Theory

Recall from the First and Second Law of Thermodynamics that the adiabatic process where entropy remains constant provides the maximum energy for work. As shown on the H-S coordinates, the difference in enthalpy, (H₁-H₂), is maximum when the lowest enthalpy (H₂) is reached at the exit conditions. The ideal expansion is, therefore, a vertical line.

On the diagram above, T₁, P₁ and P₂ are known process variables, for example, H₁ is determined by using T₁ and P₁. H₂ then can be found drawing a vertical line from P₁ to P₂ by following adiabatic isentropic expansion (expansion at constant entropy).

Non-ideal processes or real processes, however, do not present straight lines as shown on the Mollier diagram due to such factors as friction. If the expansion is not isentropic (i.e. entropy is not constant but it increases), the lowest enthalpy (H₂) cannot be reached at the exit conditions, in other words, H_2’ > H₂. This means that ΔH for the ideal expansion is greater than ΔH for the non-ideal expansion between the same pressure boundaries. The internal turbine efficiency is therefore given by:

The difference in enthalpy H_2’-H₂ is called the reheat factor and is the basis for multi-stage turbines. As can be seen on the Mollier diagram, the pressure curves are divergent. This means that the higher the pressure drop in a single stage turbine the greater the reheat factor and in turn the lower the turbine efficiency. However, if the steam is expanded through multiple stages and between each stage the steam is reheated, higher turbine efficiencies can be achieved. We will see this effect later in the Power Plant Efficiency lab.

Hints & Tips

In addition to various pressure and temperature values; log the following tags in your trends:

• Z03020
• E03018

To calculate the enthalpy values, you may use an app or online tool such as the Superheated Steam Table: https://goo.gl/GdVM4U

Theory

Excluding hydroelectric power plants, most power generating plants employ a type of boiler and steam turbine. A schematic diagram of a simple steam power plant is shown below:

High-pressure steam leaves the boiler and enters the turbine. The steam expands in the turbine and does work which enables the turbine to drive the electric generator. The exhaust steam leaves the turbine and enters the condenser where heat is transferred from the steam to cooling water. The pressure of the condensate leaving the condenser is increased in the pump thereby enabling the condensate to flow into the boiler. This thermodynamic cycle is known as the Rankine Cycle.

The Rankine Cycle Efficiency

As noted above, some heat is always lost from the steam to cooling water. In addition, feed pumps consume energy thus reducing the net work output. Rankine Cycle Efficiency then can be expressed as:

or

referring to the diagram above and using the enthalpy values in the Rankine cycle, we can write:

Improvements to the Rankine Cycle Efficiency

Effect of Pressure and Temperature on the Rankine Cycle

If the exhaust pressure drops from P₄ to P₄‘ with the corresponding decrease in temperature at which heat is rejected in the condenser the net work is increased by area 1-4-4′-1′-2’-2-1 (see diagram below)

In a similar way, if the steam is superheated in the boiler, it is evident that the work is increased by area 3-3′-4′-4-3 (see diagram below):

Superheating the steam is done by increasing the time the steam is exposed to the flue gases. The result of superheating is that for a given power output, the plant using superheated steam will be of smaller size than that using dry saturated steam.

The Reheat Cycle

Above we noted that the efficiency of the Rankine cycle is increased by superheating the steam. If metals could be found that would allow us to reach higher temperatures, the Rankine cycle could be more efficient. To improve the efficiency, the reheat cycle has been developed which is shown schematically below:

In this cycle, the steam is expanded to some intermediate pressure in the turbine and is then reheated in the boiler, after which it expands in the low-pressure turbine to the exhaust pressure. Rankine Cycle with reheat thermal efficiency can be expressed as:

The Regenerative Cycle

Another variation from the Rankine cycle is the regenerative cycle, which involves the use of feedwater heaters. During the process between states 2 and 2′ the feedwater is heated and the average temperature is much lower during this process than during the vaporization process 2′-3. In other words, the average temperature at which heat is supplied in the Rankine cycle is lower than in the Carnot cycle 1′-2′-3-4-1′, and consequently the efficiency of the Rankine cycle is less than that of the corresponding Carnot cycle. The relationship between Carnot cycle and Rankine cycle is shown below.

In the regenerative cycle, feedwater enters the boiler at some point between 2 and 2′. As a result, the average temperature at which heat is supplied is increased. A schematic of practical cycle is shown below:

The Plant Thermal Efficiency

In order to calculate the overall plant thermal efficiency, we need to adjust the formulas above to incorporate heat added in the reheater sections of the boiler:

Hints & Tips

In this lab, you are essentially calculating the Rankine Cycle thermal efficiency. However, you need to take the reheat cycle into consideration and log the following tags in your trends:

• Q02395 Reheater 1 transferred heat
• Q02375 Reheater 2 transferred heat

For Boiler Feedwater Inlet Temperature, you may use the Startup Heat Exchanger Feedwater Outlet Temperature tag#: T02447.

For the second calculation, locate the Variable List Page 0100 as shown below:

For the third calculation, make sure you closed all steam extraction valves and set T00305 to 10°C:

To calculate the enthalpy values, you may use an app or online tool such as the Superheated Steam Table: https://goo.gl/GdVM4U

Theory

Combustion of coal generates considerable quantities of byproducts, some of which are considered pollutants. The byproducts are mostly water vapor which is what we see coming out of a power plant smokestack, carbon dioxide, and nitrogen that is readily available in the air we breathe, and they do not necessarily pose any direct health hazard. However, the emissions do carry small concentrations of pollutants into the atmosphere, which translate into large quantities of hazardous emissions due to the large amount of coal combusted. The main pollutants that can cause health problems are sulfur oxides, nitrogen oxides, particulate matter (see Combustion Analysis) and such trace elements as arsenic, lead and mercury.

During the combustion process in a coal-fired power plant, nitrogen from the coal and air is converted into nitric oxide (NO) and nitrogen dioxide (NO₂); these nitrogen oxides are commonly known as NO_x. NO_x emissions contribute to the formation of acid rain.

NO_x is primarily formed by two mechanisms: thermal NO_x and fuel-bound NO_x.

Thermal NO_x formation takes place at high flame temperatures. Formation of thermal NO_x increases exponentially with combustion temperature. Fuel-bound NO_x formation is dependent upon the nitrogen content of the fuel.

The best way to minimize NO_x formation is to reduce flame temperature, reduce excess oxygen, and/or to burn low nitrogen-containing fuels.

The DeNO_x Plant Description

The purpose of the DeNO_x plant is for removal of nitrogen oxide from the flue gases. The plant employs a selective catalytic reduction method. The medium used for the reduction is ammonia gas.

The DeNO_x plant includes two selective catalytic reduction (SCR) reactors and an ash silo. Various dampers channel the flue gases either into or bypass the SCR-reactors.

Operation of the DeNO_x Plant

The DeNO_x plant is highly automatic, controlled by Programmable Logic Control sequences. The sequences are S701-Purge, S702/703-Start/stop Reactors, S704/705-Heating of Reactors, S706/707-Ammonia Injection, S708/709-Product Handling and S710/711-Soot Blowing.

Over Fire Air

To reduce NO_x, a quantity of additional air above all burner planes is supplied. This over-fire-air (OFA) reduces NO_x by enabling richer fuel mix in the high-temperature combustion zone at the burners (two-step combustion). Approximately 10 % of the combustion air is added as OFA air. OFA controller failure (MD200 malfunction 0881) is modeled in the simulator:

Over Burner Air

To further reduce NO_x generation, a portion of the secondary air is split off the main duct and directed into a third channel just above the burner. The damper controlling this over-burner-air is abbreviated OBA. OBA controller failure (MD180 malfunction 0780) is modeled in the simulator:

Fuel Quality

In the simulator, the chemical composition of the coal or other fuels can be specified. The sum of the five components C, H, S, O and N should preferably add up to 100%, to avoid confusion, but it is not strictly necessary because the C, H, S, O and N setting is always recalculated to a 100% basis prior to using in other computations. Water and inert matter (ash/slag) should then be added. The water content varies much and has a great impact on the amount of preheating required by primary air. The simulator computes the lower heat value (including water/inert matter) and theoretical combustion air needed and flue gas produced. The air/flue gas values are given in ncm/kg (ncm=normal cubic meter).

In this lab, we will burn both default and lower quality coal for a comparison. Fuel data can be changed using Variable List page 0111 on MD180, for example:

Hints & Tips

Your trend windows should look like the following:

 

Make sure your trend printouts are labeled properly otherwise, data analysis will be very confusing.

Tabulate your data as shown below:

Percentage deviation can be expressed as

and tabulated as follows:

Theory

A heat exchanger is equipment in which heat exchange takes place between two working media that enter and exit at different temperatures. The main function of heat exchanger is to either remove heat from a hot working media or to add heat to the cold working media. Depending on direction of working media-fluid flow the heat exchanger is either parallel (concurrent) flow heat exchanger or counter flow heat exchanger (see Figures below).

The terms are related to how the fluid flows through their respective flow passages relative to each other. If fluids flow in the same direction such as in Figure 1 it is termed a parallel flow. If fluids flow in opposite directions as in Figure 2 it is termed counter flow.

Parallel flow in heat exchangers occurs when both fluids enter the heat exchanger at their largest temperature difference. The temperature difference becomes less over the length of the heat exchanger. In the counter flow heat exchanger, fluids enter at opposite ends and therefore at different ends of the temperature scale Figure 2. The temperature difference between two fluids is relatively constant over the length of the exchanger.

The heat transfer process that occurs in any heat exchanger can be described by the following equations.

Considering the surface area involved in heat transfer, Newton’s Law of cooling states that the rate of heat loss is proportional to the difference in temperatures between the body and its surroundings and given by,

where α is called the heat transfer coefficient [W/m²K], area is taken in m² and ΔT is the temperature difference.

Furthermore Q, heat transferred between the hot water and cold water can be calculated as follows:

Or

where F is the correction factor which equals 1 for this SIMLAB (it takes values between 0.5 and 1). R_T is the overall resistance, U, overall heat transfer coefficient and LMTD is the Log Mean Temperature Difference.

The overall resistances can be calculated using:

Heat transfer coefficients ah and ac can be calculated using the following expression for Nusselt number for hot and cold water:

For cooling

 

For heating

And the LMTD is given by the following correlation where 1 and 2 presents the ends of the heat exchanger:

Heat Exchanger Effectiveness

Recall from the Boiler Efficiency Lab that efficiency is to do with minimizing waste and effectiveness to do with maximizing output. Here we define heat exchanger effectiveness as the ratio of actual heat transfer rate to the maximum possible heat transfer rate for the given temperatures.

Where C_min is defined either by cold or hot fluid whichever is smaller and it is defined by:

 

Hints & Tips

As always, label your trends using descriptive names. In this lab, you are changing the Heat Area Factor (heat transfer coefficient x area) of LP Feed Heater 3 and comparing the temperature data. Your evaluation will be based on LMTD and Heat Exchanger Effectiveness values.

Theory

In the Boiler Efficiency lab, we stated that Combustion Efficiency is defined as the ratio of the burner’s capability to burn fuel completely to the unburned fuel and excess air in the exhaust. In this lab, we will perform a combustion analysis.

Fossil fuels may be classified into solid, liquid and gaseous fuels. The vast majority of fuels are based on carbon (C), hydrogen (H₂) or some combination of carbon and hydrogen called hydrocarbons.

During combustion, oxygen (O₂) combines rapidly with C, H₂, sulphur (S₂) and their compounds in solid, liquid and gaseous fuels and results in the liberation of energy. Except for special applications such as oxyacetylene welding, in which a high-temperature flame is required, the O₂ necessary for combustion is obtained from air. Air contains O₂ and nitrogen (N₂), plus negligible amounts of other gasses and for engineering purposes, may be considered to have the following percentage composition by mass:

O₂: 23%
N₂: 77%

The proportions in which the elements enter into the combustion reaction by mass are dependent upon the relative molecular weights as shown below:

Element	Symbol	Molecular Weight
Carbon	C	12
Sulphur	S2	32
Hydrogen	H2	2
Oxygen	O2	32
Nitrogen	N2	28

Stoichiometric Combustion Theory

Complete combustion of simple hydrocarbon fuels forms carbon dioxide (C0₂) from the carbon and water (H₂0) from the hydrogen, so for a hydrocarbon fuel with the general composition C_nH_m, the combustion equation on a molar basis is as flows:

Where the balance should be satisfied following the moles for any mathematcial  equation:

Carbon balance:

kmol CO₂/ kmol fuel

Hydrogen balance:

 

 kmol H₂O/ kmol fuel

Oxygen balance:

 kmol O₂/ kmol fuel 

Considering that combustion occurs in air rather than in pure oxygen, the nitrogen in the air may react in the combustion process to produce nitrogen oxides. Beside, some fuels contain elements other than carbon, and these elements may react with oxygen during combustion. Also, combustion is not always complete, and the exhaust gases contain unburned and partially burned products in addition to C0₂ and H₂O.

Air is composed of oxygen, nitrogen, and small amounts of carbon dioxide, argon, and other trace components. For the purposes of the further calculation it is perfectly reasonable to consider air as a mixture of 21% (mole basis) 02 and 79 % (mole basis) N₂.  Nitrogen will be considered as an “inert” gas in the combustion calculations. The stoichiometric relation for complete combustion of a hydrocarbon fuel, C_nH_m, becomes

The balance equations are:

Carbon balance:

kmol CO₂/ kmol fuel

Hydrogen balance:

 

 kmol H₂O/ kmol fuel

Oxygen balance:

 kmol O₂/ kmol fuel 

Nitrogen balance:

 kmol N₂/kmol fuel

Flue gas compositions are presented in terms of mole fractions as kmol of product per kmol of fuel.

Example 1.  Combustion of Octane in Air

Determine the stoichiometric air/ fuel mass ratio and product gas composition for combustion of octane ( C₈H₁₈)  in air.

Carbon balance:

kmol CO₂/ kmol fuel

Hydrogen balance:

 

 kmol H₂O/ kmol fuel

Oxygen balance:

 kmol O₂/ kmol fuel 

Nitrogen balance:

 kmol N₂/kmol fuel

The combustion equation becomes:

Air/ fuel mass based ratio considering that 1 kmol fuel is 114 kg of fuel ( 8*12 + 18 *(1) = 114):

Flue gas composition on molar basis is:

Total number of kmol of flue gasses = kmol CO₂  + kmol H₂O + kmol N₂ = 8 +9+ 47 = 64 kmol flue gasses/ kmol fuel

CO₂  = 8/64 = 12.5 %

H₂O = 9/64 = 14 %

N₂ = 47/64 = 73.5%

Other components and impurities in the fuel make the calculation process more complicated. For example if sulfur exists in fuel it is usually combust into sulfur dioxide (SO₂). Ash, the noncombustible inorganic (mineral) impurities in the fuel, undergoes a number of transformations at combustion temperatures, will be neglected in the further calculation (ash will be assumed to be inert).

For most solid and liquid fuels, the chemical composition is on a mass basis, as determined in the ultimate analysis.

Mass Based Chemistry of Combustion

The combustion reactions are written following the stoichiometric rules as defined above. The quantity of matter entering into a reaction is equal to the quantity of matter in the products of the reaction.

The reaction for the complete combustion of C may be written as follows:

C+O₂=CO₂

or, if molecular weights are used,

12+32=44

1 kg C + 2⅔ kg O₂ = 3⅔ kg CO₂

The complete combustion of H₂ occurs as follows:

2H₂ +O₂ =2H₂O

4+32=36

1 kg H₂ + 8 kg O₂ = 9 kg H₂O

Sulphur burns as follows:

S +O₂ =SO₂

32+32=64

1 kg S + 1 kg O₂ = 2 kg SO₂

In addition, 1 kg of O₂ (stoichiometric mass of O₂) is contained in 1/0.232=4.3 kg air which is the stoichiometric mass of air. This air will contain 4.3-1=3.3 kg N₂. Therefore we can write:

1 kg S + 4.3 kg air = 2 kg SO₂+3.3 kg N₂

Procedure

If the analysis of fuel is given by mass, follow the steps below:

1. Total O₂ required: Determine the mass of O₂ required for each constituent and find the total mass of O₂ (Subtract any O₂ which may be in the fuel)
2. Stoichiometric air: Stoichiometric mass of air = O₂ required/0.232
3. Total mass of combustion products: Determine the % mass of each combustion product. For example, given C content of 84.9%, CO₂=84.9/100*2⅔=3.11% and find the total mass of combustion products.
4. Analysis of combustion products by mass: Suppose the total mass of combustion products in step 3 has been found as 12.09 kg/kg fuel, then CO₂=3.11/12.09*100=25.74. This means that 25.74% of the flue gas is CO₂. Repeat this calculation for each constituent.

Hints & Tips

In this lab, you are carrying out two combustion analyses. For data collection, set up your trends, a sample trend plot is shown below (Make sure your trend printouts are labeled properly otherwise, data analysis will be very confusing):

To change the fuel composition use the Variable List Page#: 0111 on MD180: