Advanced Process Integration for Low Grade
Heat Recovery
Ankur Kapil, Igor Bulatov, Robin Smith, Jin-Kuk Kim
Centre for Process Integration
School of Chemical Engineering and Analytical Science The University of Manchester
Abstract
A large amount of low-grade heat in the temperature range of 30 oC and 250 oC are readily available in process industries, and wide range of technologies can be employed to recover and utilize low-grade heat. However, engineering and practical limitations associated with the integration of these technologies with the site has not been fully addressed so far in academic and industrial communities. Also, the integration of non-conventional sources of energy with the total site can be a cost-effective and promising option for retrofit, however, carrying out its design and techno-economic analysis is not straightforward, due to variable energy demands. One of the key performance indicators for the evaluation and screening of the performance of various energy saving technologies within the total site is the potential of cogeneration for the site. A new method has been developed to estimate cogeneration potential by a combination of bottom-up and top-down procedures. In this work, the optimization of steam levels of site utility systems, based on a new cogeneration targeting model, has been carried out and the case study illustrates the benefits of optimising steam levels for reducing the overall energy consumption of the site.
There are wide range of low-grade recovery technologies and design options for the recovery of low grade heat, including heat pump, organic Rankine cycle, energy recovery from exhaust gas, absorption refrigeration and boiler feed water heating. Simulation models have been developed for techno-economic analysis of the design options for each technology and to evaluate the performance of each with respect to quantity and quality of low grade heat produced on the site. Integration of heat upgrading technologies with the total site has been studied and its benefits have been illustrated with a case study for the retrofit design.
List of contents
1 Introduction ... 4
2 Cogeneration potential ... 5
3 Optimization of steam levels ... 12
Case Study Cogeneration potential ... 15
4 Technology for utilization of low Grade heat ... 22
4.1 Vapour compression heat pump... 22
4.2 Absorption Systems ... 23
4.3 Boiler feed water (BFW) heating ... 27
4.4 Organic Rankine Cycle (ORC) ... 27
4.5 Thermo-compressor ... 28
4.6 Drying ... 29
5 Algorithm ... 29
6 Case study ... 31
7 Conclusions & future work ... 44
References ... 45 8 Appendix A ... 47 8.1 Optimization framework ... 47 8.1.1 Objective function ... 47 Optimization constraints ... 49 8.1.2 Electric balances ... 49 8.1.3 Mass balances ... 49 8.1.4 Heat balance ... 51 8.2 Equipments ... 52 8.2.1 Multi-fuel boilers ... 52 8.2.2 Gas turbines (GT) ... 53
8.2.3 Heat recovery steam generators (HRSG) ... 54
8.2.4 Electric motors (EM) ... 55
1 Introduction
The typical sources of low grade heat are listed in Table 1. The opportunity includes the waste heat recovery from liquids and gases, CHP (combined heat and power), drying, steam generation and distribution and waste heat utilization. The industrial application of low grade heat recovery is relevant to process industries, including chemical, petroleum, pulp and power, food and drink, manufacturing, iron and steel, and cement industries.
Table 1: Sources of low grade heat[1]
Opportunity Areas Industry
Waste heat recovery from gases and liquids
chemicals, petroleum, forest products
Combined heat and power systems chemicals, food, metals, machinery, forest products
Heat recovery from drying processes chemicals, forest products, food processing
Steam (improved generation, distribution and recovery)
all manufacturing
Energy system integration chemicals, petroleum, forest products, iron and steel, food, aluminium
Improved process heating/heat transfer systems (improved heat exchangers, new materials, improved heat transport)
petroleum, chemicals
Waste heat recovery from gases in metals and non-metallic minerals manufacture
iron and steel, cement
To avoid unnecessary capital expenditure for oversized equipment and to enhance controllability of the energy systems, dynamic feature of the energy supply and demand along with integration with energy recovery technology must
be incorporated into the energy study in a systematic and holistic manner. The implementation of these integrated energy saving projects within or beyond the plant may not be favoured, due to practical constraints, for example, considerable civil and piping works required, legislative limitations, different energy utilisation patterns between sources and sinks, etc. Therefore, it is vital to quantify the economic benefits of employing low grade energy recovery and its impacts on the industrial site.
2 Cogeneration potential
The extent of heat recovery and cogeneration potential is closely related to the configuration of site energy distribution systems in an industrial site, in which multiple levels of steam pressure are introduced, for example, VHP (very high pressure), HP (high pressure), MP (medium pressure) and LP (low pressure). Steam levels and its corresponding pressure is an important design variable as they can be adjusted to either minimize the fuel requirement or maximise profits by exploiting site-wide trade-off of heat recovery and power generation. Optimization of levels of steam mains is based on the manipulation of targeting models for the cogeneration potential for the site utility systems.
The performance of the system can be either optimized to obtain the best design, or to obtain the optimum operating conditions for an existing design, considering the part load performance of the equipment based on the optimum number of steam levels and their pressure. The simulation and optimization of the utility systems require an accurate and yet simpler model for each element of the system. Accurate estimation of the cogeneration potential is vital for the total site analysis as it aids in the evaluation of performance and profitability of the energy systems. The overall cost-effectiveness of power and heat from the site is heavily influenced by the optimum management and distribution of steam between various steam levels. Furthermore, optimum import and export targets for electricity can be obtained from steam levels, load and price of fuel and electricity. Also, energy efficiency for the utilisation of low grade heat will be
strongly influenced by operating and design conditions of existing energy systems. Therefore, the accurate estimation of cogeneration potential is essential for performing a meaningful economic evaluation of the design options considered for heat upgrading and/or waste heat recovery.
A number of methods are available in the literature for estimating the cogeneration potential of utility systems. The ideal shaftpower is calculated as the exergy change of the steam passing the turbine[2]. The exergetic efficiency is considered to be independent of the load and inlet-outlet conditions, and is assumed to be a constant value. The steam conditions are approximated by the saturated conditions, but the superheat in the inlet and outlet steam conditions are neglected[3]. There is a difference of up to 30% in cogeneration potential in comparison with simulations based on THM (turbine hardware model) developed by Mavromatis and Kokossis[4].
Salisbury[5] observed that the specific enthalpy of steam (i.e. enthalpy per unit mass flow) is approximately constant for all exhaust pressure values[6]. There is a linear correlation between specific power w (power per unit mass flowrate of steam) produced in the turbine and the outlet saturation temperatures. The specific power corresponds to the area of the rectangle on a graphical representation of the inlet and outlet saturation temperatures of the turbine with respect to the heat loads of steam. This methodology is based on the following assumptions: specific load (q) of steam is constant with variation in exhaust pressure and specific power is linearly proportional to the difference of inlet and outlet saturation temperatures.
Mavromatis and Kokossis[4] proposed a new shaftpower targeting tool called the turbine hardware model (THM) based on the principle of Willans line. Willans line approximates a linear relationship between steam flowrate and the power output. THM has limitations as Varbanov addressed[7]: the effect of back pressure is not taken into account, and modelling assumptions for part-load performance are too
simplistic, such that the model assumes a linear relationship over the entire range of operation.
Sorin and Hammache[8] introduced a different targeting method based on thermodynamic insights and Rankine cycle. The ideal shaftpower is a function of outlet heat loads and the difference in Carnot factor between the heat source and heat sink. The deviation of the actual expansion from the ideal expansion is defined in terms of isentropic efficiency.
New Method
Cogeneration targeting in utility systems is used to determine fuel consumptions, shaftpower production and cooling requirements before the actual design of the utility systems[8]. The previous methods available in literature have the following drawbacks. TH model does not consider the contribution of superheat in the inlet and the outlet stream in the power generation. THM parameters are based on regression parameters derived from a small sample of steam turbines, and consequently are not applicable for all the possible sizes of turbines.
In order to overcome shortcomings of previous methods, new method for cogeneration targeting has been proposed in this work, and isentropic efficiency is used in the new targeting method.
TH model for targeting does not include the superheat conditions at each level which results in significant error for estimating cogeneration potential. THM model uses an iterative procedure based on specific heat loads to calculate the mass flowrate for the turbines. The calculation of flowrates in Sorin’s methodology is based on the flow of energy. Power produced by the system is estimated with the isentropic efficiency, available heat for power generation and inlet and outlet temperatures of Rankine cycle. However, there is no justification for the assumption that thermodynamic behaviour of all the steam turbines to be used acts as that of the Rankine cycle.
The new algorithm calculates the minimum required flowrate from steam generation unit (e.g. boiler) and the levels of superheat at each steam main based on the heat loads specified by site profiles of heat sources and sinks.
The algorithm for the new procedure is given in Figure 1. The superheat temperature calculation at each steam level is made, starting with a certain superheat temperature of the steam from the boiler. The procedure is based on the assumption that steam supplied to the site utility systems from a boiler is at the superheated conditions required as VHP steam level. Figure 2 shows the temperature entropy diagram for the process. The initial conditions of superheated steam at higher pressure and temperature level are represented by point 1. The steam at lower pressure level for an isentropic expansion is shown as Point 2’ on the curve. Isentrotpic expansion with an efficiency of x% is used to determine the enthalpy at point 2. It is assumed during targeting stage that all the steam turbines are operating at their full load. The cogeneration potential of the system is dependent on the expansion efficiency of x. This parameter is dependent on the capacity of the turbine and detailed calculation is given below. Steam properties are calculated for the given entropy and pressure at the lower steam level. If the degree of superheat in the resulting LP steam main is less than required, then operating conditions of VHP is updated and then re-iterates the procedure above until the acceptable superheated conditions for LP steam main is met.
Figure 1: Algorithm for new method based on isentropic expansion
Given steam levels, inlet superheat of VHP steam, process load, BFW, Condensate temperature
Isentropic efficiency
Calculate superheat temperatures at subsequent lower steam level using isentropic efficiencies (Equation 2)
Starting from the lowest level, calculate the mass flow rates using Equation 1.
Add flow rates to determine the overall flow rates through each level (bottom up)
LP superheat temperature > LP saturation temperature + ∆T* YES STOP Increase Boiler VHP superheat NO
Figure 2: Temperature Entropy diagram for change in level
In the bottom up procedure, the temperature of the lowest steam level pressure is first used to calculate the steam mass flowrate for the expansion of steam between the lowest steam level and the higher pressure next to the lowest one. This procedure is sequentially repeated until the interval for highest steam pressure level. Flowrates at the higher levels are determined from the flowrate in the lower levels. The flowrate of steam for each expansion interval is a function of the heat load at that level and the enthalpy change to the condensate temperature at the given level. Superheated steam is condensed and supplied to downstream processes at condensate temperature of the steam.
H Q m ∆ = & & Eq 1 Where,
m& = mass flow rate
Q& = heat load for a given level
H
∆ = Enthalpy change from superheat conditions at the given level to condensate conditions at that pressure
T S 1 2’ 2 P1 P2 Real Isentropic
Isentropic efficiency calculation
It is designer’s discretion to use the most appropriate value of isentropic efficiency for the developed cogeneration targeting method presented in this paper. On the other hand, information of isentropic efficiency available in the literature can be also used. Mavromatis and Kokossis[4] developed a thermodynamic model to estimate the isentropic efficiency of single and multiple extraction turbines. Varbanov et al.[9] presented equations to determine the parameters in terms of saturation temperature. Medina-Flores and Picón-Núñez[10] modified the correlations of Varbanov et al.[9] to obtain the regression parameters as a function of inlet pressure. The regression parameters obtained by Varbanov et al.[9] from the turbine data of Peterson and Mann[11] are shown in Table 2. max , max is is W W = η − = B A W W is,max max sat T b b A= 0+ 1⋅∆ sat T b b B= 2+ 3⋅∆ Eq 2 Where, is η = isentropic efficiency is H
∆ = isentropic enthalpy change
3 2 1 0, , , , ,B b b b b A = Regression coefficients sat T
∆ = Inlet pressure of the steam
Table 2: Regression coefficients for single extraction turbines[12]
Single extraction back pressure turbines
Wmax< 2 MW Wmax>2 MW
0
The results are investigated with STAR®, which is Process Integration software for the design of utility systems for a single process or a group of processes involving power (electricity) and heat (steam) generation, and associated heat exchanging and distributing units. The design procedure of utility systems in STAR® requires information about steam flowrates, heat supply and loads, VHP (very high pressure) steam specification (e.g. VHP steam generation capacity and temperature at the outlet of the boiler). At the initial targeting stage, some of these design parameters are not known. The parameters, such as flowrate from the boiler, steam level conditions, have to be specified for the detailed design in STAR®. The information required for the calculation of cogeneration potential from the utility systems is current flowrate of steam generated, maximum and minimum flow rates of equipment, thermodynamic model and efficiency of steam turbines, steam demand and surplus for each steam main, superheat condition of steam generated from the boiler, etc. STAR® has two models isentropic and THM model for the calculation of power generation of steam turbine in the detailed design, while it uses TH and THM model for cogeneration targeting.
3 Optimization of steam levels
As explained before, the choice of steam level in the design of site utility systems are critical to ensure cost-effective generation of heat and power, and its distribution in the site. In a new design, pressures of steam level can be readily optimized. However, for the retrofitting of existing systems, opportunities for the change of steam level conditions are limited. The mechanical limitation for the steam mains limits a significant increase in steam pressure. However, long term investment with a proper optimization of the steam levels may be economically
1 b (MWoC-1) 0.00108 0.00423 2 b 1.097 1.155 3 b (oC-1) 0.00172 0.000538
viable in spite of the fact that the short term investment can not be justified[13]. VHP steam generation in the boiler and hence the fuel costs in the utility boilers can be decreased by increasing number of steam mains which increases the heat recovery potential. Number of steam mains has a significant impact on the cogeneration potential. Therefore, to minimise fuel cost with maintaining high cogeneration potential, the design should be thoroughly investigated.
Optimization model
In this study, the optimisation framework for determining the cost-effective conditions of steam mains for the site utility systems had been proposed with incorporating new cogeneration targeting method proposed in the work. The optimisation model is formulated in an NLP (non-linear programming) problem and the details of models are as follows:
Objective Function
The objective function is to minimize the amount of hot utility to be supplied from the steam generation unit (e.g. boiler). It should be noted that the method presented in this paper is generic for taking different objective functions, for example, overall fuel cost, operating profit, etc, as long as the relevant cost parameters are available.
minimise Hshiftedsink,VHP −Hheatsource,VHP
VHP k shifted
H sin , Enthalpy of shifted heat sink for VHP
VHP source heat
H , Enthalpy of heat source for VHP
Optimization Variables
i
P Pressure at i∈Steam levels (VHP, HP, MP, LP)
Four steam mains are used in the current optimisation model, as this is most common in the large-scale industrial plant, while different number of steam
mains, for example, three levels (HP, MP and LP), can be considered based on needs and operating characteristics on the plant.
Constraints
Total source and sink profiles are generated from stream data of the site. Design procedure for manipulating stream data to generate the site profiles is not a part of this study and those details can be found from Smith [13] and Klemes et al, [14]. In order to maintain feasibility of heat recovery across steam mains, constraint between sink and source site profiles is needed. First, the sink is shifted until the enthalpy of heat source at either of steam levels is the same as the enthalpy of heat source corresponding to the pinch point, and then enthalpy difference at each steam levels is always greater than zero.
0
, ,
sinki− heatsourcei ≥
shifted H
H i∈Steam levels (VHP, HP, MP, LP)
Mass balance
The mass flow rate of steam between steam levels is given:
j j k j j i H Q m m ∆ + = → → & & & Where, j i
m& → Mass flow rate of steam through turbine between i and j steam levels
k j
m& → Mass flow rate of steam through turbine between j and k steam levels
j
Q& Heat duty at j steam level
j
H
∆ Enthalpy extracted by process from superheated steam at j level to reach condensate conditions
Power is calculated base on the new design algorithm as shown in Figure 1.
Figure 3 shows the model for the determination of optimal steam pressure levels for a site utility system. The change in the steam pressure levels shifts the site sink and surplus profiles along with heat demand and supply. Cogeneration
potential for the site composite is calculated from the new algorithm. The process is repeated until optimum pressure levels corresponding to minimum value of objective function are found for the site.
Figure 3: Flowchart to determine optimum steam pressure level
Case Study Cogeneration potential
An illustrative case study is used to test the different methodologies. The four steam levels considered in this example are very high pressure (VHP), high pressure (HP), medium pressure (MP), low pressure (LP) at 120, 50, 14 and 3 bar(a) respectively. The heat demand at HP, MP and LP steam levels is 50, 40 and 85 MW respectively. The efficiency of the boiler is assumed to be 100% for the simplicity, which can be updated, according to boiler data available, and it is supplying steam at a temperature of 575oC. Water supplied to the boiler and the condensate returns are both assumed to be at a temperature of 105oC.
In this work, cogeneration targeting methods have been applied to the case studies with only back pressure turbines. However, it can be easily extended to condensing turbines. One of the additional constraints on condensing turbine is a maximum wetness permitted at the exhaust. Wetness factor in the condensing turbine can be controlled by adjusting the superheat in the steam mains, as similary treated in the consideration of degree of superheat in LP steam.
New steam level pressure
Calculate shifted sink and source profiles & heat surplus or deficit at each steam level
Cogeneration potential calculation from new algorithm
Minimum Utility requirement Optimum Pressure
Table 3: Problem Data Parameters VHP HP MP LP Pressure (bara) 120 50 14 3 Saturation Temperature (°C) 324.7 264 195.1 133.6 Heat Demand (MW) 0 50 40 85
The isentropic efficiency was calculated as given in Equation 2, while the mechanical efficiency was assumed to be 100%.
TH Model: The shaftpower targets from TH method are shown in Table 4Error! Reference source not found.. The overall shaftpower calculated from TH model is 33.02 MW. The value of conversion factor (CF) is assumed to be 0.00135.
THM Model: The targets for the three sections VHP-HP, HP-MP and MP-LP for THM model are 9.4, 4.7 and 0 MW respectively (Table 4Error! Reference source not found.). The overall shaftpower target from THM model was 14.2 MW.
Sorin’s Methodology: The work in the bottom section is used to calculate the heat load in subsequent top section as described in the methodology in the previous section. Shaftpower targets for VHP-HP, HP-MP and MP-LP of 18.2, 14.46 and 8.77 MW are shown in Table 4Error! Reference source not found..
New Method
Error! Reference source not found. Table 4 shows the shaftpower targets for VHP-HP, HP-MP and MP-LP sections of 14.99, 14.37 and 9.75 MW respectively. The main difference between the new method and existing TH and THM model is the calculation of superheat temperature for each steam main, as explained previously. Superheat temperature of the outlet LP steam should be greater than saturation temperature of LP steam to avoid condensation of vapour at the outlet
of turbine and thereby reduced performance and efficiency. The amount of superheat in VHP steam determines the superheat in LP steam. In the new algorithm, the superheat in VHP steam from the boiler is a variable and is adjusted by trial and error to ensure the superheat in LP steam.
Figure 4: Results of the new method
STAR® Simulation – Constant Isentropic Efficiency
Once the steam levels and the heat surplus and deficit are known, a detailed design procedure is used for the optimal design of the utility systems or to find out the optimum operating conditions for an existing design. However, as discussed before, the detailed design requires some additional parameters such as flowrates and superheat steam temperatures. These additional parameters are specified by trial and error. STAR® was used to test the targeting potential against the actual production from the steam turbine. The shaftpower was calculated by the isentropic model with isentropic efficiency calculated as shown in Equation 2. The utility systems consist of a boiler supplying VHP steam at 575oC. The steam is passed from the boiler to the higher pressure steam main to lower pressure steam main, via a steam turbine. Any unused steam can be passed through the vent. The process cooling and heating duty at each steam
VHP Supply Qusage = 85 MW Qusage = 40 MW Qusage = 50 MW Heat Demand (MW) VHP HP MP LP S a tu ra ti o n t e m p er a tu re ( C ) 14.99 MW 14.37 MW 9.75 MW 248.29 t/h 185.89 t/h 130.7 t/h
main level is specified as given in Figure 3Error! Reference source not found.. The overall turbine shaftpower is 39.12 MW.
Comparison of Cogeneration Targeting Results
Table 4Error! Reference source not found. shows a comparison of cogeneration targeting results from Sorin’s methodology, new method, TH and THM model in STAR®. A detailed design simulation in STAR® with the constant isentropic method is used to compare the shaftpower targets from the different methodologies. As shown in Table 4Error! Reference source not found. the total power target of 41.43 MW from Sorin’s methodology is significantly different from the detailed design procedure of 39.0 MW with an error of 6.2%. The shaftpower target obtained from TH model of 33.02 MW is 15.3% different from the shaftpower obtained from the detailed design procedure. Similarly, THM model target is 63.85% different from the actual shaftpower from the detailed design procedure. These discrepancies in the shaftpower targets are due to the assumptions used in these models. The shaftpower target obtained from the new method of 39.12 MW is only 0.31% different from the detailed design procedure in STAR®.
Table 4: Comparison of cogeneration targeting results
Optimization of steam levels
Site data was taken from an example available in the literature [15]. Site sink and source profile is shown in Figure 6Error! Reference source not found.. Four steam mains are available at very high pressure (VHP), high pressure (HP), low pressure (LP) and medium pressure (MP) respectively. Sink profile is shifted by the minimum of the enthalpy difference between the source and sink, which identifies site pinch point for the utility system.
0 50 100 150 200 250 300 -500 -400 -300 -200 -100 0 100 200 300 400 Enthalpy (MW) T e m p e ra tu re ( o C ) Sink Source Shifted Sink Profile
Figure 6: Sink and source profiles for a given site
The site utility grand composite curve (SUGCC) plots the difference between the hot and the cold composite curves as shown in Figure 7Error! Reference source not found.. The heat generation and use at individual steam level is
Methodology Total (MW) VHP-HP (MW) HP-MP (MW) MP-LP (MW) Sorin’s methodology 41.43 18.2 14.46 8.77 New Method 39.12 14.99 14.37 9.75 TH Model in STAR® 33.02 14.35 11.62 7.06 THM Model in STAR® 14.1 9.4 4.7 0
STAR® Simulation – Constant Isentropic Efficiency
shown in Figure 7Error! Reference source not found. Error! Reference source not found. and Error! Reference source not found. plot the cogeneration potential between different steam levels as expansion zones for steam turbines. The power output for these zones for the optimized case, based on the new algorithm, is found to be 7.69 MW.
0 50 100 150 200 250 300 350 400 0 20 40 60 80 100 120 140 160 180 200 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 7: Site Utility Grand Composite Curve with the optimum steam levels
0 50 100 150 200 250 300 350 400 0 10 20 30 40 50 60 70 80 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 8: Site Utility Grand Composite Curve with cogeneration areas
0 50 100 150 200 250 300 350 400 -500 -400 -300 -200 -100 0 100 200 300 400 Enthalpy (MW) T e m p e ra tu re ( o C ) Sink Source
0 50 100 150 200 250 300 350 400 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 10: Site profile with cogeneration potential area
The objective function is the minimization of the utility cost. The hot utility is supplied as VHP steam from the boiler. The optimization framework described in previous section and the model calculations are performed in Microsoft Excel®. The size of the model and the optimization problem is small and therefore solver function in Microsoft Excel® can be effectively used for the minimization of the utility cost. The number of steam levels has been assumed constant as four corresponding to VHP, HP, MP and LP respectively. Steam pressures at each level are the design variables. They affect both the level of heat recovery and the cogeneration potential, via the steam turbine network[13].
Table 5Error! Reference source not found. shows the base case conditions for the four steam levels. Optimum steam level pressure and temperature along with heat load at each level is shown in Table 6Error! Reference source not found.. The optimum pressure in the steam mains for the lowest utility cost are 180, 46.55, 12.26 and 2.25 bar in the VHP, HP, MP and LP steam loads respectively. The minimum VHP steam generation required from the boiler is 70.22 MW, while the VHP steam flowrate requirement from the boiler is 88.16 t/hr. Steam generation required at VHP mains has been reduced from 105.20 MW to 70.22 MW for the optimized case. However, the cogeneration potential reduced from 8.8 MW for base case to 7.67 MW for the optimized case. Therefore, increasing the heat recovery reduces the steam generation from the boiler as well as the cogeneration potential for this particular example. If power
generation in the site should be increased, then additional VHP steam is generated to pass through steam mains.
Table 5: Base case steam levels[15]
Pressure (bar) Temperature (oC) Heat Load (MW) Saturation temperature (oC)
180 625 105.20 357.14
50 458.74 137.01 264.09
10 322.1 125.29 180.04
2 143.63 81.98 120.36
Table 6: Optimized steam levels
Pressure (bar) Temperature (oC) Heat Load (MW) Saturation temperature (oC)
180 625 70.22 357.14
46.65 449.21 113.45 259.79
12.26 308.08 107.57 189.09
2.25 214.48 55.34 124.10
This optimisation framework can be extended to accommodate other economic scenarios (e.g. to minimise the fuel costs with maintaining the same cogeneration potential) or practical constraints (e.g. the number of steam levels allowed).
4 Technology for utilization of low Grade heat
Low grade heat source can be very useful to provide energy to the heat sink by upgrading low-grade energy (e.g. low pressure steam). The upgrade of low grade heat can be carried out by heat pump, absorption refrigeration, thermo compressor, etc, by recovering and/or upgrading waste heat from various sources (e.g. gas turbine exhaust) and utilising them with the wide range of applications (e.g. drying and boiler feedwater heating).
4.1 Vapour compression heat pump
Heat pump transfers the low grade heat at the lower temperature to higher temperature heat by the compressor. Heat pump has been used in petroleum refining, and petrochemicals, wood products, pharmaceuticals, utility system etc. [16]. Figure 11 shows a typical closed cycle heat pump. The heat from lower temperature source is transferred to the working refrigerant in the evaporator. Electric or mechanical energy is used in the compressor to increase the pressure
of the vapour from the evaporator. High grade heat at higher temperature is released from the condenser. Pressure of the vapour is reduced by throttle valve to lower its temperature and convert it to liquid to exchange heat with low grade heat source. The main issue with the utilization of the heat pump is that it uses expensive external energy to convert low grade heat into high grade heat. In general, one unit of high grade electrical energy can produce 2-4 units of high grade thermal energy.
Figure 11: Heat pump cycle [17]
Co E Q Q COP= Eq 3 Where,
COP = coefficient of performance
E
Q = Heat received at low temperature by the evaporator
Co
Q = Electric power supplied in the compressor
4.2 Absorption Systems
Low grade heat can be recovered by absorption with three different types of equipments absorption refrigeration, absorption heat pump and absorption
Condenser
Compressor Prime Mover
Evaporator
Heat from lower temperature source
Throttle valve
Mechanical work input
transformers respectively. Iyoki and Uemura [18] compared the performance of absorption refrigeration, absorption heat pump, and absorption transformer for water-lithium bromide zinc chloride calcium bromide system.
a) Absorption refrigeration – There has been extensive work in literature on absorption refrigeration system, with both experimental [19] and simulation studies [20, 21] to determine the performance of absorption refrigeration. A schematic diagram of ammonia-water absorption refrigeration cycle is shown in Figure 12. Ammonia vapour at high pressure transfers heat to neighbourhood in the condenser. Liquid ammonia from the condenser is passed through an expansion valve to reach the evaporator pressure. Heat is transferred from the low temperature heat source to convert liquid ammonia to vapour state. Ammonia vapour is absorbed by a weak solution of water and ammonia to form a concentrated solution of ammonia-water at the bottom of absorber. This concentrated solution is passed to the generator for the production of ammonia vapour while the lean solution from the generator is passed back to the absorber unit. Low grade heat is used in the generator for the production of ammonia vapour. Lean ammonia solution from the generator exchanges heat with the high concentration ammonia solution from the absorber.
The coefficient of performance for an absorption refrigeration system is defined as the ratio of heat removed from the evaporator to heat supplied in the generator. G E Q Q COP= Eq 4 Where,
COP = coefficient of performance
E
Q = Heat received at low temperature by the evaporator
G
Q = High temperature heat used in the generator
b) Absorption heat pump – A single stage absorption heat pump consists of a generator, absorber, evaporator, condenser and heat exchanger. High grade heat is supplied at higher temperature to the generator to separate the refrigerant from the solution. Low grade waste heat is supplied to the evaporator, while medium temperature heat is released from the condenser. Thermal energy at higher temperature is used to convert low grade heat into high grade heat.
Coefficient of performance of an absorption heat pump is the ratio of heat removed from the medium temperature heat removed form the absorber and condenser to the high grade heat supplied in the generator.
G C A Q Q Q COP= + Eq 5 Where,
COP = coefficient of performance
A
Q = Heat released by the absorber
C
Q = Heat released by the condenser
G
Q = High temperature heat used in the generator
c) Absorption heat transformer – The basic schematic diagram of absorption heat transformer is shown in Figure 13. Absorption heat transformer consists of
the same units as absorption heat pump. However, the main difference is that evaporator and absorber are maintained at a higher pressure, while in absorption pump they are at a lower pressure. Low grade heat is used in the generator and evaporator to produce heat at higher temperature in the absorber. The process can be described briefly as follows: High pressure refrigerant vapour from an evaporator is absorbed into the lean refrigerant absorbent solution in the absorber. High pressure strong solution of refrigerant absorbent is passed via a throttle valve to reduce the pressure. This solution exchanges heat with weak solution from a generator, before it reaches the generator. Low temperature heat in the generator is used to separate the refrigerant from the solution. Refrigerant vapour from the generator is condensed in a condenser. The refrigerant is subsequently pumped to higher pressure where it gains heat at low temperature to convert into vapour.
Figure 13: Absorption heat transformer (Ammonia water)
The ratio of high temperature heat from the absorber to the low grade heat supplied in the generator and evaporator is defined as the coefficient of performance of absorption transformer.
E G A Q Q Q COP + = Eq 6 Heat Exchanger Absorber Evaporator Generator Condenser
Where,
COP = coefficient of performance
A
Q = Heat released by the absorber
E
Q = Heat consumed in the evaporator
G
Q = High temperature heat used in the generator
4.3 Boiler feed water (BFW) heating
Low grade heat can be used to increase the temperature of make-up water to reduce the fuel cost in the boiler. Additional heat exchanger capital cost is required for exchange of heat between the boiler make up water and low grade heat. The increase in temperature of make up water using low grade heat decreases the fuel consumption in the boiler.
4.4 Organic Rankine Cycle (ORC)
A Rankine cycle for extracting electricity from waste heat sources is possible with the use of organic fluids as working fluids. Efficiency of operation of Rankine cycle depends on conditions of the cycle and working fluid. A typical organic Rankine cycle consists of an evaporator, turbine, condenser and pump respectively (Figure 14). Organic fluid such as benzene, toluene, p-xylene and refrigerants R113 and R123 [22] have been used as working fluids in ORC. Working fluid vaporises by exchanging heat with low grade heat in the evaporator. Vapour is passed through turbine for generation of electricity. Vapour is condensed in condenser at lower temperature and releases heat to the outside atmosphere. Organic fluid is raised from lower pressure to high pressure in the pump. The amount of energy consumed in pumping the fluid is considerably low.
Figure 14: Organic Rankine Cycle (ORC)
Efficiency of ORC is defined as the ratio of power generated by the turbine to the low grade energy supplied in the evaporator.
E turb ORC Q P = η Eq 7 Where, ORC η = Efficiency of ORC E
Q = Heat received at low temperature by the evaporator
turb
P = Electric power generated by the turbine
4.5 Thermo-compressor
Thermo-compressor uses high pressure steam to compress low or intermediate pressure waste steam into medium pressure steam. Figure 15 shows a thermo-compressor where high pressure steam enters as a high velocity fluid, which entrains the low pressure steam by suction. The resulting mixture is compressed and discharged as a medium pressure steam from the divergent section of the thermo-compressor. The main advantage of thermo compressor is high reliability and less compression power requirement.
Turbine
Pump
Figure 15: Thermo compressor1
4.6 Drying
Biomass (wood, bagasse, grass, straw, agriculture residues, etc.) have significant amount of moisture. This moisture reduces the theoretical flame temperature as a part of heat of combustion is used in evaporation of moisture from the biomass [23]. Calorific value and theoretical flame temperature from the biomass fuels can be increased by drying. Effective use of industrial waste heat in drying of biomass increases the overall efficiency of the process, leading to significantly lesser amount of fossil fuel to be burned and hence much less green house emissions.
5 Algorithm
Once the number of steam levels and their pressure has been determined by optimization in total site profiles, the performance of the system can be either optimized to obtain the best design, or to obtain the optimum operating conditions for an existing design, considering the part load performance of the equipment. The simulation and optimization of the utility systems require accurate and yet simpler model for each element of the system. Varbanov [9] and Aguillar [24] developed simple models for the equipments in the utility systems. Models developed by Aguillar [24] have been adopted for the purpose
1
of optimization which determines the optimum design (i.e. the configuration of utility systems) or operating conditions in this work (Appendix A).
The algorithm for evaluation of integration of low grade heat upgrade technologies with an existing site utility system is shown in Figure 16. The characteristics of low grade energy such as available heat load at temperatures for use in heat pump, ORC, and boiler feed water heating is obtained from total site sink and source profiles. HYSYS simulation is used to obtain the performance indicators such as COP, efficiency, purchase cost etc. for low grade heat upgrade technology. Heat load is varied for the HYSYS simulation to calculate the change in performance and purchase cost. This information is fed to the optimization framework for calculating the overall annual cost with integration of these design technologies. The optimization framework [24] is used for minimization of overall annual cost or operating cost minimization for a multiperiod operational, retrofit or grassroots design problem. Linear models have been derived for all the energy equipments so that MILP optimizers can be used for optimization to reduce the computational cost.
6 Case study
The various design options for low grade heat upgrade are evaluated with the help of a case study. The base case design is shown in Figure 17. The base design consists of four boilers each with capacity of 40 kg/s. There are four back pressure turbines for generation of electricity from VHP to HP and one back pressure turbine between HP and LP steam levels. Two multistage turbines are available for expansion of steam between HP-MP and MP-LP respectively. Four mechanical pumps having a steam turbo driver and an electric motor supply the feed water to the boiler.
Figure 17: Base case design [24]
Site data for heat load, electricity demands, pump electricity demand, condensate return and cooling water is shown in Table 7. The site operating seasons are divided into two major categories summer and winter, with 67% of year as winter. The ambient temperature, relative humidity, electricity natural gas and fuel oil price is shown in Table 8. The total number of working hours for the
site is assumed to be 8600 hrs per year. The latent heat values for fuel oil and natural gas are 45 and 50.24 MJ/kg respectively.
Table 7: Total site data - Requirements for the utility system
Units Winter Summer
Electricity demand MW 62 68
VHP steam demand MW 116.36 110.82
HP steam demand MW 30.61 21.4
MP steam demand MW 16.67 9.34
LP steam demand MW 88.54 73.62
Total steam demand MW 252.17 215.17
Condensate return % 80 80 Power Pump 1 MW 5.2 5.0 Power Pump 2 MW 1.3 1.1 Power Pump 3 MW 2.2 2.0 Power Pump 4 MW 0.6 0.6 Process CW demand MW 200 300
Table 8: Site conditions
Season Units Winter Summer
Fraction of the year % 67 33
Ambient temperature oC 10 25
Relative humidity % 60 60
Electricity prices Peak ($/kWh) 0.07 0.08
Off- Peak ($/kWh) 0.05 0.05
Peak hours /day Hrs 7 12
Fuel Oil price $/kg 0.19 0.19
Natural gas price $/kg 0.22 0.22
Raw water price $/ton 0.05 0.05
Grand composite curves (GCC) of the individual process are modified by removing the pockets corresponding to additional heat recovery within the process. These modified process GCC are then combined together to form the total site sink and source profile (Figure 18(a)). Sink profile is shifted until the source and shifted sink profile touch each other (Figure 18(b)) or the source and the sink steam generation and consumption lines touch each other corresponding to site pinch. Site utility grand composite curve (SUGCC) represents the horizontal separation between the source and the sink. Steam demand at VHP, HP, MP and LP levels are 110.8, 21.4, 9.3 and 73.6 MW
respectively. Power generation potential is represented as areas in SUGCC with VHP-HP, HP-MP and MP-LP cogeneration potential of 79.8, 58.4 and 49.1 MW respectively (Figure 18(c)). -4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C ) -4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e mp e ra tu re ( o C ) (a) (b) 0 50 100 150 200 250 0 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C ) (c)
Figure 18: Site composite curves; (a) Site source and sink composite curve (b) Site source and shifted composite curve with the cogeneration potential area (c) Site utility grand composite curve (SUGCC)
Integration of heat pump
HYSYS model heat pump
A model of heat pump has been simulated in HYSYS. It consists of four equipments evaporator (E-102), compressor (K-100), condenser (E-100) and a throttle valve (VLV-100). Refrigerant R112-a is used as a working fluid. Low grade heat is supplied in the evaporator at the temp of 115oC. High grade electric energy is used in the compressor to raise the pressure of the vapour. LP steam
is generated from the condenser at temperature of 150oC. Throttle valve is used to reduce the pressure of the vapour liquid mixture from the condenser.
Figure 19: Vapour compression heat pump
Figure 20 shows the variation of COP for heat pump system with respect to variation in the evaporator duty. COP varies within a small range from 3.24-3.31 and can be assumed to be constant for the refrigerant (R-112a) and the corresponding heat pump cycle (Figure 19). COP of 3.3, means that 1 MW of electric energy and 2.3 MW of low grade energy generate 3.3 MW of high grade energy.
3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.3 3.31 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Evaporator Duty C O P
Figure 20: COP with respect to evaporator duty
Purchase cost of heat pump
Purchase cost of heat pump is calculated as the sum of the cost of evaporator, condenser, and compressor. Purchase cost of heat pump is approximated based on a linear correlation between the cost and the evaporator duty.
B H A
PCheatpump = ×∆ eva+ Eq 8
Where,
pump heat
PC = Purchase cost heat pump
eva H ∆ = Evaporator duty (MW) A, B = Regression coefficients A = 0.1 MM$/MW B = 1.15 MM$ Purchase cost y = 0.0001x + 1.1491 0 2 4 6 8 10 12 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Evaporator duty (kW) P u rc h a s e C o s t (M M $ )
The total site source and sink profile before and after integration of the heat pump is shown in Figure 22 and Table 9. LP steam demand changes from 73.62 to 18.67 MW in summer and from 88.54 to 33.59 MW in winter. Low grade heat is extracted from the site source only till 115oC corresponding to temperature diff of 10oC in the evaporator of the heat exchanger. COP of heat pump as calculated from HYSYS simulations is 3.3. Therefore, the external electricity consumption from the site increases as shown in Table 10 from 68.82 to 85.42 MW in summer and from 62.2 to 78.8 MW in winter.
Table 9: LP steam demand before and after integration of heat pump
Summer (MW) Winter (MW)
Before heat pump 73.62 88.54
After heat pump 18.67 33.59
Table 10: Electricity demands before and after integration of heat pump
Summer (MW) Winter (MW)
Before heat pump 68.82 62.2
After heat pump 85.42 78.8
-4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 22: Site composite curve with heat pump integration
Annualized capital cost with operational optimization of the existing plant
Operational optimization of total site annual cost with the integration of heat pump is shown in Table 10. External power cost increases from 22.67 MM$ to
35.03 MM$ after integration of heat pump, while fuel cost decreases from 93.08 to 82.09 MM$. Total annual cost increases to 118.67 MM$/yr from 116.32 MM$/yr after integration of heat pump. Therefore, with these costs of fuel and electricity and the capital cost of heat pump it is not economic to set up a heat pump.
Table 11: Annual costs before and after integration of heat pump
External Power (MM$) Fuel Cost (MM$)
Before heat pump 22.67 93.08
After heat pump 35.03 82.09
Integration of Organic Rankine Cycle (ORC)
HYSYS model ORC
HYSYS is used to calculate the efficiency and the purchase cost function for ORC. ORC set up consists of an evaporator (E-100), turbine (K-100), condenser (E-101) and a pump (P-100). Benzene is used as the organic working fluid. Low grade heat at 110 oC is used to vaporize benzene at high pressures (1.145 bar). Benzene vapour is used to drive a turbine along with reduction in pressure (14.5 kPa). Vapour stream from turbine at low pressure condensed in the condenser (27oC). Pump is used to pump the low pressure organic liquid stream to high pressure (1.145 bar) before being fed to the evaporator.
Figure 23: Organic Rankine Cycle (ORC) Efficiency of ORC
Figure 24 shows the variation of efficiency of ORC with respect to evaporator duty. The efficiency of ORC is approximately constant around 11% with the variation in evaporator duty.
0 2 4 6 8 10 12 0 2 4 6 8 10 12 Evaporator duty (MW) E ff ic ie n c y
Figure 24: ORC efficiency with evaporator duty Purchase cost of ORC
Purchase cost of ORC is given as the total cost of equipments such as condenser, evaporator and turbine. The cost of the evaporator and condenser is
obtained from the online database2, while turbine cost is obtained from Peters et al. [25]. Purchase cost of ORC is approximated based on a linear correlation between the cost and the evaporator duty.
B H A PCORC = ×∆ eva + Eq 9 Where, ORC
PC = Purchase cost ORC
eva H ∆ = Evaporator duty (MW) A, B = Regression coefficients A = 0.01 MM$/MW B = 25.1 MM$ y = 1E-05x + 0.2506 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 10000 20000 30000 40000 50000 60000 70000 80000 Evaporator Duty (kW) P u rc h a s e C o s t (M M $ )
Figure 25: Linear correlation between purchase cost and evaporator duty
The total site source and sink profile after integration of heat pump is shown in Figure 26. Low grade heat corresponding to 62.11 MW is saved corresponding to a temperature of 105oC. Cold utility requirement is reduced by 62.11 MW. As shown before with the efficiency of 11%, the amount of electrical energy is reduced from 68.82 to 61.99 MW during summer and from 62.2 to 55.39 MW during winter. Purchase cost of ORC corresponding to given evaporator duty is 17.13 MM$.
-4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 26: Site composite curve with ORC integration
Table 12: Electricity demands before and after integration of ORC
Summer (MW) Winter (MW)
Before heat pump 68.82 62.2
After heat pump 61.99 55.39
Absorption refrigeration
HYSYS model of absorption refrigeration
Absorption refrigeration system (Figure 27) consists of absorber (T-101), pump (P-100), heat exchanger (E-104), generator (T-103), evaporator (E-100), and condenser (E-103). Heat is released at temperature of 32oC to the surrounding at a pressure of 13 bar in the condenser (E-103). Ammonia vapours are passed through a throttle valve (VLV-101) to reduce the pressure to 14.50 kPa before they can absorb heat from the surroundings at low temperature (-5oC) as refrigeration load in the evaporator (E-100). Ammonia vapour is absorbed with the lean solution of ammonia in the absorber (T-101). Heat is released to the surroundings from the absorber. Concentrated solution of ammonia water is pumped from 14.59 kPa to 13 bar into the generator. Low grade heat is used in the generator (T-100) to separate ammonia from the concentrated solution to produce a lean solution of ammonia water. Heat is exchanged between outgoing
lean solution of ammonia water and incoming strong solution in exchanger T-103.
Figure 27: HYSYS model of absorption Refrigeration Coefficient of performance
Low grade heat is used to provide the heat for refrigeration load for the system. The low grade heat supplied in the generator is 265.4 kW, while 67.86 kW of heat is removed as refrigeration load from the evaporator, with a COP of 0.26.
-4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 28: Low grade heat can be used for refrigeration load on site Boiler feed water heating
Low grade heat is used to raise the temperature of make up water to deaerator from 25oC to 101.3oC. This reduces the cost of fuel consumed in the boiler. The benefits of BFW heating depends on condensate recycling process and condensate management. BFW heating doesn’t change the hot utility requirement from the base case. However, the cost of fuel required to supply the hot utility required decreases from 93.08 to 80.57 MM$/yr due to decrease in the heating required for boiler feed water. The overall energy cost decreases from 117.83 MM$/yr in the base case to 107.63 MM$/yr.
-4000 -300 -200 -100 0 100 200 300 400 50 100 150 200 250 300 350 Enthalpy (MW) T e m p e ra tu re ( o C )
Figure 29: Temperature of make up water to deaerator is increased by low grade heat
Comparison of design options Techno economic analysis
Table 13Error! Reference source not found. shows the comparison between the various low grade heat upgrade options. Heat pump decreases the hot utility requirement by reducing the low pressure steam demand for the system. Hot and low utility cost in the system decreases from 93.08 to 82.09 MM$/yr and 0.98 to 0.90 MM$/yr respectively. However, heat pump increases the electricity import cost for the site from 23.77 to 36.06 MM$/yr. The overall operating cost increases from 117.83 to 119.06 MM$/yr with the introduction of heat pump. Therefore, heat pump is not economic for the current case study with the given cost of electricity and fuel. Integration of ORC decreases the cold utility requirement and therefore reduces the total utility cost from 94.06 to 94.02 MM$/yr. Electricity produced from ORC reduces the cost of electricity import from 23.77 to 20.21 MM$/yr. The total energy cost decreases from 117.82 MM$/yr in the base case to 114.23 MM$/yr for integration with ORC. Absorption refrigeration reduces the cold utility cost from 0.98 to 0.90 MM$/yr. However, the main advantage of absorption refrigeration is reduction in electricity cost in vapour compression
refrigeration by 5.46 MM$/yr. BFW heating reduces the cost of hot utility requirement from 93.08 to 80.57 MM$/yr. Total energy cost decreases from 117.83 to 106.63 MM$/yr. This corresponds to an annual savings of 9.51% in the operating cost. BFW heating is the most economical options amongst the heat upgrade technologies. However, benefits of BFW heating depends on the condensate recycle policy and condensate management.
Table 13: Techno economic evaluation of low grade heat upgrade technologies
Options Hot utility (MW) Cold utility (MW) Hot utility cost (MM$/yr) Cold Utility cost (MM$/yr) Total utility cost (MM$/yr) Electricity import (MM$/yr) Total energy cost (MM$/yr) Winter Summer Winter Summer
Base case 252.17 215.17 368 368 93.08 0.98 94.06 23.77 117.83 Heat Pump 197.23 160.23 344.11 344.11 82.09 0.90 82.99 36.07 119.06 ORC 252.17 215.17 344.11 344.11 93.08 0.94 94.02 20.21 114.23 Absorption refrigeration 252.17 215.17 344.11 344.11 93.08 0.90 93.98 23.77 117.75 BFW heating 252.17 215.17 368 368 80.57 0.98 81.55 25.08 106.63
7 Conclusions & future work
The selection of steam level conditions is important as this significantly affects heat and power management for the industrial site. A new cogeneration targeting model has been developed in this work, as existing models have been shown to give misleading results, compared to detailed design procedure. This new model is based on isentropic expansion and the results obtained from the new model have been shown to agree well with the results from the detailed isentropic design method simulated in STAR®. The new method has been incorporated in the optimisation study which systematically determines of the levels of steam mains at minimum utility requirement.
Multiple options such as heat pumping, CHP, integrated gas turbines, absorption refrigeration, drying, etc, are available for upgrading low grade heat. Heat pump can reduce the LP steam requirement and subsequently the fuel consumed in the boiler. However, electrical consumption in the site increases with the integration of heat pump. The overall operating cost increases with the heat pump for the current case study for the current ratio of fuel to electricity price.
ORC decreases the annual operating cost for the total site by reducing the electricity demand from the site. Absorption refrigeration only reduces the demand of cold utility. However the major savings comes from reduction in the electricity demand for an existing vapour compression refrigeration system on the site. Heating of boiler feed water decreases the fuel consumption in boiler and hence the overall operating cost of the site. In conclusion BFW heating the optimum option for integration with the total site in this case study. However, the best heat upgrade technology is dependent on the site fuel and electricity cost, condensate management system, and characteristics of low grade heat (quality and size). The developed methodology will be applied to further extended to other case studies. Integration of renewable energy sources such as solar, wind, geothermal etc to the total site will be considered in future work. The variation in renewable energy sources will be incorporate to the framework. The transfer of low grade heat across the fence for neighbourhood integration will be considered in future work. The cost benefit of over the fence process integration needs to be evaluated.
Acknowledgement
Financial support from Research Councils UK Energy Programme (EP/G060045/1; Thermal Management of Industrial Processes) is gratefully acknowledged.
References
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8 Appendix A
8.1 Optimization framework
8.1.1 Objective function
The present work used overall operating cost along with annual capital cost for the new design heat upgrade technology as the minimization function.
(
FuelCst PowCst WatCst EmmCst)
F FixOpCstOpCst op cst + ⋅ + + + = Eq 10
Where,
op cst
F Factor to increase operating cost by a percentage (fraction)
OpCst Overall annual operating plant cost (MM$/yr)
FuelCst Overall fuel cost for the site utility system (MM$/yr)
PowCst Overall electricity cost for the site utility system (MM$/yr)
WatCst Overall water cost for the site utility system (MM$/yr)
EmmCst Overall emission cost for the site utility system (MM$/yr)
FixOpCst Fixed charge for operating cost (MM$/yr)
Capital cost for any additional unit is defined as a function of the purchase cost (PurCstn) for each piece of equipment.
fix n
n inst
cepci F PurCst Cap
F CapCst + ⋅ ⋅ =
∑
Eq 11 Where, cepciF Chemical engineering plant cost index
inst
F Installation factor to consider other plant expenses
fix
Cap Fixed capital cost for the whole plant (MM$)
n
PurCst Purchase cost for n equipment unit (MM$)
Total cost for the whole site is given by the following expression
ann F CapCst OpCst TotCst = + ⋅ Eq 12 Where,
TotCst Total annualized cost (MM$/yr)
