Optimal control of energy losses in multi-boiler steam systems

Energy 34 (2009) 1260–1270

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Optimal control of energy losses in multi-boiler steam systems Janusz Bujak* ´ skiego 6, 85-950 Bydgoszcz, Poland Polish Association of Sanitary Engineers, Division Bydgoszcz, Rumin

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 August 2008 Received in revised form 1 May 2009 Accepted 2 May 2009 Available online 13 June 2009

This paper describes the development of a mathematical model to determine the optimized energy losses for a set of boilers (with a wide operating margin) supplying a common load. The model can be applied to steam systems that have a group of liquid- or gas-fired shell boilers available for use. The study shows that when the model is applied, the total energy losses of a few boilers working in unison are lower than when a traditional cascade system is used. The differences in energy loss can even reach approximately 12%. The model shows that increasing the heat load from 0 to 30% yields increasing differences in the energy losses between the standard (traditional) and optimized conditions, up to a maximum value of 79 kJ/s. As the steam demand grows from 30 to 100%, the total difference in energy losses between the standard and optimized conditions decreases systematically. When the multi-boiler system operates at full thermal power (100%), there are no differences in the energy losses. The greatest energy loss differences occur in the heat load range from 10 to 80%. There will be a reduction in the primary fuel used by about 40,300 N m3 per year if the model is applied. The optimization system can be put into operation in existing and proposed plants. The payback period on investment for the optimization controller is less than half a year.  2009 Elsevier Ltd. All rights reserved.

Keywords: Energy losses Mathematical model Multi-boiler system Optimization Steam boiler

1. Introduction Many physical simulation models and Artificial Neural Networks (ANNs) have been developed and described for devices such as the components of boiler rooms, power plants or heat and power stations. These physical simulation models are based on the physics of the processes involved, and they consist of equations representing these processes. These ANN models develop the relationships between selected inputs and outputs through training. The previously described models mainly concern individual steam boilers, rather than multi-boiler systems. A boiler is undoubtedly an important piece of equipment in power plants or combined heat and power stations (CHP). However, the steam unit constitutes only one element of the whole productive (output) system, i.e., the source of heat and electricity. Kalogirou [1] has presented a brief review of the applications of ANN in various energy systems. The use of soft computing techniques for the simulation of thermodynamic systems has been presented by Kesgin and Heperkan [2]. A few authors [3,4] have reported the

* Fax: þ48 523 270339. E-mail address: [email protected] 0360-5442/$ – see front matter  2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2009.05.005

capability of ANN to replicate an established correspondence between points of an input domain and points of an output domain in order to interpret the behavior of phenomena involved in energy conversion plants. Many publications present physical modeling of boilers [5–15] and they have shown that physical modeling is difficult and complicated. There have been some works [16–19] reporting on the modeling of conventional coal-fired boilers using ANN, but none of them use real plant data. A substantial portion of the literature concerns steam boilers with high thermal ratings that are operated and maintained by professionally qualified personnel. Models describing the total heat source are rare [20] and only refer to the energy sector. Boilers catering only to steam generation in the thermal range of 0.5–40 MW are usually operated by workers with a low skill profile. Generally, there is a demand in industry for hot water or saturated steam at a pressure of 0.03–2.0 MPa for technological purposes. The most commonly used unit is a shell boiler fired with liquid or gaseous fuels. A steam system using shell boilers to satisfy the needs of a board machine was described by Bujak [21]. In contrast to the energy sector (heat-generating plants and professional CHPs), heat sources in industrial settings are not the primary focus of the system. Unlike large public utilities with combined heat and power plants, industrial boiler utilities are usually operated by general purpose personnel. Therefore, technologies in industrial

J. Bujak / Energy 34 (2009) 1260–1270

Nomenclature specific heat of flue gas (steam boiler) (kJ/kg K) specific heat of flue gas (economizer) (kJ/kg K) heat flux losses through the external surfaces of the saturated steam system and heat exchangers from the steam boilers to the particular heat centers (kJ/s) enthalpy flux of saturated steam carried away from the E_ i-c-ss steam boiler (kJ/s) enthalpy flux of water from the boiler blow-down E_ i-l-bd (kJ/s) enthalpy flux of water from the boiler blow-off (kJ/s) E_ i-l-bo enthalpy flux of flue gases (kJ/s) E_ i-l-chl E_ i-l-chl-d dry flue gas loss (sensible heat loss) (kJ/s) E_ i-l-chl-w wet flue gas loss (latent heat loss) (kJ/s) enthalpy flux of air used for the ventilation of the E_ i-l-chv boiler combustion chamber during the ventilating burner start (kJ/s) heat flux lost to the atmosphere through the external E_ i-l-esb boiler surface (kJ/s) E_ i-l-ic-CO chemical enthalpy flux of flue gases – carbon monoxide (kJ/s) E_ i-l-ic-CH4 chemical enthalpy flux of flue gases – methane (kJ/s) E_ i-l-ic-CnHn chemical enthalpy flux of flue gases – hydrocarbons (kJ/s) E_ i-l-ic-SO chemical enthalpy flux of flue gases – sulfur monoxide (kJ/s) E_ i-loss-sb total flux of energy lost by the steam boiler (kJ/s) heat flux recovered by the economizer (kJ/s) E_ i-r-eco enthalpy flux of air supplied to the steam boiler for the E_ i-s-a combustion process (kJ/s) enthalpy flux of fuel supplied to the steam boiler (kJ/s) E_ i-s-f enthalpy flux of make-up water supplied to the steam E_ i-s-fw boiler (kJ/s) usable heat flux carried away from the steam boiler (kJ/s) E_ i-uh energy flux lost by the multi-boiler unit (kJ/s) E_ mb steam boiler capacity (t/h) Gi-sb water enthalpy carried away from the steam boiler due hi-bd to its blow-down (kJ/kg) water enthalpy carried away from the steam boiler due hi-bo to its blow-off (kJ/kg) calorific value of carbon monoxide (kJ/kg) HCO calorific value of methane (kJ/kg) HCH4 calorific value of hydrocarbons (kJ/kg) HCnHn calorific value of sulfur monoxide (kJ/kg) HSO blow-down valve flow coefficient (m3/h) Kv flux of water mass carried away from the boiler due to mi-bd its blow-down (kg/s) flux of flue gas mass after the steam boiler (kg/s) mi-fg flux of flue gas mass before the economizer (kg/s) mi-fge flux of saturated steam mass produced by the steam mi-ss boiler (kg/s) flux of vapor mass in flue gas (kg/s) mi-v-fg number of burner blow-off cycles ni operating pressure of saturated steam in a steam boiler pi (bar) r enthalpy of steam condensation (kJ/kg) concentration of salt or silica in the water feeding si-s-fw a steam boiler (mg/l) maximum concentration of salt or silica in water ss-max feeding a steam boiler (mg/l)  flue gas temperature after the steam boiler ( C) ti-fg  flue gas temperature before the economizer ( C) ti-fge-1 ci-fg ci-fge E_ a-loss

ti-fge-2 tref u(x)s Qmb Qr-mb Qi-max Qi-r xi-CO xi-CH4 xi-CnHn xi-SO

1261

flue gas temperature after the economizer ( C) reference temperature – (reference level 25  C) standard measurement uncertainty for element ‘x’ thermal power of the multi-boiler system (kJ/s) actual quantity of heat carried away from the multiboiler installation to the steam system (kJ/s) maximum thermal power of the steam boiler (kJ/s) actual thermal power of the steam boiler (kJ/s) weight concentration of carbon monoxide in flue gases (kg/kg) weight concentration of methane in flue gases (kg/kg) weight concentration of hydrocarbons in flue gases (kg/kg) weight concentration of sulfur monoxide in flue gases (kg/kg)

Greek symbols Dp differential pressure in front of and behind the blowdown relief valve (bar) e coefficient of energy efficiency (%) fi actual heat load of the optional steam boiler (%) fr-mb actual heat load of the multi-boiler system (%) f1 actual heat load of steam boiler number 1 (%) f2 actual heat load of steam boiler number 2 (%) fn actual heat load of steam boiler number n (%) si-b-off duration of one blow-off cycle measured from the burner’s start until the flame appears (s) ri-bd blow-down water density (kg/m3) Subscripts GM gas meter – multi-boiler unit HM heat meter – saturated steam HM1 measurements of energy flux used for central heating HM2 measurements of energy flux used for domestic hot water HM3 measurements of energy flux used for technology HM4 measurements of energy flux in the saturated steam HM5 measurements of energy flux in the feed water NG-50 natural gas comprising 97% methane P steam pressure on the steam pressure collector the steam pressure when the SB1 burner is switched off P1off the steam pressure when the SB1 burner is switched on P1on the steam pressure when the SB2 burner is switched off P2off the steam pressure when the SB2 burner is switched on P2on the steam pressure when the SB3 burner is switched off P3off the steam pressure when the SB3 burner is switched on P3on SB1 steam boiler 1 producing saturated steam SB2 steam boiler 2 producing saturated steam SB3 steam boiler 3 producing saturated steam feed water temperature for the central heating system t1-ch temperature of water returning from the central t2-ch heating system feed water temperature for the domestic hot water t1-dw system temperature of water returning from the domestic hot t2-dw water installation feed water temperature for the technological system t1-tw temperature of water returning from the technology t2-tw natural gas temperature tg feed water temperature tw Q thermal power thermal power of SB1 Q1 thermal power of SB2 Q2 thermal power of SB3 Q3

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J. Bujak / Energy 34 (2009) 1260–1270

boiler plants should be simple, easily operable by general operators, and highly efficient. This paper deals with the primary management of heat production in order to minimize heat losses in multi-boiler industrial systems fired with gaseous and liquid fuels. This work also presents a mathematical model for energy losses and optimal control in multi-boiler systems using the Simplex method. This Simplex algorithm makes use of the physical model of a steam boiler described by Bujak [22]. The aim of this study is to optimize a group of several steam boilers in order to lower the total loss of heat as much as possible. The optimization task involves the possibility of setting up heat loads for individual boilers (with the assumption that their total thermal power is the same as the actual thermal power of the boiler room) in order to minimize the total energy losses of the steam boilers. The steam units can be of varying sizes, and may include their own accessories. The boilers can also work at an optional heat load and a varied operational state (e.g., clean, slightly dirty or very dirty, covered either with soot or boiler scales).

E_ i-uh ¼ E_ i-c-ss  E_ i-s-fw

(2)

E_ i-loss-sb ¼ E_ i-l-chl þ E_ i-l-ic þ E_ i-l-bo þ E_ i-l-bd þ E_ i-l-chv þ E_ i-l-esb  E_ i-r-eco

ð3Þ

we obtain a formula for the energy balance of a multi-boiler system with n steam units: n  X

E_ i-s-f þ E_ i-s-a



¼

i¼1

n  X E_

i-uh

þ E_ i-loss-sb



(4)

i¼1

The coefficient of energy efficiency for this system can be written as: n   P E_ i-uh

e¼

i¼1

n P ðE_ i-uh þ E_ i-loss-sb Þ

(5)

i¼1

3. Traditional control system for multi-boiler installations 2. Energy losses of the multi-boiler system This optimization modeling meets the objectives of the efficiency targets set by the European Union. The EU wastes more than 20% of its energy due to inefficiency. MEPs call for an energy savings of 9% by 2016. Countries of the EU would also like to meet the target of improving energy efficiency by at least 20% by 2020. The energy efficiency of steam boilers producing saturated steam or hot water depends on the rate of heat loss by the boilers. The manufacturers of shell boilers [23–25] determine their thermal capacity according to PN-EN 12953-11 [26]. In the case of gaseous fuels, the loss includes the energy loss in flue gases, the heat loss through the boiler’s external surface to the environment, and the loss from incomplete combustion. In reality, most boiler heat loss is due to technical and operational conditions influencing the efficiency of heat production. The heat losses of a steam boiler can be determined by two methods: indirect and direct. The indirect method involves determining total heat losses. Generally, it is performed via calculations (i.e., an analytical method). The direct method involves the measurements of utilized fuel and of heat flux transferred to the medium in the boiler, i.e., usable heat. The energy losses constitute the difference between the energy flux supplied to the boiler and the usable heat produced by the boiler. This paper describes boiler heat losses determined by the indirect method using an optimization model. The obtained results were verified using an example of an actual boiler room via the direct method. The energy balance of the multi-boiler system (where the number of boilers equals ‘n’) working at a defined heat load and heated with liquid and gaseous fuels can be written as follows: n  X i¼1

E_ i-s-f þ E_ i-s-a þ E_ i-s-fw



¼

n  X E_

i-c-ss

þ E_ i-l-chl þ E_ i-l-ic

Boiler systems supplying steam are provided with a redundancy of 100% or more in order to avoid the unavailability of steam at any point in time. Fig. 1 shows a schematic diagram of a hydraulic connection of a multi-boiler system producing saturated steam. A pressure regulator (P), which is placed on the collector, controls the work of the steam boilers SB1, SB2, and SB3 depending on the pressure within the collector. Fig. 2 shows the cutting-in and cutting-out pressure levels of the three steam boilers. This type of cascade control in multi-boiler systems is commonly used in industrial settings, where liquid and gas-fired shell boilers prevail. Many would claim that this method of control has dominated industrial boiler rooms. The steam boiler (SB1) performs as a basic leading unit, producing saturated steam at a pressure of p1. When the steam pressure ‘P’ on the main collector (Fig. 1) decreases to below the pressure p1on, a steam boiler burner (SB1) is switched on. When the demand for saturated steam is lower than the thermal power of the steam boiler (SB1), the pressure in the main collector increases until p1off, and then the SB1 burner is switched off. In the case of a demand for steam greater than Q1 but smaller than Q2, the burner of a steam boiler (SB2) at a pressure of p2on is also switched on. When steam received through the process receivers exceeds the value Q2, an SB3 burner is switched on at a pressure of p3on. A decrease in demand for steam will cause the boilers to switch off in the opposite sequence. This means that SB3 will be switched off first, then SB2, and finally SB1. As can be seen, the idea of cascade control is based on the leading boiler working. The subsequent steam units are only put into operation when the demand for saturated steam (thermal power) exceeds the capabilities of SB1. All in all, this kind of system for multi-boiler installations is quite simple, but the main issue is with its expense.

4. Mathematical modeling to optimize energy losses

i¼1

þ E_ i-l-bo þ E_ i-l-bd þ E_ i-l-chv  þ E_ i-l-esb  E_ i-r-eco

4.1. Theoretical basis of the optimization modeling

ð1Þ

After transposing the component of enthalpy flux in feed water onto the right-hand side of the equation, and after considering the following equations:

The Simplex method of linear programming has been used to control optimal energy losses in multi-boiler systems. The aim of the optimization model is to set up the heat loads of the individual steam boilers under the assumption that their total thermal power

J. Bujak / Energy 34 (2009) 1260–1270

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saturated steam

P

SB 1

SB 2

SB 3

feed water Fig. 1. Steam boilers – hydraulic connections.

is the same as the actual thermal power of the multi-boiler system, such that the total boiler heat loss incorporated into this system is as low as possible. As an option, the boilers can be of differing capacities, and can be outfitted with different devices. Hence, the total energy lost by the n boilers in the multi-boiler system can be written as the following objective function:

E_ mb ð4r-mb Þ ¼ I1k  E_ kn  In1 ¼

k X n  X

 E_ ji-loss-sb ð4i Þ /min

(e) k ¼ the number of components for which the energy flux gain or loss of the ith boiler (j ¼ 1, ., k) is considered; (þ) stands for loss and () stands for gain; (f) n ¼ the number of boilers in the multi-boiler system (i ¼ 1, ., n); P k Pn _ (g) j¼1 i ¼ 1 ðE j;i-loss-sb ð4i ÞÞ ¼ total loss depreciated by possible gains for the ith boiler, where E_ j,i-loss-sb(fi) stands for the jth loss or gain of energy flux for the ith boiler, where E_ j;i-loss-sb ð4i Þ˛C0; ND. (h) f1, f2, ., fi ¼ the independent heat load of the ith boiler.

(6) The set of bounded functions dependent on the decision variables can be written as:

j¼1 i¼1

depending on the decision variable matrix:

0%  41  100%

(8)

where:

0%  42  100%

(9)

E_ mb ¼ energy flux lost by a multi-boiler system; fr-mb ¼ actual heat load of the multi-boiler system; I1k and In1 ¼ unit matrices with the dimensions of 1  k and n  1; (d) E_ kn ¼ the components matrix, for which the energy flux gain or loss of the ith boiler is considered for the jth component, with the dimensions of k  n;

Y  

4r-mb ¼ ½ 41 42 . 4n 

(7)

(a) (b) (c)

0%  4n  100%

Concurrently, it must be assumed that the actual thermal power of the multi-boiler system (n boilers) is equal to the total thermal power of the n steam boilers resulting from the heat load of each boiler, represented by the appropriate component of the decision variable matrix. fr-mb: T Qr-mb ¼ 4r-mb  Qmax

P (bar) p1 off

p2 off

p1 on

p3 on

Qr-mb ¼ G  Qmax  In1 SB1

0

SB1+SB2

Q1

Q3

Fig. 2. A multi-boiler cascade system as a function of pressure.

(12)

where:

SB1+SB2+SB3

Q2

(11)

Introducing the additional condition of Eq. (12), the energy flux losses of the multi-boiler installation can be optimized for any heat load experienced by the system:

p3 off

p2 on

(10)

Q (kJ/s)

(a) Qr-mb ¼ the actual thermal power of the multi-boiler system (n boilers); (b) Qmax ¼ the maximum thermal power matrix of the ith boiler, denoted as:

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J. Bujak / Energy 34 (2009) 1260–1270

Qmax ¼ ½ Q1-max

Q2-max

.

Qn-max 

(c) G ¼ a preset total heat load of the multi-boiler system (n boilers) with the assumption that G˛C0%; 100%D. (d) Inþ1 ¼ a unit matrix with the dimensions of n  1. The optimization model is flexible enough to exclude an optional steam boiler or group of boilers from use by introducing the following additional constraint:

0%  4i  0%

(14)

or by taking the assumed level of operation as a preset:

y%  4i  y%;

where y˛ð0  100Þ

(15)

When, in turn, we only want to constrain the thermal power of one boiler or a group of boilers, it is enough to alter the above constraint in the following way:

0%  4i  y%;

where y˛ð0  100Þ

The individual elements of formula (1) and the right-hand side of Eq. (3) were determined in the following way:

The procedure of determining the maximum allowable values of salt and silica in boiler water was adopted according to the European Union Regulations [27]. D. Enthalpy flux of water from the boiler blow-down:

E_ i-l-bd ¼ mi-bd hi-bd

(24)

In practice, the blow-down process is carried out periodically, with the use of a time controller (blow-down timer) and a blowdown relief valve. The valve opening time is preset on the controller, as are the intervals between particular opening periods. The standard time period for valve opening is from 1 s to 3 s, and the time period between the openings is between 1 h and 5 h. The lost enthalpy flux of blow-down water in this case is:

r E_ i-l-bd ¼ i-bd

pffiffiffiffiffiffi DpKv hi-bd 36002

(25)



E_ i-l-chv ¼



  0:00112  p2i þ 0:0518  pi þ 0:477 Gi-sb  si-b-off  ni 60

(26)

A. Enthalpy flux of flue gases: - dry flue gas loss (sensible heat loss):

(17)

- wet flue gas loss (latent heat loss):

E_ i-l-chl-w ¼ mi-v-fg  r

(23)

E. Enthalpy flux through the air used for ventilation of the steam boiler combustion chamber during the start-up of the ventilating burner [28]:

4.2. Energy losses of the steam boiler

E_ i-l-chl-d ¼ mi-fg  ci-fg  ti-fg  tref

m s h E_ i-l-bo ¼ i-ss i-s-fw i-bo ss-max  si-s-fw

(16)

A detailed application of the above system of equations is shown in Section 4.3.



preset (maximal) salinity threshold of the boiler water, the relief valve disposes of the excess blow-off matter.

(13)

(18)

The heat flux loss during burner start-up occurs in the first phase of work, while the combustion chamber is being ventilated with air supplied from the environment. More often than not, the air is the same temperature as the environment, i.e., approximately a dozen degrees, which cools the combustion chamber. The chamber ventilation lasts several dozen seconds. F. Heat flux lost through the external surfaces of the steam boiler to the environment (includes both convection and radiation terms):

B. Chemical enthalpy flux of flue gases – incomplete combustion:

Ei-l-esb ¼

23  Gi-sb ð1:523  Gi-sb Þ0:52  pi  0:28 p þ 100 5000 i

E_ i-l-ic-CO ¼ mi-fg  xi-CO  HCO

(19)

E_ i-l-ic-CH4 ¼ mi-fg  xi-CH4  HCH4

(20)

G. Heat flux recovered by the economizer:

E_ i-l-ic-Cn Hn ¼ mi-fg  xi-Cn Hn  HCn Hn

(21)

  E_ i-r-eco ¼ mi-fge  ci-fge ti-fge-1  ti-fge-2

E_ i-l-ic-SO ¼ mi-fg  xi-SO  HSO

(22)

(27)

(28)

4.3. Example calculations and results C. Enthalpy flux of water from the boiler blow-off (only in steam boilers): During boiler operations, salts in the boiler water become denser. Hence, water alkalinity and density also increase. This process can lead to significant operational difficulties, depending on salt concentrations, and in some cases may even lead to boiler destruction. Thus, steam boilers are equipped with blowoff units. A blow-off connection is placed at the height of the water surface, i.e., on the boundary between the liquid and steam zones. The highest concentration of salt occurs here, and it is visible as characteristic salt foam. Therefore, the temperature of the blow-off matter is equal to the water boiling temperature at the specific steam pressure. After exceeding the

Example calculations were carried out for a multi-boiler system consisting of three shell boilers. The aim of the optimization of their operation was to find operating conditions that would achieve minimal total energy losses. Calculations were also made of energy losses for the same system working in a cascade, and the results of the two calculations were then compared. Basic boiler data: -

boiler construction: shell boiler thermal power of the source: Qmb ¼ 5880 kJ/s number of boilers: 3 units (1960 kJ/s each) operating saturated steam pressure: pi ¼ 0.8 MPa

J. Bujak / Energy 34 (2009) 1260–1270

- condensate return: 70% - water treatment station: demineralization - blow-down: timing of valve opening, 4 s/h

1265

Table 2 The input and output parameters of SB1, SB2 and SB3.

The steam boilers are fired with natural gas NG-50. The calorific value of the gas is 36.2 MJ/Nm3. A detailed description of natural gas composition is shown in Table 1. Table 2 shows the input and output parameters of the three steam boilers. The parameters are identical because the boilers have equal thermal power and are complete with the same accessories. The procedure described in Section 4.1 was applied to the multiboiler system for the full range of the heat loads (0–100%). Calculations were made by the Solver function in Microsoft Excel. Example calculations are shown below. The following assumptions were made:

Heat load (%) Heat load (kJ/s)

20 392

Input parameters Flux of feed water mass (kg/h) Feed water temperature ( C) Flux of natural gas (N m3/h)

662.4 1270.8 1882.8 2491.2 3099.6 102.0 102.0 102.0 102.0 102.0 45.2 90.4 135.6 180.8 226.0

Output parameters Usable heat flux (kJ/s) Pressure of saturated steam (kPa) Flux of flue gas (kg/h) Flue gas temperature ( C)

372.8 800 680.4 189.3

Other parameters Total flux of energy lost by steam boiler (kJ/s) Coefficient of energy efficiency (%)

79.2 82.5

40 784

60 1176

80 1568

100 1960

770.4 1158.6 1540.1 1914.9 800 800 800 800 1360.8 2044.8 2725.2 3405.6 204.6 219.9 235.1 250.4 133.7 85.2

197.6 85.4

268.1 85.2

345.3 84.7

- a multi-boiler system consists of three steam boilers; - the maximal thermal power of the ith boiler (Qi-max) is:

G ¼ 50% Qmax ¼ ½ 1914:9

1914:9

1914:9 

(29)

- the total thermal power of the multi-boiler installation is G ¼ 50%; - the number of components, k, for which a gain or loss of the ith boiler is considered is 8. Due to these assumptions, the components matrix E_ 83 (Section 4.2), for which we consider the heat flux gain or loss for the ith boiler, is of the following form:

E_ 8*3

2 _ Ei-l-chl-d;1:1 6 E_ i-l-chl-w;1:2 6 6 E_ 6 i-l-ic-CO;1:3 6 _ 6 Ei-l-bo;1:4 ¼ 6 6 E_ 6 i-l-bd;1:5 6 _ 6 Ei-l-chv;1:6 6 4 E_ i-l-esb;1:7 E_ i-r-eco;1:8

E_ i-l-chl-d;2:1 E_ i-l-chl-w;2:2 E_ i-l-ic-CO;2:3 E_ i-l-bo;2:4 E_ i-l-bd;2:5 E_ i-l-chv;2:6 E_ i-l-esb;2:7 E_ i-r-eco;2:8

3 E_ i-l-chl-d;3:1 _E 7 i-l-chl-w;3:2 7 E_ i-l-ic-CO;3:3 7 7 7 E_ i-l-bo;3:4 7 7 E_ i-l-bd;3:5 7 7 7 E_ i-l-chv;3:6 7 7 E_ i-l-esb;3:7 5 E_ i-r-eco;3:8

(30)

The objective function can be written as:

E_ mb ð4r-mb Þ ¼ I18 E_ 83 I31 ¼

8 X 3  X

 E_ j;i-loss-sb ð4i Þ /min

j¼1 i¼1

(31) The decision variable matrix is of the following form:

4r-mb ¼ ½ 41 42 43 

(32)

The model constraints are as follows:

0%  41  100%

(33)

0%  42  100%

(34)

0%  43  100%

(35)

(36)

Using the SOLVER function, the minimum value of the objective function was obtained for the given decision variables at a system heat load of G ¼ 50%. These results are shown in Table 3. As seen in Table 3, in the case of a multi-boiler system comprised of three identical steam units, the minimal total energy flux loss occurs when each unit is at a 50% load and is equal to 488 kJ/s. The methodology introduced above was applied in order to estimate minimal energy flux losses for the remaining heat loads in the multi-boiler system – 0% < G < 100%. The results are shown in Table 4. As seen in the case analyzed above, the lowest energy flux losses of the system were obtained at the regular (steady) heat load of each steam boiler. This case is unique since each boiler has identical power and is equipped with identical accessories. In this case, the three boilers (SB1, SB2, SB3) always work in union, irrespective of the installation heat load. For comparison, Table 5 shows the results of the energy flux loss calculations for the same multi-boiler system working in cascade (traditional installation). Along with an increase in heat load, subsequent boilers (SB2, SB3) are switched on successively depending on the required power. Table 6 shows the total difference in energy losses for the threeboiler system between the first case, where the optimization algorithm was applied to the system, and the second case, where the traditional (cascade) system was used. Table 6 illustrates the increase in heat load from 0 to 30% along with the simultaneous increase in the difference of energy losses, which reach a maximum value of 79 kJ/s. As the heat load increases from 30 to 100%, the total difference in energy losses decreases systematically. When the multi-boiler system operates at its full thermal power (100%), there are no differences in energy losses. The greatest differences occur in the heat load range from 10 to 80%.

Table 3 Computation results for the minimal energy flux loss for the multi-boiler system. Number of boilers

Table 1 Chemical composition of natural gas. Methane

fr-mb (%) fi (%)

Ethane

Propane

CO2

Nitrogen

Others

1.06

0.37

0.05

0.81

0.20

(%) 97.51

Qi-max (kJ/s) Qi-r (kJ/s) S(E_ j-loss-sb(fi)) (kJ/s) Total minimum losses (kJ/s)

1

2

3

50 50 1914.9 957.5 164.7 494.1

50 1914.9 957.5 164.7

50 1914.9 957.5 164.7

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J. Bujak / Energy 34 (2009) 1260–1270

Table 4 Total energy flux losses for the multi-boiler system, after the optimization process. L.P.

1 2 3 4 5 6 7 8 9 10 11

Boiler plant and boiler load

Total energy flux losses

Boiler room

SB1

SB2

SB3

E_ mb (kJ/s)

Qi-r (%)

Qi-r (%)

Qi-r (%)

SB1 þ SB2 þ SB3 Pk Pn _ j¼1 i ¼ 1 ðEj;i-loss-sb ð4i ÞÞ (kJ/s)

0 588 1176 1764 2352 2940 3528 4116 4704 5292 5880

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

128 170 238 313 401 488 593 696 804 918 1036

The optimization program controls the energy losses of the multi-boiler system. When the chemical enthalpy of the optional fuel is known, the fuel consumption can be calculated in a simple way. The program also has an optional concurrent function of minimizing fuel consumption. 4.4. Practical use of the model The optimization model for heat losses in multi-boiler installations can be used in boiler rooms equipped with shell boilers fired with liquid or gaseous fuels. Fig. 3 illustrates a method for primary control of the three boilers’ operations so as to minimize the energy losses. The data shown in Table 4 were obtained using the optimization model. The enthalpy flux meter (HM) for saturated steam transfers the information about the actual heat load of the multiboiler system (Table 4, column 2). Concurrently, each burner continuously transfers information about its actual heat load. The main controller monitors this information and compares it with the set loads (Table 4, columns 3–5). When the actual heat loads of burners do not correspond with the set ones, the controller verifies these loads. Naturally, the set value of the steam pressure (P) on the main collector plays the leading role in the whole control process. The above algorithm can be implemented using a Siemens S7200 driver. Using the computer software PC Access and Microsoft Excel, a simple visualization of programs based on a SIMATIC S7200 driver can be carried out. The PC Access program enables users to preview variables and preset them. The PC Access program is a user-friendly OPC Server that can be used to carry out visualization both in a Microsoft Excel spreadsheet and in any other application of Windows 2000/XP as an OPC client. Table 5 Total energy losses of the multi-boiler cascade system. L.P.

1 2 3 4 5 6 7 8 9 10 11

A wired/physical connection between the PC and the drivers can be set up using:

Boiler plant and boiler load

Total energy flux losses

Boiler room

SB1

SB2

SB3

E_ mb (kJ/s)

Qi-r (%)

Qi-r (%)

Qi-r (%)

SB1 þ SB2 þ SB3 Pk Pn _ j¼1 i ¼ 1 ðEj;i-loss-sb ð4i ÞÞ (kJ/s)

0 588 1176 1764 2352 2940 3528 4116 4704 5292 5880

0 30 60 90 100 100 100 100 100 100 100

0 0 0 0 20 50 80 100 100 100 100

0 0 0 0 0 0 0 10 40 70 100

128 190 283 392 467 553 656 747 824 923 1036

 PC/PPI cable – protocol PPI,  communications processor CP5512 (PCMCIA)/CP5611 (PCI) – protocol PPI,  communications processor CP 243-1/CP 243-1 IT – functions S7 after protocol TCP/IP. The simplest method of visualization involves connecting the cable PC/PPI with Microsoft Excel. This system requires the following elements:      

PC computer with Windows 2000/XP, optional driver S7-200 (CPU 22X), a cable for programming PC/PPI, software for STEP 7-Micro/Win V4.0, software for PC Access V1.0, software for Microsoft Excel.

4.5. Profitability of investments in steam plant modification Steam boilers are generally used in industrial settings and hospitals where saturated steam is needed for production. In such situations, the reliability of the steam delivery conditions is crucial, since production is not possible without the steam. For this reason, a boiler room is usually equipped with several steam units. It is not common for one unit to constitute 100% of a ‘cold reserve.’ The units are selected such that the other boilers can guarantee operation of the basic technological processes should one fail. Thus, such boiler rooms do not operate at high or very high heat loads. The heat load of the boiler room in question was investigated from 1 November 2004 to 30 November 2004, in the hospital in Bydgoszcz (Fig. 4). This chart shows that the heat load of the boiler room fluctuated between 14% and 29% over the testing period. The greatest differences in the energy losses between the optimization and cascade systems occur in this range. The average value of the heat load was 21% and, at this value, the difference in energy losses was 48.4 kJ/s (Table 6). Taking into account the fact that the boiler room efficiency at this heat load was approximately 65%, about 8 Nm3 of natural gas with a calorific value of 9.2 kWh would be required to produce this quantity of heat. Over the month under investigation, this amounts to a total required production of 5760 Nm3. The economic profitability of the investment has been analyzed by comparing the real costs of steam production to the hospital in 2004 with the hospital’s possible savings after modernization. The analysis was carried out with the following assumptions: - the annual costs (real) of steam production before modernization – $ 450,000; - the annual costs (estimated) of steam production after modernization – $ 400,000; - the investment costs (optimization system) – $ 25,000; - type of fuel – natural gas. As can be seen, the cost of the investment will be recovered within half a year. Table 6 The total difference of energy losses between the optimization model and the cascade system. Boiler room load Total difference Total difference

(%) (kJ/s) (%)

0 0 0

10 20 11

20 45 16

30 79 20

40 66 14

50 65 12

60 63 10

70 51 7

80 20 2

90 5 1

100 0 0

J. Bujak / Energy 34 (2009) 1260–1270

1267

CONTROLLER

FEED WATER

SATURATED STEAM NG-50

SB3

NG-50

SB2

NG-50

SB1

FEED WATER

FEED WATER

SATURATED STEAM

P

SATURATED STEAM

SATURATED STEAM

P

HM

OPTIMIZATION MODEL

Fig. 3. A diagram of multi-boiler system control using the optimization model.

installation and through heat exchangers on their way from the steam boilers to the particular heat centers.

5. Verification of the optimization model 5.1. Description of the measurement system

E_ mb þ E_ a-loss ¼ GM 

5 X

ðHMiÞ

(37)

i¼1

The equation component E_ a-loss is responsible for the heat flux losses through the external surfaces of the saturated steam

5.2. Accuracy of measurement analysis Uncertainties in the measurement of energy flux losses were determined by the total differential method. In the first step, the individual uncertainties were computed. Standard uncertainties were determined in the measurements of the usable heat as the enthalpy flux of the water feeding the hospital heating system, the domestic hot water installation, and the ventilation system according to formula (38):

uðH13 Þs ¼ HM13

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  u 2      uðmÞ 2 uðt1 Þ 2 uðt2 Þ 2 ð cp Þ þ þ þ m t1 t2 cp

(38)

where m, cp, t1, and t2 stand, respectively, for water mass flux, specific heat, supply and return temperatures in the central heating

HEAT LOAD OF THE MULTI - BOILER ROOM WITH THREE BOILERS 100,0

HEAT LOAD [%]

Energy loss calculations for the multi-boiler system made with the optimization model were verified by the direct method, corresponding to the left-hand side of Eq. (4). Taking into consideration that the reference level for the given balances is a temperature of 25  C, and that the temperature of the air used for natural gas combustion is also 25  C, the heat flux in the air used for combustion can be omitted. The quantity of chemical energy used as fuel was measured with a gas meter (GM; Fig. 5). The measurements of gas volume were made at an average pressure of about 3 bar. Simultaneously, pressure and gas temperatures were continuously measured, such that gas volume under standard conditions could be determined. By maintaining the gas volume at standard conditions (p ¼ 1 bar, t ¼ 0  C) and determining the calorific value by analyzing the range of mean qualitative parameters provided by the Gas Plant in Gdan´sk, the amount of energy in natural gas NG-50 was determined. The quantity of heat in feed water was calculated based on of the feed water volume measurements (HM5) and feed water temperature measurements (sensors tw). The usable heat produced for the hospital as saturated steam was measured with a heat meter (HM4). The heat meters HM1, HM2 and HM3 measured the usable heat as enthalpy flux in the water feeding the hospital heating system, the domestic hot water installation, and the ventilation system, respectively. The direct method formula for energy flux losses is obtained by combining formula (4) with the measurement system diagram in Fig. 5:

80,0 60,0 40,0 20,0 0,0 2004-11-01 2004-11-06 2004-11-11 2004-11-16 2004-11-21

2004-11-26

PERIOD OF TIME Fig. 4. Heat load of the multi-boiler room (three boilers).

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technological water

P

HM4

saturated steam

HM3

t1-tw

t2-tw HM2 t1-dw

domestic water

feed water

HM5

HM1

t1-ch

central heating

tw

t2-dw

t2-ch

natural gas

SB3 NG-50

NG-50

GM P

SB2 NG-50

SB1

tg Fig. 5. The measurement system of the multi-boiler installation.

system, the domestic hot water and the ventilation water, as appropriate. The standard uncertainties in the measurements of the usable heat as the enthalpy flux of the saturated steam and heat supplied to the boilers as the enthalpy flux of feed water were determined according to formula (39):

uðHM45 Þs ¼ HM45

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     uðh45 Þ 2 uðm45 Þ 2 þ m45 h45

(39)

where m4–5 and h4–5 stand for the mass fluxes and enthalpies of the saturated steam and feed water, respectively. The standard uncertainty in the measurement of the chemical enthalpy as natural gas supplied to the multi-boiler system was

uðE_

mb Þs

E_ mb

provided by the measurement system manufacturer (GM) as 2.0%. The results of individual uncertainties are shown in Table 7. The value of the complex standard uncertainty in the measurement of the energy flux loss in the multi-boiler system was calculated using the uncertainty propagation method, according to the formula: The results of formula (40) are shown in Table 8.

5.3. Comparison of the computational model to the empirical data Methods of statistical description were used [29] to compare the computational model to the empirical data. Therefore, the following position and dispersion measures were applied:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi             uðGMÞ 2 uðHM1 Þ 2 uðHM2 Þ 2 uðHM3 Þ 2 uðHM4 Þ 2 uðHM5 Þ 2 ¼ þ þ þ þ þ GM HM1 HM2 HM3 HM4 HM5

(40)

Table 8 Measurement uncertainties for energy flux losses in a multi-boiler system. Table 7 Standard measurement uncertainty for individual uncertainties. HM1

HM2

HM3

HM4

HM5

690 4.6

620 4.1

921 6.1

276 1.8

(kJ/s) 269 8.6 269 25.8

Work according to the optimization algorithm Standard measurement uncertainty for energy flux loss Extended measurement uncertainty for energy flux loss

240 8.3 240 24.9

GM

(kJ/s) 2305 15.4

Cascade work Standard measurement uncertainty for energy flux loss Extended measurement uncertainty for energy flux loss

5424 36.2

J. Bujak / Energy 34 (2009) 1260–1270

1269

ENERGY FLUX LOSSES (kJ/s)

ENERGY FLUX LOSSES OF THE MULTI - BOILER SYSTEM WITH THREE STEAM BOILERS 1000 800 600 experimental results - optimization system

400

experimental results - cascade system

200

computation results - optimization system computation results - cascade system

0 0

10

20

30

40

50

60

70

80

90

100

HEAT LOAD OF THE MULTI - BOILER SYSTEM (%) Fig. 6. Validation of the computational model with empirical data.

Table 9 Validation of the computational model with the empirical data of energy flux losses. Type of error

Max

Mean

Standard deviation

Cascade work Matching error (%)

2.64

0.42

0.94

Work according to the optimization algorithm Matching error (%) 2.56 0.41

0.92

Table 10 Coefficient of energy efficiency before and after the optimization process – experimental results. Boiler room load (%)

10

20

30

40

50

60

70

80

Before optimization process (%) 67.6 75.5 77.6 79.8 81.1 81.2 81.3 81.1 After optimization process (%) 72.2 80.3 82.5 83.3 83.7 83.8 83.8 83.5 Energy efficiency improvement (%) 4.6 4.7 4.9 3.5 2.6 2.6 2.5 2.4

- arithmetic mean, the central number in the arithmetic progression; - standard deviation, the average deviation of the value of energy flux loss from the arithmetic mean. To evaluate the compatibility of the simulation model with the empirical data, the results obtained from the mathematical model were compared with the results obtained from the experiment. The input data for both models were the same. The sample results are shown in Fig. 6, and the calculations are given in Table 9. As can be seen in Table 9, the maximum deviation of the empirical data from the mathematical model in the case of the cascade work was 2.64%, and the maximum deviation of work in the optimization system was 2.56%. The average deviation was 0.42% for the cascade work and 0.41% for the optimization system. Table 10 illustrates the experimental results of energy efficiency before and after the optimization process. It shows that for the steam load variation in the range of 10–80% the energy efficiency improvement is between 2.4 and 4.9%. The average annual value totals 4.7%. 6. Conclusion This paper presents a methodology for the optimization of the energy efficiency of a group of steam boilers in a boiler room. The use of continuous intelligent control of a multi-boiler system is

found to improve the energy efficiency as compared to the traditional control of setting the valve pressures of multiple boilers differently. The results obtained from the optimization model have been compared with those from a traditional cascade system. This model has shown that increasing the heat load from 0 to 30% yields increasing differences in the energy losses between the standard and optimized conditions, up to a maximum value of 79 kJ/s. For steam load variation between 30 and 100%, the total difference in energy losses decreases systematically from 79 kJ/s (at 30%) to 0 kJ/ s (at 100%). The benefits of the optimization process are evident in the heat load range from 10 to 80%. This optimization modeling meets the objectives of the efficiency targets set by the European Union. The EU wastes more than 20% of its energy due to inefficiency. MEPs call on energy saving of 9% by 2016. Countries of the EU would also like to meet the target of improving energy efficiency by at least 20% by 2020. The experimental study shows that for the steam load variation in the range of 10–80% the energy efficiency improvement is between 2.4 and 4.9%. The average annual value totals 4.7%. The optimization method contributed to the reduction of natural gas consumption by 5760 N m3 over the testing period (one month). There would be a reduction in primary fuel use by about 40,300 Nm3 per year if the model is applied. This optimization system can be put into operation in existing and proposed plants. The capital cost of the control system pays back within half a year. In spite of the low number of skilled personnel manning these steam generating boiler plants, the proposed optimization solution is still appropriate, as it is simple to install and supervise. This cost-effective and easy to use system has the potential to create significant energy savings in boiler room operations.

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