error (ISE) for allcontrol loops. It is obvious from the simulation results that the NLPI and GSPI
provide better performance over the classical PI controller. Due to the moderate
nonlinearity of the process, the nonlinear controllers outperform the PI.
Table 4 ISE values corresponding to Figure 3.
Controller X p 1 M 2 M T 2 S T
PI 2.16x10-6 0.0052 7.23x10-4 5.76x10-7 0.2505
NLPI 4.93x10-7 − − 1.73x10-7 0.2030
GSPI 4.97x10-7
− − 6.89x10-8
0.0762
Table 5 ISE values corresponding to Figure 4.
Controller X p 1 M 2 M T 2 S T
PI 7.25x10-8 2.11x10-4 0.0017 0.0011 0.0044
NLPI 1.65x10-8 − − 1.73x10-4 0.0026
GSPI 1.65x10-8 − − 2.33x10-4 0.0024
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Figure 3 Effect of a pulse input change in feed concentration (changed from 0.05to 0.0525 kg/kg at time = 5 hr and then from 0.0525 to 0.05 kg/kg at time = 15hr).
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Figure 4 Effect of a pulse input change in feed temperature (changed from 85 to90
0C at time = 5 hr and then from 90 to 85
0C at time = 15 hr).
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4.2.2 Set point tracking
Figure 5 displays a comparative servo performance between PI, NLPI and GSPI
control algorithms against a pulse change in set point value of the final productcomposition (step increase: 0.2607 → 0.27 kg/kg at time = 5 hr; step decrease:
0.27 → 0.2607 kg/kg at time = 15 hr). This simulation experiment confirms thatthe PI controller shows relatively poor performance compared to other two PIs.
The performance in terms of ISE values is analyzed in Table 6. Overall, the GSPI
showed best performance due to its ability of timely changing the gain.
Table 6 ISE values corresponding to Figure 5.
Controller X p 1 M 2 M T 2 S T
PI 2.77x10-5 0.01917 0.0090 2.59x10-6 0.1866
NLPI 2.22x10-5
− − 2.09x10-6
0.1381GSPI 2.25x10-5 − − 1.03x10-6 0.0568
5 CONCLUSIONS
This article presents the open-loop as well as closed-loop operation of a
commercial double-effect tomato paste evaporation system. The model structure
developed based on backward feeding approach consists of differential algebraicequations. Open-loop simulation shows that the sample evaporator is a stable
process. Three multi-loop control strategies, namely traditional PI, NLPI and
GSPI, have been synthesized to investigate the comparative performance.Simulation experiments based on set point tracking and disturbance rejection
show that the classical PI controller provides relatively poor performance over the
NLPI and GSPI algorithms. The quantitative performance analysis has also beenincluded by computing ISE values.
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Yadav and Jana: Simulation and Control of an Evaporator
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H(T) Enthalpy of pure vapor solvent (steam) at temperature T (kJ/kg)
K Proportional gain
M Mass holdup of liquid product (kg)
P Liquid product flow rate (kg/hr)S Steam flow rate (kg/hr)
t Time (hr)T Temperature (
0C)
U Overall heat transfer coefficient (kJ/hr.m2.0C) or manipulated variable
V Vapor flow rate (kg/hr)
X Mass fraction (kg solids/kg stream)
τ Integral time constant (hr)
Subscripts
f Feed p Final product
S Steam
sp Set point0 Steady state
1 First effect
2 Second effect
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Yadav and Jana: Simulation and Control of an Evaporator
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Cadet, C., Toure, Y., Gilles, G., Chabriat, J.P. “Knowledge Modelling and Non-
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Chemical Product and Process Modeling, Vol. 5 [2010], Iss. 1, Art. 6
DOI: 10.2202/1934-2659.1443