35

ESRL Module 6b.

Combustion Emissions Plug Flow Reactors (CE-PFR)

Prepared by F. Carl Knopf, Chemical Engineering Department, Louisiana State University

Documentation Module Use Expected Learning Outcomes/Objectives Upon completion of the module, students will be

able to: Combustion Emissions Plug Flow Reactor.pdf 7 Examples files Student Assignments

Student Assignments Currently In Development Laboratory Course -Kinetics Course (both undergraduate and graduate)

(1) All the objectives from ESRL 6a. (2) Explain how key parameters including reactor type and design can be used to minimize emissions.

This module is a continuation of Module 6a - Combustion Emissions Perfectly Stirred Reactors (CE-PSR). As explained in Module 6a (see Figures 1 and 2) we will to keep the primary zone and the intermediate zone as PSR but the best representation of dilution zone is a PFR. If we look back at Figure 2 (Module ESRL 6a.) we see that a gas turbine combustor can be modeled as a series of PSRs and PFRs with recycle, in order to predict emissions. Here we want to develop the material balance equation for the PFR when elementary combustion reactions are available; we will also develop the PFR energy balance in a later section. A plug flow reactor is depicted in Figure 7.

Figure 7 Plug-Flow Reactor and PFR volume element a.) PFR with inlet and outlet conditions; b.) PFR volume element with inlet conditions at and outlet at Δ

iniin CQ ,,

ziz CQ ,, zzizz CQ ,,

iR

Q

z

zAV c

outiout CQ ,,

36

The unsteady-state material balance for each species in the PFR within the volume element (Figure 7b) can be written (molar accumulation = flow in – flow out + generation by reaction),

| | (42)

Dividing by ( is not a function of time) and taking the limit as → 0 gives,

(43)

For combustion within the gas turbine, the PFR is empty (no catalyst), and if the reactor has a constant cross-sectional area, , the reactor length, , can be expressed in terms of the reactor

volume as , giving .

(44)

Recognizing that the fluid volumetric flow rate is related to the fluid velocity as, we can

also write Equation (44) in a commonly found form,

(45)

We can set the time-derivative = 0 in Equation (44), giving us a set of ODEs for the concentration of each species as,

(46)

In order to use Equation (46) we can write the dependent variables, and , as single variable

, as giving our working material balance equations for the PFR as,

(47)

When using Equation (47) we will modify our concentration-based generation equations, , by

replacing with . Solving the PFR material balance is conceptually straightforward – we know

the composition, T , and P of the feed stream and we can use Equation (47) to integrate in the direction until the end of the reactor or some specified exit condition is reached. We can use the

ideal gas law to account for the change of at any in terms of the known feed conditions as,

37

∑ ,

∑ , (48)

Where the subscript in indicates feed conditions – which are known and constant.

■ At this point you may want to reread the introductory section - The Energy Balance for an Open System with Reaction – which can be found on pages 19-21 of this module.

Plug Flow Reactor (PFR) for Combustion Processes – The Energy Balance Problem

The energy balance for the PFR can begin with Equation (34) which can be written for the incremental volume element of constant cross-section in Figure 7b as,

(53)

(49) or

(50)

where is the fluid specific density in the volume element, is the flow rate (kg/s), is the specific internal energy (J/kg), and and are the heat and work rate terms now per unit length of reactor. Following our same discussion of individual terms in Equation (50) as for the PSR energy balance, with and incorporating the definition for flow-work and neglecting the combination of shaft and boundary work we can write,

(51)

38

Dividing by and taking the limit as → 0 gives,

1 1

(52)

At steady state, the composition, temperature and pressure at any point in the reactor do not change with time, so the accumulation of energy in the reactor (the LHS of Equation (52)) can be set to zero and the energy balance for the PFR becomes,

(53)

Here again, as discussed in the development of the PSR energy balance equation, the heats of reaction are implicit in the definition of the enthalpy. PFR with Isothermal or Linear Temperature Profile There are at least three different PFR temperature profiles we need to consider. The PFR can be

isothermal and here we can supply the ODE

= 0 to maintain the temperature profile at a

fixed . We can assume a known temperature profile (generally a linear function of z) in the

PFR; if the temperature profile is linear,

=

. In either of these two cases, an overall

energy balance can be performed after the PFR material balance problem is solved. This energy

balance is simply

or depending on desired units of

cal/cm-s or cal/s. for an Adiabatic PFR using an iterative process

For an adiabatic PFR ( = 0), the temperature profile in the PFR will not be known, and the outlet temperature for each step is generally determined using an iterative process. As shown in Figure 8, an adiabatic energy balance can be used from the PFR inlet conditions to position z in the reactor in order to determine . An iterative process is required to find ( , ) which often requires that be bounded and then the interval refined. The process then assumes constant temperature at over the differential volume element as shown in Figure 8b and , values determined. We then can set and the process repeats. For each step we are basically iterating on such that the overall energy balance (Equation (53)) closes (the energy balance can be from the PFR inlet or over any differential element as the process is adiabatic).

39

Figure 8 Adiabatic Energy Balance to find ; energy balance from PFR inlet shown in Figure 8a to PFR conditions at z as shown in Figure 8b. for an Adiabatic PFR without using an iterative process

For the adiabatic PFR ( = 0), a good approximate solution to the temperature profile can be obtained by accounting for the heat of reactions, , for the major global reactions over each step. We use this approach in the provided PFR code as it allows direct calculation (no iterations) for . Our existing thermodynamic properties base provides species heat capacity data and heats of formation from the elements, (at 298.15 K, 1atm); it is straightforward to find heats of reaction from this information as shown in the next 2 examples. Example 9 Heat of Reaction for Methane (Global) Combustion at Reference Conditions The global reaction for gas phase methane combustion is, 2 → 2

and the heat of reaction (cal/mol) at reference conditions (298.15 K, 1atm) is found as, , 2 , , 2 ,

94054 2 57798 17895 2 0 191755 / Here open the provided file Heat of Reaction.xlsm; we have discussed the data base provided in this file in the PSR section. In cell B45 we determine the heat of reaction for the global methane reaction. The temperature is fixed in cell B16 and species heat of formation values at 298.15 K are found in cells I4::I13. These values are also echoed in cells B20::B29 as at 289.15 K (the reference temperature) there is no contribution from , for each species. ■

iniini hN ,, outiN ,

zziN ,

zTT

0Q

z

zizi hN ,,

0, ,,,, ziziiniini hNhNbalanceEnergy

40

We will need to adjust the heat of reaction at standard conditions ( ( , )) to the heat of reaction at conditions in the combustor ( ( , )). Here we assume that that the pressure correction to each species is zero (ideal gas). Even if a gas phase pressure correction ⁄ is necessary, it will generally be small. If needed it can be calculated using real gas equations of state. To adjust the standard heat of reaction to combustor/reactor conditions we use species heat capacities with the ideal mixture assumption,

, , , ,

(54)

Example 10 Heat of Reaction for Methane (Global) Combustion at Combustor Conditions Assume the combustor conditions at some point in the PFR are 1000K and 10 atm, determine the heat of reaction for the global methane combustion reaction, 2 → 2

1000 , 10 298.15 , 1 ,

.

2 ,

. ,

.

2 ,

.191334 /

Here again use the provided file Heat of Reaction.xlsm; simply change the temperature in cell B16 to 1000K and species enthalpy (heat of formation values + , contribution) will be updated in cells B20::B29. Do note there is no “pressure effect” here; the same heat of reaction result would be obtained at any selected pressure and 1000 K. ■ Solution of the PFR Material and Energy Balance Problem Using CVODE Lawrence Livermore National Laboratory currently provides CVODE as open source code for the solution of stiff ODEs. CVODE can be traced to the stiff ODE solver LSODE (ca 1980) and GEAR (ca 1970). Creating the dlls to allow Excel to serve as a pre- and post-processor for CVODE can be time consuming and we provide both 32-bit and 64-bit dlls in this module. To use the Excel-based CVODE we need to supply the “unsteady-state” material balance equations (Equation (47) where here distance z is replacing time as the independent variable), including for each species. The species net generation rate , includes both forward and reverse reactions and here we compute from the equilibrium constant , for the given PFR temperature. In , is

41

replaced by and is determined from Equation (48). The approach we have taken is to calculate

and on the Excel sheet, and provide the material balance equations in a VBA program which calls the dlls for CVODE. Example 11 PFR Elementary Reaction 2NO2 = 2NO + O2 Isothermal with Tout Fixed An interesting example/problem is the reaction of nitrogen dioxide to nitric oxide and oxygen. It is actually difficult to find an elementary reaction with known rate kinetics (Table 6) and one in which a change in moles occurs. The few elementary reactions with a change in moles tend to favor the forward or reverse kinetics making it difficult to observe pressure effects (Le Chatelier's principle). Table 6 Nitrogen dioxide elementary reaction, forward reaction rate constant (Westly, 1980) /

Reaction A (g-mol,cm3,s) (T in K) (cal/g-mol) 2 ⇔ 2 2.0 E+12 0 26,824.5

In Module ESRL5 using GFE-NO2.xlsm we found at 1000K and 1000 atm the reaction, 2NO2 = 2NO + O2 gave an equilibrium composition of:

y_ O2 0.167 y_NO 0.335

y_ NO2 0.498 And as explained on page 3 of this current module (ESRL6), at long times and using thermodynamically consistent rate expressions (Learning Objective 4 on page 2) both a PSR and a PFR should give equilibrium compositions all when using the same fixed . Excel Sheet - PFR The PFR solution file for this reaction is supplied, 1 PFR (2NO2=2NO+O2).xlsm. This file contains all the needed thermodynamic properties, the VBA code accessing the thermodynamic properties, and the kinetics equations for this reaction. To get things started, note that in cell M12, Flag = 2 to indicate isothermal operation with the outlet temperature is known/fixed. The outlet temperature (1000K) and pressure (1000atm) are fixed in cells B6 and B5. In Columns C/D we fix the inlet composition to the PSR as: 500 mol/s O2; 1000 mol/s NO; and, 0 NO2. In column H of the Excel PFR sheet we do obtain the equilibrium composition (Learning Objective 4 on page 2). The long PFR “reaction time/distance” is fixed in cell B11, here at 100 cm. In cell A64 we are running the simulation to 100 cm. Can you explain the relation between this distance in a PFR and the retention time in a PSR. The overall enthalpy balance, in – out in cell O13 does not = 0; we did not specify an adiabatic system but rather we have specified the outlet temperature to be 1000K. In this module, enthalpy only depends on temperature (not pressure); recall we are calculating enthalpy from Cp equations

42

with no P dependence. This ideal gas assumption can be reasonable in combustion systems and in many real gas system where enthalpy is often only very weak function of pressure. Now change the inlet composition in Column D to: 0 mol O2; 0 mol NO; and, 1000 mol NO2, and run the macro CVodeDenseCustom_Macro. The required initial conditions/initial feed composition are calculated in cells B49-B51 and these cells will reflect any feed changes. You should obtain the same result here as with 1000 mol NO2 feed. Does this seem reasonable to you? Please think about this result and Learning Objective 4 on page 2. Now ….. return the code to the original feed conditions of: 500 mol O2; 1000 mol NO; and, 0 mol NO2 and run the macro CVodeDenseCustom_Macro. You can change anything in BLUE on the Excel sheet PFR and run the CVODE Macro. CVODE supplies iteration results to the Excel sheet in cells A::E55 to A::E64. The columns are distance, and moles (in mol/time) of O2, NO and NO2 and . Excel Sheet – Thermodynamic Data If you open the Excel Thermodynamic Data sheet you will see Cp coefficients and physical property information in cells A::L4 to A::L13 and cells A::G20 to A::G29. The value in cell B16 is important, it is the temperature being used to calculate properties which are then read from this sheet and stored as needed in the VBA code or the Excel PFR sheet. Go back to the PFR sheet and change the outlet PFR temperature to 1200K and run the Macro. Then check the thermodynamic data sheet, you will see cell B16 is now 1200K. Change the PFR temperature out back to 1000K and run the macro again. All physical properties and reaction equilibrium constants are based on the temperature found in cell B16. The properties being used for this reaction, 2 ⇔ 2 , are highlighted in grey. Very important is row 34. At the selected temperature in cell B16, this row provides: the reaction equilibrium constant in column C; the forward rate constant in column H; the concentration based equilibrium constant in Column I; and, the reverse or backwards rate constant in column J. With these data, the last piece of the puzzle is assembling the ODEs (Equation (47)) representing the PFR into the VBA code. Excel-VBA code Open the VBA code (Alt F11) and open the PFR Module. In Function fun there is some bookkeeping, 'Establish Molar Flow Rate Out (N_out) and Volumetric Flow Rate (Q) at z

N_out = y1 + y2 + y3 Q_out = Q_in * (T_out / T_in) * (P_in / P_out) * (N_out / N_in)

43

where the _out indicates the z position in the PFR, y1 = ; y2 = ; y3 = and we are

using use Equation (48), ∑ ,

∑ ,; Equation (48) can be used at any z

position in the PFR as the “in” refers to conditions at the entrance to the PFR. Additional important code is found as,

'Read k_F and k_Rev from Thermodynamic_Data sheet k_1F = Sheets("Thermodynamic_Data").Cells(34, 8) k_1Rev = Sheets("Thermodynamic_Data").Cells(34, 10) ' ' Establish species generation term ' generation term for O2 R_O2 = (k_1F * (y3 / Q_out) ^ 2 - k_1Rev * (y2 / Q_out) ^ 2 * (y1 / Q_out)) Call set_Ith(ydot, 1, yd1) 'generation term for NO R_NO = (2 * k_1F * (y3 / Q_out) ^ 2 - 2 * k_1Rev * (y2 / Q_out) ^ 2 * (y1 / Q_out)) Call set_Ith(ydot, 2, yd2) 'generation term for NO2 R_NO2 = (-2 * k_1F * (y3 / Q_out) ^ 2 + 2 * k_1Rev * (y2 / Q_out) ^ 2 * (y1 / Q_out)) Call set_Ith(ydot, 3, yd3) 'balance for O2 yd1 = Area * R_O2 Call set_Ith(ydot, 1, yd1) 'balance for NO yd2 = Area * R_NO Call set_Ith(ydot, 2, yd2) 'balance for CO2 yd3 = Area * R_NO2 Call set_Ith(ydot, 3, yd3)

We read the forward and reverse rate constants, k_1F and k_1Rev, from the thermodynamic data

sheet at the selected temperature. The generation term for O2, is

and for the PFR we replace with ⁄ ; here is Q_out. Notice that

R_O2 will have units mol/cm3. Then the material balance for O2, from Equation (47),

44

in the VBA code, yd1 = ; is the tubular reactor cross sectional area which is given in cell

B10 as 962.1 cm2 ; R_O2 is the rate of oxygen/time-cm3 generated or consumed in the PFR differential volume. The statement Call set_Ith(ydot, 1, yd1) is used to keep track of the estimate for the moles of oxygen exiting the differential volume. It is important to appreciate that CVODE via Equation (47) is controlling the position z down the PFR. After each step z + ∆z becomes the new z and the process continues until the reactor length in cell B11 is reached. ■ Notes on using the macro CVodeDenseCustom_Macro: You can make changes in Sub fun() for variables and parameters. In Sub

CVodeDenseCustom_Macro() you must identify the row on the Excel sheet for: NEQ; NOUT; RTOL ; T0 ; T1 ; TMULT or set the values in the subroutine (see rows 41-46). You must also set the initial conditions as shown here starting in row 49. The reader may want to download available manuals for CVODE from Lawrence Livermore National Laboratories (Collier et al., (2008) and Hindmarsh and Serban (2009)). The parameters used in this example will solve most kinetics combustion problems. Example 12 Adiabatic PFR Elementary Reaction 2NO2 = 2NO + O2 In Example 11 we found the isothermal PFR exiting composition at 1000K and 1000 atm for the reaction, 2NO2 = 2NO + O2 . We want to solve the same problem with an adiabatic PFR. The solution to this kinetics problem can be found again using 1 PFR (2NO2=2NO+O2).xlsm and the macro named, CVodeDenseCustom_Macro. Make sure the code is set to the original feed conditions of: 500 mol O2; 1000 mol NO, and, 0 mol NO2. Make sure that in cell M11 the Flag = 1 to indicate adiabatic operation. Run the macro CVodeDenseCustom_Macro. You should find the PFR adiabatic outlet temperature = 1139.16 K and the mole fractions exiting the PFR as,

y_ O2 0.224 y_NO 0.448

y_ NO2 0.328 In Example 12 we are determining the adiabatic temperature at each z position as we step down the PFR. Here following Examples 9 and 10 we determine , or ,

allowing the energy balance,

45

, , , (55)

In the VBA code,

If QOutFlag = 1 Then yd4 = Area * R_O2 * -1 * Sheets("Thermodynamic_Data").Cells(34, 12) / (y1 * CP(1) + y2 * CP(3) + y3 * CP(6)) Call set_Ith(ydot, 4, yd4)

Here Sheets("Thermodynamic_Data").Cells(34, 12) = , , ; R_O2 = the moles/time of O2 that have been generated over the ∆z section; y1 = ; y2 = ; y3 =

and CP(1) = , ; CP(2) = , ; CP(6)= , ; each of the terms are evaluated at . The (-1) accounts for the convention (products – reactants) being used to form the heat of

reaction. Now ….. the same as we did in Example 11 change the inlet composition in Column D to: 0 mol O2; 0 mol NO; and, 1000 mol NO2, and run the macro CVodeDenseCustom_Macro with the adiabatic flag =1 and the length 100 cm. Do you obtain the same adiabatic outlet temperature? What is happening here? Recall our global reaction in Example 9, can you turn CO2 and H2O back into methane and oxygen in a single PFR? Return the code to the original feed conditions of : 500 mol O2; 1000 mol NO; and, 0 mol NO2 and run the macro CVodeDenseCustom_Macro – make sure everything is O.K. ■ Example 13 Pressure Consistency Check for GFE, PSR and PFR There can be some confusion over the effect of pressure on our reaction kinetics and Gibbs Free Energy minimization. We are using the ideal gas assumption which means . But pressure does affect equilibrium composition (see ESRL Module 5 Equation ( )) and pressure does affect the PSR and PFR as concentration based rate units g-mol/cm3 are being used. To better see this pressure dependency, consider our reaction, 2NO2 = 2NO + O2 at 1000 K and P = 1 atm and P = 1000 atm. Using the provided codes (we have run the codes previously in the module and in ESRL Module 5) you will find the results in Table 7. For all systems make the feed: 0 mol O2; 0 mol NO; and, 1000 mol NO2. For the GFE system set Flag = 0 for Tout to be fixed in Cell F4 and = 1000 K; Pout in Cell B11 = 1 or 1000 atm. For the PSR system set Flag = 0 for Tout to be fixed in Cell F4 = 1000 K; Pout in Cell B11 and retention time in cell B5. For the PFR set Flag = 0 for Tout to be fixed in Cell F4 = 1000 K; Pout in Cell B11 and length in cell B5.

46

Table 7: Pressure Effects using the 2NO2 = 2NO + O2 Reaction Reactor Type GFE PSR PFR GFE PSR PFR Length (cm)/

Residence Time (s)

100

1000000

100

100

T (K) fixed 1000 1000 1000 1000 1000 1000 P (atm) 1 1 1 1000 1000 1000 y_ O2 0.3194 0.3191 0.3194 0.1674 0.1671 0.1670 y_NO 0.6389 0.6382 0.6389 0.3348 0.3341 0.3341

y_ NO2 0.0417 0.0428 0.0417 0.4978 0.4988 0.4988 ■

Emissions from a Simplified Gas Turbine System using PFRs Example 14 Solve the Isothermal PFR with the Reaction Set in Table 1 Methane and air at 650 K and at a flow rate of 28,385 g/s are added to the PFR. The PFR is isothermal at 1600 K, with length 10 and cross sectional area = 962.1 . The air is 21% oxygen and 79% nitrogen on a molar basis. Assume pressure drop is negligible. Determine the outlet composition of the reacting species. The solution to this kinetics problem using CVODE is provided in the Excel file 1 PFR (7 Reactions).xlsm with the macro named, CVodeDenseCustom_Macro.

Figure 9 PFR For methane and air combustion We briefly detail the key VBA code (in Function fun)

'Establish Molar Flow Rate Out (N_out) and Volumetric Flow Rate (Q) at z N_out = y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 Q_out = Q_in * (T_out / T_in) * (P_in / P_out) * (N_out / N_in)

sg /28385

cm10

21.962 cmAc

0685.0

73591.0

19562.0

4

2

2

CH

N

O

y

y

y KT 1600atmP 10

47

where the _out indicates the z position in the PFR, y1 = ; y2 = ; y3 = ; y4 = ; y5 = ; y6 = ; y7 = ; y8 = ; y9 = ; and we are using use Equation (48),

∑ ,

∑ ,; Equation (48) can be used at any z position in the PFR as the

“in” refers to conditions at the entrance to the PFR.

Additional important code is the forward and backwards (or reverse) rate constants from the Excel sheet 'Read k_F and k_Rev from Thermodynamic_Data sheet

k_1F = Sheets("Thermodynamic_Data").Cells(33, 8) k_1Rev = Sheets("Thermodynamic_Data").Cells(33, 10) k_2F = Sheets("Thermodynamic_Data").Cells(34, 8) k_2Rev = Sheets("Thermodynamic_Data").Cells(34, 10) k_3F = Sheets("Thermodynamic_Data").Cells(35, 8) k_3Rev = Sheets("Thermodynamic_Data").Cells(35, 10) k_4F = Sheets("Thermodynamic_Data").Cells(36, 8) k_4Rev = Sheets("Thermodynamic_Data").Cells(36, 10) k_5F = Sheets("Thermodynamic_Data").Cells(37, 8) k_5Rev = Sheets("Thermodynamic_Data").Cells(37, 10) k_6F = Sheets("Thermodynamic_Data").Cells(38, 8) k_6Rev = Sheets("Thermodynamic_Data").Cells(38, 10) k_7F = Sheets("Thermodynamic_Data").Cells(39, 8) k_7Rev = Sheets("Thermodynamic_Data").Cells(39, 10)

And recall that , the generation term for O2, was determined in Example 3,

' ' Establish species generation term ' generation term for O2 R_O2 = (-k_2F * (y5 / Q_out) * (y1 / Q_out) + k_2Rev * (y3 / Q_out) * (y4 / Q_out) _ + k_3F * (y4 / Q_out) ^ 2 * (M / Q_out) - k_3Rev * (y1 / Q_out) * (M / Q_out)) _ + (-k_5F * (y6 / Q_out) ^ 2 * (y1 / Q_out) + k_5Rev * (y8 / Q_out) ^ 2 * (y9 / Q_out) ^ 4) _ + (-k_6F * (y9 / Q_out) ^ 2 * (y1 / Q_out) + k_6Rev * (y7 / Q_out) ^ 2) 'balance for O2 yd1 = Area * R_O2 Call set_Ith(ydot, 1, yd1)

We read the forward and reverse rate constants, k_2F and k_2Rev, etc., from the thermodynamic data sheet at the selected temperature and for the PFR we replace with ⁄ ; here is Q_out. Notice that R_O2 will have units mol/cm3. Then the material balance for O2, from Equation (47),

2OR

48

in the VBA code, yd1 = ; is the tubular reactor cross sectional area which is given in

cell B10 as 962.1 cm2 ; O2in is the moles oxygen/time into the PFR as [mol/s] found on the Excel PFR sheet in cell B49. The statement Call set_Ith(ydot, 1, yd1) is used to keep track of the estimate for the moles of exiting oxygen. It is important to appreciate that CVODE via Equation (47) is controlling the position z down the PFR. After each step z + ∆z becomes the new z and the process continues until the reactor length in cell B11 is reached.

Flag = 2 Here we are setting

= 0 in the VBA code using yd11 = 0, ElseIf QOutFlag = 2 Then yd11 = 0 Call set_Ith(ydot, 11, yd11) The forward and backwards rate constants are calculated on the Excel sheet. Earlier in this module we showed how data from Prothero (1969) or the NIST-JANAF or TRC tables could be used to calculate the molar enthalpy and molar entropy for provided species. These enthapies and entropies were calculated using species formation data and the integral of . It was then possible to calculate the Gibbs free energy, G, as . On the provided Excel Thermodynamic Data sheet these calculations are in Rows 20 -29. For each of the seven reactions 1, . . . , 7 we can calculate ln

∑ ,

, . Extending Equation (24) to the sytem of reactions,

∑ ,

, , and from Equation (6) ; see rows 33-39. The outlet

temperature is set on the Excel sheet in cell B16. For texts where the general reaction, , is written

→

← , you will find . The total enthalpy of the feed

stream is 1,391,834 cal/s; the total enthalpy of the product stream leaving the PFR (7 reactions) is -2,327,737 cal/s. Table 8 Comparison of Simple PFR solution with GRI-Mech 3.0 Complete Mechanism

Conditions / Species (mol fraction)

Solution from the 7 Reaction Mechanism (Table 1)

Solution using complete GRI-Mech 3.0

Temperature (K) 1600 1600 Pressure (atm) 10 10

(g/s) 28,385 28,385 27.7158 27.970

(cal/s) -3,719,571 -2,121.497 0.067355 0.07685958 0.729133 0.720868526 1.70999E-20 1.75339E-07

7.27052E-17 0.000520914 2.41423E-24 2.07278E-10 5.4423E-14 0.00010129

49

0.13422 0.131109224 0.01697 0.037460305 0.00145 0.001991569 0.05087 0.029472427 1.0 0.998384011

Note: Table 8 solution results for GRI-Mech 3.0 can be found in the Excel file 1 PFR (GRI-Mech 3.0) – Example 14.xlsm. GRI-Mech 3.0 coding is discussed below.

Table 8 shows that the results from the simple 10 species, 7 reaction model compared to the detailed GRI-Mech 3.0 results (with 53 species and 325 reactions). There are significant differences in the energy balances as well as the moles out of several species, especially, CH4, CO, and CO2. Energy balance differences can be traced to the values used in each code; both codes have ~ the same energy input but differ on the energy content of the products. We emphasize that in order to accurately determine emissions from a combustion process, the full GRI mechanism should be used; we provide Excel files with the complete GRI-Mech 3.0 later in this module. ■ Example 15 Solve the Adiabatic PFR with the Reaction Set in Table 1 Starting with our solution (7 Reaction) to Example 14, change the Flag in Cell M19 to indicate adiabatic operation. Run the PFR. You will immediately notice that the outlet temperature is 651.16 K. Change the inlet feed temperature from 650 K to 750 K in Cell B4 and run the adiabatic PFR again. Now the outlet temperature is 2083.99 K. Can you explain what is happening? ■ Modeling the combustor system following Figure 9/10 is problematic. There is no way to ensure combustion will occur in the PFR if we use it to model the flame zone in Figure 2. In Example 15 if the inlet T to the PFR is 650 K no ignition occurs, but an inlet temperature of 700 K created ignition conditions. In a more realistic PFR we would need to account for axial mixing and heat conduction. As a final example before we provide the rigorous solution using GRI-Mech 3.0 let us model the combustor as a series of PSRs followed by a PFR. We can use the temperature profile option in the PFR to match the combustor outlet temperature to measured/reconciled data. Example 16 Solve 2PSR + PFR in Series with the Reaction Set in Table 1 As a final example/assignment let us combine our PSR and PFR developments to predict emissions from the simplified gas turbine system shown in Figure 10. In Figure 10 the flows, temperatures, PSR retention times and PFR cross section and length are based on a GE LM2500 aeroderivative gas turbine combustor. Here combustion product gas recirculation has been eliminated.

50

Figure 10 Simplified Model of a Gas Turbine Combustor Air and fuel at 10 atm and 650 K with mol fraction composition, 0.19562, 0.73591, 0.0685 undergoes combustion in PSR-1 with an estimated outlet temperature of ~ 2050 K and a residence time of 0.002 s. PSR-1 is assumed adiabatic and we will need to determine the outlet temperature. Dilution air with mole fraction composition, 0.21, 0.79, is added after the PSR-1 flame zone. This single air addition to PSR-2 (via Mixing Point A) represents the air injection and subsequent cooling found in both the intermediate and dilution zones of the gas turbine. PSR-2 has a residence time of 0.001 sec; assume PSR-2 is adiabatic. Currently in the provided Excel sheets for PSR1 and PSR2 we are setting the initial temperature estimate in PSR1 to be 1800K and the initial temperature estimate in PSR 2 to be the temperature of the entering feed stream; the user can change these initial temperature estimates as detailed in Examples 7 and 8. The temperature drop/increase in PFR-1 (the dilution zone) is linear from PSR-2 outlet to 1416 K (measured outlet temperature of the combustor) over its known length of 35 and cross sectional area of 962.1 . Assume the methane combustion reactions are those given in Table 1. Solution: The solution can be found in Excel file 2 PSR + 1PFR (7 Reactions).xlsm with the macro named, GT_Combustor. Results from this Excel files are summarized in Table 9. Comparable results from GRI-Mech 3.0 are provided in Table 10 (and discussed below). Table 9 Solution to the Gas Turbine Combustor System using Table 1 Reaction Set

Conditions /mol fraction PSR-1 Mixing Point A PSR-2 PFR-1

PSR-1Flame/Primary

Zone2100 KAir

PSR-2Recirulation/Intermediate

Zone

PFR-1Dilution

Zone

Fuel

K2100~

AirDilution

K1416K650

sec002.0 sec001.0

Katms

g650,10,76.617,40

s

g385,28

atm10

cmL 35

21.962 cmAc 0685.0

73591.0

19562.0

4

2

2

CH

N

O

y

y

y

79.0

21.0

2

2

N

O

y

y

AK1350~

51

(K) 2055.76 1295.65 1302.93 1416 (atm) 10 10 10 10 (g/s) 28,385 69,002.92 69,002.92 69,002.76

27.8427 28.4271 28.4537 28.4667 (cal/s) or (cal/cm-s) 0 0 0 2,207,577

0.063092 0.14830 0.147886085 0.14750178 0.73247 0.76584 0.766205039 0.766554631 1.013E-06 0.00000 4.257E-07 4.25904E-07

5.221E-06 0.00000 2.186E-06 2.18723E-06 1.797E-11 0.00000 8.800E-16 2.35523E-15 5.203E-06 0.00000 8.343E-08 3.73443E-16 0.134598 0.05653 0.05696159 0.057092203

0.007659 0.00322 0.002657531 0.001859968 0.001686 0.00071 0.000309198 0.000204888 0.060484 0.02540 0.025977862 0.026788575 1.0 1.0 1.0 1.0

There are very few differences in 2 PSR + 1 PFR compared to 2PSR. 1.) On the Excel sheet GT_Combustor you can control the amount of air sent to the PSR2 and the PFR by using the split fraction in Cell G37. 2.) On the Excel sheet PFR (rather than retention time) you will need to specify the reactor cross-sectional area and the reactor length. Is there a relation between PFR length and retention time in a PSR? Some comments on the results above: PFR-1: The feed stream to PFR-1 shows = 1302.93 K, and = 10 atm. The temperature leaving PFR-1 is fixed at 1416 K to match the reconciled temperature leaving the combustor. The additional equation,

1416 1302.93

100

(with initial condition, 0 = 1302.93 K), is added to the ODE reaction set to account for the linear temperature change along the PFR. The exiting stream has a total enthalpy in Cell N14 of 7132944 cal/s, therefore 2,207,577 cal/s or 63,074 cal/cm-s have been added; the positive quantity means heat has been added to the PFR from the surroundings. It can often be easier to think of this positive quantity in terms of heat gain, for example, the heat gain in the PFR is 63,074 cal/cm-s. Emission Calculations The emissions are detailed after Example 17 where we solve this identical problem using the complete full GRI-Mech 3.0 mechanism. The species mol fractions from the PSR-1 to PSR-2 to the PFR-1 show similar trends when using either the simplified kinetics (Table 1) or the full GRI-Mech 3.0 results but the values / magnitudes are different.

52

Rigorous Kinetics Combustor Modeling Using GRI-Mech 3.0 The GRI-Mech 3.0 (http://www.me.berkeley.edu/gri_mech/) is an optimized mechanism for modeling natural gas combustion and NOx formation. The Berkeley web site provides (free of charge) reaction mechanisms and rate coefficients accounting for some 53 combustion species and 325 elementary combustion reactions. Also provided are species thermochemical data and transport properties. However, the user must code the desired reactor types and system configuration as well as interfacing the reactor code to the thermodynamic data base. The system (reactors and kinetics equations) will require solution by an ODE solver. There are programs available which have accomplished these tasks including: the free academic-based program Cantera (http://www.cantera.org/docs/sphinx/html/index.html) and the commercial code Chemkin (http://www.reactiondesign.com/products/chemkin/chemkin-2/). We have assembled the complete GRI-Mech 3.0 mechanism and thermodynamic data base in the reactor configurations indicated in Table 10 for your use; CVODE is used as the ODE solver. Table 10: Available Reactor Configuration with complete GRI-Mech 3.0

Reactor Configuration Excel File Name 1 PSR 1 PSR (GRI–Mech 3.0).xlsm 1 PFR 1 PFR (GRI–Mech 3.0).xlsm

1 PSR followed by 1 PFR 1 PSR + PFR (GRI–Mech 3.0).xlsm 2 PSR in series followed by 1 PFR 2 PSR + PFR (GRI–Mech 3.0).xlsm

Comments on using codes provided in Table 10: i.) A single PFR is not a good choice to model the entire combustion processes. It is often difficult to establish the combustion “lift-off” point in the reactor. A single adiabatic PFR may not converge to the appropriate/desired length indicating temperature convergence problems. These convergence problems are shown in the provided 1 PFR file. ii.) Following GRI-Mech 3.0 the code switches between the low-temperature and high-temperature Cp data at 1000 K. Low-temperature and high-temperature Cp data are available in each of the Excel files on the sheet “Thermodynamic Data.” The choice between low-temperature and high-temperature Cp data must be determined by the user when calculation are performed directly on the Excel sheet.

The provided code/files follow the same input as all the previous examples in this module and will produce results comparable to Cantera and Chemkin . The provided GRI-Mech 3.0 code does include many important features which have not been detailed in this module including enhanced third body effects, and both Troe and Lindemann falloff considerations. For a discussion of these important additions the interested reader should see: Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics (1993); Chemkin – A Software Package for the Analysis of Gas Phase Chemical and Plasma Kinetics (2000); and, Gardiner and Troe (1984). If you look at the provided code you will recognize the reactor equations we have developed in this module. For the adiabatic PFR, we account for the temperature change using Equation (55),

53

∑ ∆ , ,

∑ ,

and for the heat of reaction term we account for for 5 major species, , , , , using the following 5 global reactions (see Example 10),

2 ↔ 2

↔ 12

↔ 2

↔ H g 12O g

12H g

12O g ↔ O

These equations will account for the adiabatic PFR temperature at longer distances, but may not be accurate at short distances. At short distances the user may want to consider adding a search routine to the code to demine the adiabatic PFR outlet temperature at each CVODE step. In some cases, the known temperature profile option (Flag = 1) can be used with Tout varied until the adiabatic energy balance closes. A word of caution – all the GRI-Mech 3.0 based codes in Table 10 will take some time to run on a typical PC platform – be prepared for ~30+ minutes to run 2 PSR + PFR. Example 17 Solve 2PSR + PFR in Series with the GRI-Mech 3.0 Mechanism Here we want to solve Example 16 using GRI-Mech 3.0 and compare GRI-Mech 3.0 mechanism results to our simple Table 1 kinetics results. The solution is provided in 2 PSR + 1 PFR (GRI–Mech 3.0).xlsm and results are summarized in Table 11. Table 11 Solution using Complete GRI-Mech 3.0

Conditions /mol fraction PSR-1 Mixing Point A PSR-2 PFR-1 (K) 2098.61 1315.5 1613 1416

(atm) 10 10 10 10 (g/s) 28,385 69002.92 69002.92 69002.76

27.937 28.468 28.468 28.483 (cal/s) or (cal/cm-s) 0 0 0 1,926,786

0.058651 0.14656 0.146653 0.146633911 0.734878 0.76689 0.767258 0.767294527 7.71E-05 3.23E-05 2.94E-05 2.94577E-05

0.000222 9.32E-05 4.92E-06 2.60155E-07 1.19E-09 4.98E-10 7.98E-14 4.15679E-15 2.74E-05 1.15E-05 6.18E-07 2.56645E-09 0.135285 0.056709 0.057309 0.057345026

54

0.001063 0.000446 0.000159 8.2042E-05 0.000265 0.000111 6.5E-06 3.38659E-07 0.06727 0.028199 0.028516066 0.028594666 0.997738 0.999052 0.999935758 0.9999802

We can compare results in Table 11 (GRI-Mech 3.0) to results in Table 9 (simple 7 Reaction system). The species mol fractions generally show the same trend from PSR-1 to PSR-2 to the PFR exit. However the values for the species mol fractions and adiabatic temperatures are different. For example, a key emission species is . Results from the simplified kinetics for

differ some two orders of magnitude from the full GRI-Mech 3.0 results (which will also account for other species). This occurs, in part, because in the simplified kinetics we have not accounted for all the formation mechanisms (see Miller and Bowman (1989); Hill and Smoot (2000)). At the PFR exit, some species mol fractions are close, for example, and and

are well within ~1%. The important point here is the entire GRI-Mech 3.0 mechanism should be used if you are trying to quantify or predict emissions from natural gas fired turbines. But because the provided GRI-Mech 3.0 code takes considerable time to run ……the experience gained using the 7 reaction system is valuable.

Closing Remarks We introduced elementary reaction kinetics and saw how kinetic sets could be used in combination with perfectly stirred reactors (PSR) and plug flow reactors (PFR) to model gas turbine combustor emissions. The kinetic sets for combustion processes were stiff ODEs and here we provided the CVODE from Lawrence Livermore National Laboratory for problem solution. The GRI-Mech 3.0 mechanism (Smith et al. /web site) is currently the industry standard for methane and natural gas combustion. We provide the GRI-Mech 3.0 code for PSR and PFR combinations but it is slow to execute on a PC platform. We explored use of a simple “reduced-set” 7 reaction system to provide fast execution times and allow exploration of species trends in various reactor system configurations. Ultimately the concentrations of NOx, CO and other pollutants depend on complex fluid flow, mass transfer, and kinetics effects. For example, actual residence times in different sections of the combustion zone may be uncertain due to back-mixing and other fluid flow processes. There are on-going improvements in the physical models and detailed kinetics equations used to predict emissions. Here the use of computational fluid dynamics with 1000s of volume elements may be the best approach to combustion modeling, but we can certainly appreciate that CFD with the complete GRI-3.0 Mech would be computationally very challenging.

55

Detailed mechanisms for other species are available in the literature and here the reader is referred to El-Mahallay and Habik (2002), Glassman and Yetter (2008) and Miller et al. (1990). An excellent overview of combustion kinetics and combustion modeling is also provided in Turns (2000). ■ Acknowledgements This work was completed as part of the National Science Foundation Phase II grants: NSF Award 0716303 “Integrating a Cogeneration Facility into Engineering Education” (September 2007 – 2012); and NSF Award 1323202 “Collaborative Proposal: Energy Sustainability Remote Laboratory” (September 2014 – 2016).

References / Additional Reading Andreini, A., and B. Facchini. Gas Turbines Design and Off-Design Performance Analysis with Emissions Evaluation. Journal of Engineering for Gas Turbines and Power. 126(1): 83-91, (2004). Chapra, S.C., and R.P. Canale. Numerical methods for Engineers (6th Edition). McGraw Hill, New York, NY (2010). Chase, M.W., C.A. Davies, J.R. Davies, D.J. Fulrip, R.A. McDonald, and A.N. Syverud, JANAF Thermochemical Tables, (3rd edition), J. Phys. Chem. Ref. Data 14: Suppl. 1 (1985). Collier, A.M., A.C. Hindmarsh, R. Serban, and C.S. Woodward. “User Documentation for KINSOL v2.6.0,” Technical Report UCRL-SM-208116, LLNL (Lawrence Livermore National Laboratory), (2008). de Nevers, N. Physical and Chemical Equilibrium for Chemical Engineers. John Wiley and Sons, New York, NY (2002). El-Mahallay, F., and S.E. Habik. Fundamentals and Technology of Combustion. Elsevier, Oxford, U.K. (2002). Folger, H.S. Elements of Chemical Reaction Engineering (4th edition). Prentice Hall, Englewood Cliffs, NJ (2006). Glassman, I., and R.A. Yetter. Combustion (4th edition). Academic Press / Elsevier, Burlington MA (2008).

56

Gordon, S., and B.J. McBride. “Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications I. Analysis” NASA Reference Publication 1311 (National Aeronautics and Space Administration), (October, 1994). Gautam R. and W.D. Seider. Computation of Phase and Chemical Equilibrium: Part 1. Local and Constrained Minima in Gibbs Free Energy. AIChE Journal. 25(6): 991-999 (1979). Hill, S.C. and L.D. Smoot. Modeling of Nitrogen Oxides Formation and Destruction in Combustion Systems. Progress in Energy and Combustion Science. 26: 417-458 (2000). Hindmarsh, A.C., and R. Serban. “Example Programs for CVODE v2.6.0,” Technical Report UCRL-SM-208110, LLNL (Lawrence Livermore National Laboratory), (2009). Kelly, C.T. Solving Nonlinear Equations with Newton’s Method. SIAM, Philadelphia, PA (2003). Kee, R.J., F.M. Rupley and J.A. Miller. Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics', Sandia Report SAND89-8009B UC-706, Reprinted January 1993. Miller, J.A. and C.T. Bowman. Mechanism and Modeling of Nitrogen Chemistry in Combustion. Progress in Energy and Combustion Science. 15: 287-338 (1989). Miller, J.A., R.J. Kee, and C.K. Westbrook. Chemical Kinetics and Combustion Modeling. Annu. Rev. Phys. Chem. 41: 345-387 (1990). Prothero, A. Computing with Thermochemical Data. Combustion and Flame. 13: 399-408 (1969). Punuru, J., personal communication (2011). Reynolds, W.C., “The Element Potential Method for Chemical Equilibrium Analysis: Implementations in the Interactive Program STANJAN,” Department of Mechanical Engineering, Stanford University (1986). Rodriguez-Toral, M.A. “Synthesis and Optimization of Large-Scale Utility Systems.” Ph.D. dissertation, The University of Edinburgh (1999). Rodriguez-Toral, M.A., W. Morton, and D.R. Mitchell. Using new packages for modeling, equation oriented simulation and optimization of a cogeneration plant. Computers and Chemical Engineering. 24: 2667-2685 (2000). Smith, G.P., D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, and W.C. Gardiner, V.V. Lissianski, and Z. Qin. http://www.me.berkeley.edu/gri_mech/. Smith, J.M., H.C. Van Ness, and M.M. Abbott. Chemical Engineering Thermodynamics (6th edition). McGraw Hill, New York, NY (2001).

57

Swithenbank, J., I. Poll, M.W. Vincent, and D.D. Wright. Combustion Design Fundamentals. Fourteenth International Symposium on Combustion, The Combustion Institute (1972). Tsuji, H., A.K. Gupta, T. Hasegawa, M. Katsuki, K. Kishimoto, and M. Morita. High Temperature Air Combustion – From Energy Conservation to Pollution Reduction. CRC Press, Boca Raton, FL (2003). Turns, S.R. An Introduction to Combustion – Concepts and Applications (2nd edition). McGraw Hill, Boston, MA (2000). U.S. Department of Energy, “Carbon Dioxide Capture from Existing Coal-Fired Power Plants,” Publication No. DOE/NETL-401/110907, DOE Office of Fossil Energy’s National Energy Technology Laboratory, Pittsburgh, PA (revision date November (2007). Wagman, D.D. Data Bases: Past, Present and Future. Pure and Applied Chemistry. 64(1): 37-48, (1992). Yamamoto, T., T. Furuhata, N. Arai, and A.K. Gupta. Prediction of NOx Emissions from High-Temperature Gas Turbines: Numerical Simulation for Low-NOx Combustion. JSME International Journal, Series B. 45(2): 221-230 (2002). Zeldovich, Y.B. The Oxidation of Nitrogen in Combustion Explosion. Acta Physicochimica USSR 21: 577-628 (1946). Zhang, H., A. Bonilla-Petriciolet, and G.P. Rangaiah. A Review on Global Optimization Methods for Phase Equilibrium Modeling and Calculations. The Open Thermodynamics Journal. 5(Suppl 1-M7): 71-92 (2011).

58

Student Assignments (under development) Figure A1 shows the main components of an aeroderivative-type gas turbine cogeneration system for electricity and steam generation. These components include: an air compressor, combustion chamber, gas turbine for air compression, power turbine for electricity generation and, a heat recovery steam generator for steam production. For this module we are primarily interested in the combustion chamber – that is where the emissions are created.

Figure A1 Gas turbine cogeneration system – air cooler, gas turbine and HRSG The seven key steps in the cogeneration process are:

1. Ambient air (shown as state 0 in Figure A1) is sent through a heat exchanger (the Air Cooler) to adjust its temperature to a nominal 60 F (state 1). Chilled water is used as the cold fluid in the Air Cooler. The incoming air is adjusted to 60 F prior to entering the air compressor in order to help maintain turbine efficiency. Chilled water is often needed and design conditions for the Air Cooler actually assume an average ambient air temperature of 87.5 F (state 0).

2. The cooled air is then sent to the Compressor to increase pressure (state 2).

3. Natural gas, compressed air, and injected steam/water are “burned” in the Combustion

Chamber (state 3). The natural gas is delivered from the pipeline at 77 F.

59

4. The combustion products are sent through the Gas Turbine (state 4). The shaft of this turbine is coupled to the Compressor. All work done by the Gas Turbine is used to power the Compressor.

5. The combustion products then expand to nearly atmospheric pressure in the Power Turbine

(state 5). The shaft of this turbine is coupled to a generator to produce electricity for the process.

6. The combustion products are sent through the heat recovery steam generator (HRSG),

consisting of two heat exchangers to recover heat before venting to the atmosphere. In the Evaporator the combustion products transfer heat to vaporize heated water into steam.

7. In the Economizer, the combustion products heat the feed water before this water is sent to

the Evaporator.

Assignments II – VI use the 7 reaction models we developed in this module. Assignments VI and VII use the complete GRI-3.0 Mech we developed in this module.

Assignment I - Data Reconciliation (Data for Two Different Combustor Designs Provided) Note to Instructors: You can skip Assignment I and simply provide students the reconciled values for Case A or Case B – see ESRL6 Faculty Only Folder. If you are not familiar with data reconciliation, you will need to read pages 1 – 15 of ESRL Module 2 – Data Reconciliation in a Cogeneration System and watch the associated video; the video and handout (ESRL Module 2) are coupled to make the process fairly quick. For Assignment 1 complete the data reconciliation process for just the combustor using data for: Case A: Steam Injected Combustor. Table A1 provides data for the steam injected combustor. or Case B: Water Injected Combustor. Table A2 provides data for the water injected combustor. Here the combustor is operating differently from the combustor in Module 2 as we are using steam/water injection to lower the amount of NOx formed. You will need to account for steam/water injection in your material and energy balances. I have provided a solution template Combustor Data Recon Solution Template Case A/Case B.xls which will help with this process. For the objective function, at the data reconciliation solution, you should obtain a value less than 0.3. Table A1 Case A Steam Injected Combustor - Measured Values and Instrument Standard

Deviations with Nomenclature

Name Description Value Units Standard Deviation

Ambient Pressure 14.696 psia 1

60

Ambient Temperature 547.17 R 2 Air flow rate 143.33 lb/s 20

Air P entering Compressor 14.696 psia 1 Air T entering Compressor 519.94 R 5 Air P leaving Compressor 243.7 psia 1 Air T leaving Compressor 1260.48 R 10 Natural Gas flow entering Combustor 2.6208 lb/s 0.07 Natural Gas lower heating value 21501 Btu/lb 200 Natural Gas T entering Combustor 536.67 R 10 Steam injection rate entering Combustor 2.64 lb/s 0.07 Steam injection T entering Combustor 909.67 R 10

Products gas P leaving Combustion Chamber 243.7 psia 1 Products gas T leaving Combustion Chamber 2400 R 150

Combustion products flow rate 150.6208 lb/s 20

, Heat loss in Combustion Chamber 1125 Btu/s 250

, Air enthalpy at state 2 Btu/lb

, Injected Steam enthalpy at state 2 Btu/lb

, Combustion products enthalpy state 3 Btu/lb

leaving in Stack Gas 35 ppm 1 ______________________________________________________________________________ Table A2 Case B Water Injected Combustor - Measured Values and Instrument Standard

Deviations with Nomenclature

Name Description Value Units Standard Deviation

Ambient Pressure 14.696 psia 1 Ambient Temperature 547.17 R 2 Air flow rate 143.33 lb/s 20

Air P entering Compressor 14.696 psia 1 Air T entering Compressor 519.94 R 5 Air P leaving Compressor 243.7 psia 1 Air T leaving Compressor 1260.48 R 10 Natural Gas flow entering Combustor 2.6208 lb/s 0.07 Natural Gas lower heating value 21501 Btu/lb 200 Natural Gas T entering Combustor 599.67 R 10 Water injection rate entering Combustor 2.64 lb/s 0.07 Water injection T entering Combustor 536.67 R Fixed

Products gas P leaving Combustion Chamber 243.7 psia 1 Products gas T leaving Combustion Chamber 2400 R 150

Combustion products flow rate 150.6208 lb/s 20

, Heat loss in Combustion Chamber 1125 Btu/s 250

, Air enthalpy at state 2 Btu/lb

61

, Injected Steam enthalpy at state 2 Btu/lb

, Combustion products enthalpy state 3 Btu/lb

leaving in Stack Gas 35 ppm 1_____________________________________________________________________________ Table A3 provides needed enthalpy data. Table A3 is explained in ESRL Module 2. Here the reference state is 77 F all species vapor phase. The , will be needed for water injection. Table A3. Enthalpy coefficients – linear fit of enthalpy data as

, , ,

, -146.446 0.257997

, -339.7232 0.6116

, / -368.57817 0.5510

, -1050.0

, -199.574 0.295265 Note to Instructors: You can skip Assignment I and simply provide students the reconciled values for Case A or Case B – see ESRL6 Faculty Only Folder. ■ Assignment II – Preliminary Design Using Example 8 of this Module - the system of 2 PSRs in series - determine the residence times needed (PSR1 and PSR2) to produce the measured NOx found from the cogeneration system (35 ppm). PSR1 will represent the flame zone and PSR2 will represent both the intermediate and dilution zones. Here the retention time in the first PSR will be the most important. Aeroderivative-type gas turbines for industrial use generally have a design flame zone equivalence ratio between 0.6 and 0.7. Make sure both PSR1 and PSR 2 are adiabatic. Use your reconciled data (Assignment 1 Case A or Case B) to complete Table A4 using 2 PSR (7 Reactions).xlsm. The variables that should be investigated are PSR1 primary zone (flame zone) equivalence ratio, PSR1 retention time, and PSR2 retention time. When using the provided emissions code (both 7 Reactions and Gri-Mech 3.0) it is important to remember that the feed is assumed to be vapor phase. For Case B Water Injected Combustor it is a reasonable approximation to assume that the air and water mix at the compressor exit and prior to injection into the combustion chamber. This mixing will lower the temperature of the air temperature from the compressor by vaporizing the water. You will need to determine this adiabatic mixing temperature using your reconciled values. We will want to use this adiabatic mixing temperature as the temperature of both the air and water feed in the emissions code but keep the natural gas feed at its reconciled value (~140 F).

62

Based on your reconciled values from Assignment I (Case A or Case B) + any additional runs to help with Table A4 interpolation – what values for ϕ, , and best match/represent the data found from the combustor/cogeneration system? After you determine the best match for ϕ, , and be sure to run one simulation with the reconciled measurements and without water injection for discussion purposes. Table A4 The influence of equivalence ratio and residence times on NOx formation

ϕ 0.6 0.01 0.01 0.6 0.02 0.001 0.6 0.02 0.01 0.6 0.03 0.001 0.6 0.03 0.01 0.6 0.04 0.001 0.6 0.04 0.01 0.6 0.05 0.001 0.6 0.05 0.01 0.7 0.01 0.01 0.7 0.02 0.001 0.7 0.02 0.01 0.7 0.03 0.001 0.7 0.03 0.01 0.7 0.04 0.001 0.7 0.04 0.01 0.7 0.05 0.001 0.7 0.05 0.01

■ Assignment III – Combustor Physical Design Here we want to use results from Assignment II to “size” the annular combustor. We know that the combustor length is fixed at 90.5 cm. Determine the cross-sectional area that would be needed be needed to produce the residence times you determined in Assignment II. ■ Assignment IV – Equilibrium Considerations In ESRL Module 5 we found that the equilibrium NOx concentration leaving the combustor was ~500 ppm. Comment on how long of a retention time will be need in PSR1 to reach equilibrium values. ■ Assignment V – Operational Questions Needing Your Combustor Design After completing Assignment II (Case A or Case B) we want to use your developed model to address changes in operational strategies that ACTUALLY are be considered at here LSU.

63

(1.) LSU /the combustor operator would like to reduce the amount of water/steam being injected to the combustor. This injected water is expensive to prepare as it goes through several stages of clean-up including packed-bed filtrations, reverse osmosis, and resin and activated carbon adsorption. The injected water is simply lost up the stack. Based on your final design, how much can the water flow to the combustor be reduced if permitting allows up to 40 ppm NOx. Remember as the water/steam flow is reduced the temperature in the PSR Flame Zone will increase which will increase the observed NOx. (2) LSU/the combustor operator may soon be asked to REDUCE the amount of NOx being produced. We are in a non-attainment area. Tighter EPA restrictions are expected to lower allowable NOx to 30 ppm. What do you recommend? ■

Assignment VI – NOx Emissions using GRI-3.0 Mech and GE LM2500 Specifications The complete GRI-Mech 3.0 mechanism may require ~ 30+ minutes to run on a typical PC making any design studies for Assignment VI very time consuming. After completing Assignment II (Case A or Case B) and Assignment III, use Example 16 of this Module - the system of 2 PSRs (both adiabatic) and 1 PFR in series to solve your system obtaining the reconciled outlet temperature from the combustor. Here now PSR1 represents the flame zone, PSR2 the intermediate zone and the PFR represents the dilution zone. Keep your determined retention times from Assignment II, your cross sectional area from Assignment III and use a length of 30 cm in the PFR. That will increase the length of the combustor (when compared to the design developed in Assignment III) but that is not important here. Next use the complete GRI-Mech 3.0 mechanism - to produce the measured NOx and temperatures found from the combustor. Use your Assignment II results for the PSR retention times, your cross sectional area from Assignment III and PFR length of 30 cm - use Example 17 of this Module. Do the results from the complete GRI mechanism match your 7 reaction system? Is it unexpected that the 7 reaction system produces results far different from a system with 325 reactions?

Finally let us use the complete GRI-Mech 3.0 mechanism with our reconciled data in the gas turbine system (GE LM2500) that actually generated the data. We can predict the NOx emissions for this system and compare it to the measured value of 35 ppm. Design data for the GE LM2500 are provided.

Combustor Design from GE LM2500 Specifications Cross sectional area (equivalent) for annular combustor = 962.1 cm2. Length = 90.5 cm. Volume = (962.1 cm2) (90.5 cm) = 87,070 cm3. Assume the combustor volume is roughly allocated as 2/5 primary zone, 1/5 intermediate zone, and 2/5 dilution zone and determine the retention time in the flame zone (PSR1), the retention time

64

in the intermediate zone (PSR2) and the dilution zone length (PFR). Be sure the equivalence ratio is 0.7. ■

Closing Remarks for Assignments II-VI: The 7 reaction system is a crude approximation of the gas turbine combustor kinetics. But it does allow trends and changes in the operating conditions to be quickly determined.

Results from the complete GRI-3.0 mechanism are correct and the provided codes are applicable to any similar combustion system. You may be surprised that our results from Assignment VI are not “spot on” with the measured NOx emissions. This last piece of the puzzle is addressed in Assignment VII.

■

Assignment VII – NOx Emissions GRI-3.0 Mech/ GE LM2500 Advanced Design Mixing in the flame zone is a very complex process. It is not accurate to assume one single or average equivalence ratio can represent the flame zone. A distribution of equivalence ratios in parallel PSRs (about the known average value) is needed to more accurately model the flame zone. We have had reasonable success modeling the flame zone using 11 PSRs, each PSR with a different equivalence ratio (paper in preparation, 2015). The effect of equivalence ratio on predicted NOx is very non-linear. You can show yourself this by running the GE LM2500 from Assignment VI with an equivalence ratio of 0.8. Explain how to change the model of 2 PSR + PFR (GRI-3.0 Mech) if 1/3 of the total feed to the combustor sees the 0.8 equivalence ratio. How will the PSR retention times and the PFR design be changed? You should find that the NOx emissions will more than triple compared to the results in Assignment VI.