Introduction and Methods of Calculation (2024)

It is a well known fact that the initial cost of boiler is a small part of total costs associated with the boiler over its lifetime. In the operational life of a boiler, major costs arise out of the fuel costs. Ensuring efficient operation of boiler is critical to optimize the fuel costs.

It is not always true that a boiler will work at its rated efficiency. Almost all the times, it has been found that the boilers operate at much lower than the rated efficiencies if proper efficiency monitoring is not done.


Boiler Efficiency

Boiler efficiency is a combined result of efficiencies of different components of a boiler. A boiler has many sub systems whose efficiency affects the overall boiler efficiency. Couple of efficiencies which finally decide the boiler efficiency are :

  1. Combustion efficiency
  2. Thermal efficiency

Apart from these efficiencies, there are some other losses which also play a role while deciding the boiler efficiency and hence need to be considered while calculating the boiler efficiency.


Combustion Efficiency

The combustion efficiency of a boiler is the indication of burner’s ability to burn fuel. The two parameters which determine the burner efficiency are unburnt fuel quantities in exhaust and excess oxygen levels in the exhaust. As the amount of excess air is increased, the quantity of unburnt fuel in the exhaust decreases. This results in lowering the unburnt fuel losses but elevating the enthalpy losses. Hence, it is quite important to maintain a balance between enthalpy losses and un burnt losses. Combustion efficiency also varies with the fuel being burnt. Combustion efficiency is higher for liquid and gaseous fuels than for solid fuels.


Thermal Efficiency

The thermal efficiency of a boiler specifies the effectiveness of the heat exchanger of the boiler which actually transfers the heat energy from fireside to water side. Thermal efficiency is badly affected by scale formation/soot formation on the boiler tubes.


Direct and Indirect Boiler Efficiency

The overall boiler efficiency depends on many more parameters apart from combustion and thermal efficiencies. These other parameters include ON-OFF losses, radiation losses, convection losses, blow down losses etc. In actual practice, two methods are commonly used to find out boiler efficiency, namely direct method and indirect method of efficiency calculation.


Direct efficiency

This method calculates boiler efficiency by using the basic efficiency formula-

η=(Energy output)/(Energy input) X 100

In order to calculate boiler efficiency by this method, we divide the total energy output of a boiler by total energy input given to the boiler, multiplied by hundred.


Calculation of direct efficiency-

E= [Q (H-h)/q*GCV]*100

Where,

Q= Quantity of steam generated (kg/hr)

H= Enthalpy of steam (Kcal/kg)

h= Enthalpy of water (kcal/kg)

GCV= Gross calorific value of the fuel.


Indirect Efficiency

The indirect efficiency of a boiler is calculated by finding out the individual losses taking place in a boiler and then subtracting the sum from 100%. This method involves finding out the magnitudes of all the measurable losses taking place in a boiler by separate measurements. All these losses are added and subtracted from 100% to find out the final efficiency. Blow down valve is kept closed during the procedure. This method should be implemented as per the norms provided in BS845 standards. The losses calculated include stack losses, radiation losses, blowdown losses etc.


Comparison of direct and indirect efficiency

Both the methods of finding out boiler efficiency mentioned above have some advantages and some disadvantages associated with them. The greatest advantage of indirect method is that it also speaks about the sources of losses. By finding out indirect efficiency, one can come to know where the losses are increased and can be reduced. On the other hand, direct efficiency values are closer to reality as compared to indirect efficiency on account of uncovered losses such as radiation losses, ON-OFF losses etc. But direct efficiency can only tell us about the magnitude of overall loss. No information about individual losses and their magnitudes is conveyed from direct efficiency calculation. There always exists some difference in the values of direct and indirect efficiencies. Indirect efficiency is measured at a particular time whereas direct efficiency is measured over a period of time and hence, losses on account of fluctuating loads, boiler on-off etc. are also taken into consideration.


Real time efficiency monitoring

Boiler efficiency does not remain fixed and large variations from ideal values take place during the course of operation. Shifting to real time efficiency monitoring can improve the boiler efficiency significantly depending upon the boiler type and actual conditions at site. In nutshell, monitoring and maintaining the boiler efficiency for the overall operational life of the boiler is a must to cut fuel bills and reduce carbon footprint.

Introduction and Methods of Calculation (2024)

FAQs

What are the methods of calculation? ›

Advanced Calculation Methods
  • Human Calendar Method — learn the algorithm used by experts.
  • Cross-Multiplication — multiply huge numbers at exceptional speed.
  • Cross-Division — divide by long numbers such as 4.52188.
  • Fraction Addition and Subtraction — with advice on when and how simplify answers.

What are the methods of calculating sample size in research? ›

Sample size can be calculated either using confidence interval method or hypothesis testing method. In the former, the main objective is to obtain narrow intervals with high reliability. In the latter, the hypothesis is concerned with testing whether the sample estimate is equal to some specific value.

How do you calculate the sample size for 80 power? ›

To have 80% power to detect an effect size, it would be sufficient to have a total sample size of n = (5.6/0.5)2 = 126, or n/2 = 63 in each group. Sample size calculations for continuous outcomes are based on estimated effect sizes and standard deviations in the population—that is, ∆ and σ.

What is the formula for Kish sample size? ›

n eff/norm = ∑ i = 1 n w i max i = 1 n w i . In kish1965, there is a better way to estimate the effective sample size: n eff/kish = ( ∑ i = 1 n w i ) 2 ∑ i = 1 n w i 2 .

What are the 4 rules of calculation? ›

The '4 rules' (addition, subtraction, multiplication and division) are at the heart of calculation and problem solving.

What are the four basic methods of calculation in mathematics? ›

The four basic operations in mathematics are addition, subtraction, multiplication, and division. Addition is combining values to find a total, subtraction is finding the difference between values, multiplication is serial addition, and division is splitting a number into equal groups.

What three factors are needed to calculate sample size? ›

In general, three or four factors must be known or estimated to calculate sample size: (1) the effect size (usually the difference between 2 groups); (2) the population standard deviation (for continuous data); (3) the desired power of the experiment to detect the postulated effect; and (4) the significance level.

What is the most correct method of determining a sample size? ›

What is the correct method of determining sample size? Using statistical techniques like power analysis, the minimal detectable effect size, or the sample size formula while taking into account the study's goals and practical limitations is the best way to calculate the sample size.

What is the difference between sample size calculation and power calculation? ›

Strictly speaking “power” refers to the probability of avoiding a type II error in a comparative study. Sample size estimation is a more encompassing term that looks at more than just the type II error and is applicable to all types of studies. In common parlance the terms are used interchangeably.

What is a good sample size? ›

Sampling ratio (sample size to population size): Generally speaking, the smaller the population, the larger the sampling ratio needed. For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample.

How to determine effect size for sample size calculation? ›

Generally, effect size is calculated by taking the difference between the two groups (e.g., the mean of treatment group minus the mean of the control group) and dividing it by the standard deviation of one of the groups.

What is the best formula for calculating sample size? ›

There are many formulas used for calculating sample size. One of the most common formulas used is Yamane's formula: n = N/(1+N(e)2.

What is the effective sample size calculation? ›

The effective sample size (ESS) is an estimate of the sample size required to achieve the same level of precision if that sample was a simple random sample. Mathematically, it is defined as n/D, where n is the sample size and D is the design effect. It is used as a way of summarizing the amount of information in data.

How to calculate sample size using design effect? ›

The effective sample size is the sample size for an estimator ˆθ from a complex sample divided by the design effect of ˆθ, i.e. neff=n/deff(ˆθ). In other words, the effective sample size is the size of an SRS that would yield the same variance as that produced by the complex design.

What are the different types of calculations? ›

You can perform the following basic mathematical operations: addition, subtraction, multiplication, division, calculating powers, and calculating square roots.

What are the 3 methods in math? ›

The three-way principle of mathematics states that there are three ways to solve a math problem: verbally, graphically, or by example. Learn how to use these methods and explore the strengths and limitations of each.

What are calculation techniques? ›

A calculation technique or model is used to analyse the interaction of design options with fixed constraints. Such a process is necessarily iterative, with adjustments made to parameters over which control is possible, until an optimum design solution is achieved.

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