Matlab program computes thermal efficiency of fired heater

Two basic methods are normally employed for the calculation and estimation of the thermal efficiency of fired heaters, viz. the direct and the indirect methods, where the net calorific value is used in the former and the gross calorific value is used in the latter. Two Matlab programmes based on these methods were written and applied for the calculation of the thermal efficiency of a crude oil heater. The results are presented in the form of Sankey diagrams.


Introduction
The thermal efficiency of fired heaters is an important performance factor, particularly in view of the current trend of rising fuel costs.The successful design and operation of a fired heater must aim at the highest possible thermal efficiency with due regard to other performance and pollution considerations.On operating fired heaters, thermal efficiency is one of the most significant parameters that must be closely monitored by plant personnel.
Furnace thermal efficiency [1] is usually defined as the percent ratio of the total heat absorbed in a furnace to the total heat input, where the heat absorbed is calculated from the difference between the heat input and heat losses comprising both stack heat losses and radiation heat losses.The total heat input is the sum of the calorific value of the fuel (gross or net) and the sensible heat of all incoming streams including the combustion air, fuel and atomization steam (if used).The usual European practice is to calculate the thermal efficiency using the net or lower calorific value, while in the U.S.A. the calculation is mostly based on the gross or higher calorific value.Efficiency = 100 × (Total heat input -Stack heat losses -Radiation heat loss) Total heat input Radiation heat losses through furnace walls depend on the material composing the insulating refractory lining and its thickness.However, for an economically optimum insulating lining these losses are low.For furnaces of 10 MW or more, they range from 2 to 5% of the lower heating value.Radiation heat losses depend also on the size of the furnace, where greater heat losses are to be expected in small furnaces as the ratio between the walls area and the volume of the radiation section decreases with furnace size increase.Heat losses are for the most part due to the hot flue gases discharged through the stack.They are a function of the flue gas flow rate and temperature.The flue gas flow rate increases with excess air, so the furnace should operate with the least possible excess air while ensuring at the same time complete combustion of the fuel.Operation with too little excess air may lead to unburned fuel losses that may be greater than the efficiency gained by reducing the excess air.Incomplete combustion is undesirable not only on account of calorific value loss, but also because of fouling problems often associated with the unburnt fuel.
Flue gas temperature, on the other hand, is the main factor in furnace heat losses, and the thermal efficiency may be greatly improved if the flue gases are cooled before being discharged from the chimney.In order to cool the flue gases, a cold fluid must be available that needs to be heated.Flue gas cooling is limited, however, by corrosion problems caused by sulphuric acid condensation due to the presence of sulphur compounds in the fuels burned [2].If the flue gases are cooled, excess air will no longer have any importance since all the heat transferred to the excess air will be recovered from it.If the fluid to be heated is at a temperature that is too high to give a sufficiently low flue gas temperature, i.e. a satisfactory thermal efficiency, either one of these two solutions may be used: (1) Steam production, which does not reduce fuel consumption, but is advantageous if the steam can be exploited, (2) Recycling the flue gas and utilizing its heat for preheating the combustion air.Preheating the combustion air allows a thermal efficiency of approximately 90% of the net calorific value, but this requires an air blower.

Methods for efficiency calculation
There are two main methods for determining efficiency: the input-output or direct method [2,3] and the heat-loss or indirect method [4,6].In the input-output method, which is based on the ratio of useful output (heat absorbed by the heated fluid) to the heat input (i.e.fuel), accurate measurements of quantities of fuel, steam, air, fuel calorific value and flue-gas analysis are required.This is quite an elaborate procedure, where a couple of days may be required to stabilize the unit and ensure reliable readings.
The amounts of heat per unit U of fuel (weight (kg) or volume (m 3 )) are as follows: Heat In: Combustion air: H air = sensible heat of air kJ/U = Cp air ×(t comb -15) Fuel atomization fluid (for liquid fuel when applicable): H f luid = sensible heat of atomization fluid kJ/U = Cp f luid ×(t f luid -15) Therefore, the total heat input is the sum of the fuel NCV and the sensible heat of air, fuel and fuel atomization fluid (for liquid fuel when applicable).Namely:

Heat Out:
Heat duty = heat absorbed by the heated fluid = Q u kJ Flue gases: The sensible heat of flue gases is determined from a summation of the enthalpy values for flue gases produced /unit of fuel, a step which would require the calculation of the flue gas components /unit of fuel.H f luegases = Sensible heat of flue gases kJ/U = Cp f luegases ×(t g -15) The flue gases are: kJ/U Losses through fired heater walls ,Q losses The radiation heat losses, Q losses /kg of fuel is determined by multiplying the NCV by radiation loss expressed as a percentage.Generally this loss is between 2 and 5%. Q In general, the total heat output is the sum of the sensible heat of flue gases and the losses through fired heater walls.
The useful energy or heat absorbed Q u by the heated fluid can be written as: Therefore, the thermal efficiency of fired heater can be written as: The molar Heats at constant pressure for air and flue gases are given in Table 1 [7]: Tab. 1. Molar heats at constant pressure for air and flue gases: The main advantages of the direct method can be summarized in four points, namely: 1 It is a quick and easy method for assessing the efficiency of fired eaters.
2 It requires few parameters for computation.
3 It needs few instruments for monitoring 4 It makes it easy to compare evaporation ratios with benchmark figures.
Its disadvantages on the other hand are that there is no breakdown of losses by individual streams, and no clues are provided as to why the efficiency of the system is lower.

The Indirect Method for determining the fired heater efficiency
The indirect method, also called the heat loss method, is based largely upon the direct method in the sense that all inputs are calculated, and from this certain percentages of losses occur in combustion, radiation, flue gas etc, which can be subtracted from the total of 100%.With this method it is possible to gain insight where the losses in efficiency occur and then be able to reduce these losses to increase the efficiency .The efficiency can be calculated by subtracting the heat loss fractions from 100 as follows: The ASME Power Test Code heat method is used to determine the losses, the features of which are [5]: Efficiency is computed on both GCV and NCV basis.Effect of relative humidity is considered.Heat loss can be inputted if known Unaccounted-for losses also can be inputted.Up to 19 constituents can be handled if gaseous fuel is used.
Only the fuel analysis need be inputted, the calorific values and flue gas analysis are computed.
If the duty by the fluid is given, the total fuel, air and flue gas quantities are obtained.
Various losses are itemized on GCV basis.The data required for the calculation of fired heater efficiency using the indirect method are: Ultimate analysis of fuel (H, O ,S ,C, N), moisture content and ash content.
Percentage of oxygen or CO 2 in flue gas.Flue gas temperature.Ambient temperature and humidity of air in kg/kg of dry air GCV of fuel Percentage of combustible in ash (in case of solid fuels) GCV of ash (in case of solid fuels) A detailed procedure for calculating fired heater efficiency using the indirect method is given below [4,5,6]. Step Step 3: Calculate actual mass of air supplied /kg of fuel (AAS) AAS = (1+EA/100)×theoretical air Step 4: Estimate all heat losses: The following equations are used to determine the losses in a fired heater after combustion calculations are performed.Poor design or combustion results in a lot of unburned fuel, especially coal, to go along with ash to the bottom of the heater or to be carried away with flue gases.This is normally nil for oil and gaseous fuels, but for coals it varies from 0.25 to 1.0%.However, field data from similar units give good guidance.
3 Loss due to radiation, L 6 : Since it is impossible to prevent any insulated surface from radiating energy to a lowertemperature source such as ambient air, some losses are inevitable.Heater surfaces, although insulated, are 15 to 25 o C above ambient temperature.ABMA has published a chart that gives the radiation losses [5].
4 Unmeasured losses, L 7 : Each manufacturer must take care of certain normally unmeasured losses.CO formation leads to some losses, though low.Ash in the ash pit and flue gases is heated to the temperature at the pit and the stack temperature respectively by the energy in the fuel, which is a loss.
If CO is formed instead of CO 2 , it is a loss of 24,656 kJ/kg.This is the difference between the heat of reactions of : C + O 2 → CO 2 and C + 1 / 2 O 2 → CO.Loss due to CO formation L 6 is given by: The thermal efficiency can be calculated by substracting the heat loss fractions from 100 as follows: Efficiency of furnace (fired heater) E =100-(L1+L2+L3+L4+L5+L6+L7) The main advantage of the indirect method is that a complete mass and energy balance can be obtained for each individual stream, which makes it easier to identify options to improve fired heater efficiency.Its disadvantages include the time consumed and the laboratory facilities required for analysis.
The Sankey Diagram and its Use [9,10]: Sankey diagrams summarise all the energy transfers taking place in a process.The thicker the line or arrow, the greater the amount of energy involved.
Sankey diagrams are widely used in technology where material and energy balances have to be visualized.The flow rates and quantitative relations of a process can thus be visually created.The end result is thorough understanding of all the process steps and their interrelationship.Sankey diagrams have proven to be an outstanding tool in environmental technology projects for analyzing material and energy related problems.
The sankey diagram is a very useful tool for representing an entire input and output energy flow in any energy equipment or system such as boilers, fired heaters and furnaces after carrying out energy balance calculation.
The first consideration for the preparation of the diagram is to determine its basis.Typically a basis is selected as the flow rate of the quantity under consideration, such as the fuel input.Later, the flow streams are drawn where two parallel lines whose distance apart is proportional to the flow rate represent a stream.

Application of the above described methods:
Using computer programmes greatly simplify the procedure for the computations involved in both methods for thermal efficiency calculation.Some computer programmes are available in the literature [8], written in Basic, but no programmes exist in other more advanced computer languages.In this paper, two programs written in Matlab [11] are given for the calculation of heater efficiency based on the two methods available for its calculation, the direct and the indirect methods.The first program (Appendix 1), based on the indirect method, may be used to calculate all heat losses and the thermal efficiency for all types of fuel.The second programme (Appendix 2) is based on the direct method and may be used to calculate complete energy balance for all types of fuel also.
Two examples are given below in order to illustrate the use of the programmes.

Example 1
Liquid fuel is fired with 40% excess air in a fired heater .Ambient temperature =15 • C , exit gas temperature = 446 Flue gas temperature : 446˚C Running the program.In the RUN mode, the screen asks for the selection of the type of fuel used in the heater.To select fuel oil, INPUT (a =1) for the selection of fuel oil and INPUT (a=2) for selecting fuel gas.
For fuel oil, the screen asks for data as shown in Table 1.The results are shown in Table 2.
For fuel gas, the screen asks for data as shown in Table 3 .The results are shown in Table 4.

Example 2
Fuel gas is fired with 25% excess air in a fired heater.Ambient temperature =15˚C , exit gas temperature =446˚C and relative humidity is 40% Heater name: Crude oil heater.Type: Horizontal, box-type .Service: Heating of crude oil for distillation.Fuel: Natural gas .For both types of fuel, the energy balance for the entire system is summarized in Sankey diagrams (Fig. 1 for fuel oil and Fig. 2 for gas oil).The values are shown as percentages of the total energy released by the combustion of the fuel in the furnace.

Conclusions
This paper presents a review of the methods used in the calculation of the thermal efficiency to predict fired heater efficiency.
The paper is divided into two parts.The first part concentrates on a description of thermal efficiency methods, with special attention given to the direct method, and how to prepare a Sankey diagram in order to determine energy balance (input and output heat) for fired heaters, the thermal efficiency is then calculated .
The second part deals with the indirect method for calculating the thermal efficiency of fired heaters, for which a basic program was previously written and published [8].In this paper a Matlab programme is written for both the direct and the indirect methods.Nowadays, programming by Matlab is widely used in all scientific fields and in engineering sciences in particular.
However, the use of the direct method to calculate the thermal efficiency is to be preferred due to its many advantages.It also requires no laboratory facilities or analysis.Furthermore, the time required for the computations involved is much less than that for the indirect method.

Fig. 1 .
Fig. 1.Sankey diagram for the energy balance of a fired heater, where fuel oil is used.

Fig. 2 .
Fig. 2. Sankey diagram for the energy balance of a fired heater, where fuel gas is used

1
Dry gas loss, L 1 =100×M dg ×0.96×(t g -t a )/GCV %endenumerate Where: M dg = mass of dry products of combustion/kg of fuel)+(mass of N 2 in fuel on 1 kg basis )+(mass of N 2 in actual mass of air supplied) 2 Percentage heat loss due to evaporation of moisture present in fuel.=100×1.88×humidityfactor ×AAS× (t g -t a )/GCV 2 Unburned fuel loss, L 5 : This is a figure based on experience, excess air used, type of furnace, burner design, unit size, etc.