Integrated Method of Monitoring and Optimization of Steam Methane Reformer Process
2. Model Description
Steam reforming is the conversion of steam and hydrocarbons into a mixture of hydrogen, carbon monoxide, carbon dioxide, and unconverted reactants. Steam may be replaced either partially or
completely by carbon dioxide as reactant [11]. The reforming of natural gas with steam utilizes reforming reactions and water–gas shift reaction. Besides these two main reactions there are nine other possible reactions in the SMR process. With respect to simplifying the model for industrial users, only first three reactions presented in Table1were used for description of industrial SMR [9–11]. According to literature data only those reactions are critical for thermodynamic and kinetic consideration [10,11].
Table 1.Steam methane reformer (SMR) reactions used in the model.
Reaction Description Reaction ΔHo298
(kJ/mol) Steam-methane reforming 1, SR1 CH4+H2O↔CO+3H2 206.10 Water–gas shift, WGS CO+H2O↔CO2+H2 −41.15 Steam-methane reforming 2, SR2 CH4+2H2O↔CO2+4H2 165.00 Carbon dioxide-methane reforming CH4+CO2↔2CO+2H2 247.30
The net reforming reaction is strongly endothermic and occurs by increasing the number of moles. The overall effect of increasing reforming temperature on the effluent gas composition is to reduce the methane and carbon dioxide content and increase carbon monoxide and hydrogen content.
On decreasing reforming temperatures, the effects are reversed. The pressure of the system is so nearly fixed that reforming pressure should be considered invariable. However, increasing pressure has an effect similar to reducing temperatures and reformer designs always represent a compromise in economics. The water gas shift reaction is exothermic with shifting of the carbon monoxide favored by low temperature. However, the rate of reaction is favored by high temperature. It can be seen that with methane the stoichiometric requirement for steam per carbon atom is 1.0. However, it has been demonstrated that this is not practical because all primary reformer catalysts developed so far tend to promote carbon (char) forming reactions under such SMR conditions. Those reactions can only be suppressed by using an excess of steam, with the result that the minimum steam per carbon atom ratio is approximately 1.7 [12]. The reforming reaction itself is also promoted by an excess of steam and hence the ratios of 3.0 to 3.5 are commonly used in practice [12]. However, lower steam-to-carbon ratios are attractive from the economic point of view.
Important considerations during operation of SMR are the type of furnace used to transfer heat to the reactants, the catalyst properties such as activity, lifetime, size, and strength, operating conditions such as feed composition, pressure, temperature, and desired product composition. The catalyst in all of the SMR furnaces is contained in heat resistant alloy tubes that typically have outside diameters from 80 to 180 mm, wall thickness of 9 to 20 mm and overall length of 10,000 to 13,000 mm [12]. Fired lengths in commercial SMR furnaces vary from approximately 200 to as much as 3500 mm [12]. Firing is usually controlled such that tube wall temperatures are maintained at values that will give a reasonable tube lifetime. By design and industry practice, maximum allowable tube wall temperatures are set to give an in-service lifetime of 100,000 h when taking into account the stress-to-rupture properties of the particular alloy used in manufacturing the tube [13]. As noted by Schillmoller et al. [13] an increase in temperature of only 38◦C above design with the common HK-40 material (25% chrome, 20% nickel alloy) can shorten the tube lifetime from 10 to 1.4 years. The general SMR furnace classifications according to firing pattern are the following: top fired, side fired, and bottom fired [12]. All of the SMR furnaces have combustion heat recovery sections used for preheating feed streams, boiler feed water, etc. The schematic diagram of the top-fired SMR based on Kellogg Inc. design located in Petrokemija Plc., Kutina, used in the model is given in Figure2.
Figure 2.The schematic diagram of the top-fired SMR based on Kellogg Inc. design used in the model.
Catalyst activity has an important effect on the tube wall temperature in all SMR furnaces and is usually monitored by the plant operators by portable measurement devices. The heat transfer through the walls of the reformer tubes influences the catalyst activity. Of the total heat being transferred, the high activity catalyst uses more for the endothermic reforming reaction and less for raising the gas temperature. Besides that, feed gases can vary in composition from being nearly pure methane to the heavy hydrocarbons such as naphtha. As a result, specific catalyst formulations have been developed so far for different feed gas compositions. Xu and Froment [11] used in their work catalyst which contained 15.2% nickel, supported on magnesium spinel with a BET surface area of 58 m2, nickel surface area of 9.3 m2/gcat, and with the void fraction of 0.528. The catalyst used in simulation contained 14.5% nickel, supported on calcium aluminate with BET surface area of 57 m2, nickel surface area of 12.0 m2/gcat, and with the void fraction of 0.51963. The mentioned catalyst characteristics are in good alignment with the work of Xu and Froment [11] and therefore literature kinetics data are applicable for the model in spite of the fact that different catalyst support was used in the simulation procedure.
With respect to achieve an energy savings and to ensure mild temperature conditions against tubes during operation of SMR it is of utmost importance to maintain the catalyst performance at the best possible level. Therefore, a reliable and rapid mathematical model was important to be designed for continuous monitoring and evaluation of the steam methane reformer catalyst in an existing installation. Taking into account all theoretical explanations and literature review, model assumptions are given as follows:
1. The reaction mixture follows ideal gas law;
2. All reformer tubes within the furnace are identical; the overall performance of the reformer tubes is achieved by multiplication of one tube by the number of all other tubes;
3. The system operates in a dynamic state;
4. A 1-D analysis was used for mass flow, heat and momentum transfer. All important process variables are uniform at any cross section of the catalyst bed in the reformer tubes;
5. The model converts all higher hydrocarbons to an equivalent methane before any tube integrations take place. Kinetic expressions for SR1, SR2, and WGS reactions are only used;
6. There is no axial diffusion of mass and heat;
7. The model is heterogeneous;
8. There is no external mass and heat transfer resistance between the catalyst and the process gas;
9. Diffusion resistance between the catalyst is considerable and the same is considered;
SMR catalyst performance is usually evaluated in terms of its methane approach to equilibrium (ATECH4), furnace tube wall temperatures, heat flux, pressure drop, and presence or absence of hot bands on the tubes. TheATECH4is the difference between the actual gas temperature exiting the catalyst (T1) and the temperature at which the measured outlet gas composition would be at equilibrium (T2).
By definition, the actualATECH4cannot be less than zero. The temperature at which the outlet gas composition would be at equilibrium is determined in the model by calculating from the material balance the equilibrium constant for the SR1 reaction defined by [9,10]:
KSR1= pCO·p3H
2
pCH4·pH2O =1.198×1017exp −26830
T
(1) and determining the corresponding temperature from aT2-KSR1correlating equation in the model, whereKrepresents chemical equilibrium constant, andpis partial pressure of corresponding component (in bar), whileTis the temperature (in K). Due to elevated temperature and pressure, the gaseous reaction mixture in the SMR process is not ideal and does not obey Mendeleev–Clapeyron ideal gas law.
However, the Dalton law of partial pressure can be used in the model because the main assumption is that the reaction mixture behaves as an ideal gas.
Properly designed SMR should, with new catalyst, haveATECH4much lower than 5–10◦C.
Those plants having effective desulphurization systems often have furnaces operating withATECH4in the 0–5◦C range. When evaluations give these type approaches, it can be said the catalyst is giving satisfactory performance. CalculatedATECH4of 5–10◦C could be considered in the intermediate range and performance classified as acceptable, depending, of course, on the specific design in question.
TheATECH4above 10◦C would correspond to marginal performance and would generally become a factor in discharging the catalyst. According to this it appears that continuous monitoring and evaluation procedure ofATECH4is a feasible perspective to keep catalyst performance at the best available level.
In many SMR furnace designs there can be a significant difference between measured outlet gas temperature and the actual outlet gas temperature. The measuring point is often in an outlet gas header, and because of heat losses from the bottom of the SMR furnace and exit lines, the resulting temperature is lower than the true catalyst exit value. For these cases, theATECH4may well turn out to be a negative number. If the measured outlet gas composition is sufficiently accurate, the actual gas temperature exiting the catalyst can be calculated by assuming the gas is at equilibrium with respect to the WGS reaction [9,10]:
KWGS= pCO2·pH2
pCO·pH2O=1.767×10−2exp 4400
T
(2) The model assumes that WGS reaction reaches equilibrium in a SMR but the SR1 reaction does not.
However, a clearance can be made for the deviation from equilibrium by anATECH4and thus at a given exit temperature bothKSR1andKWGSare known [14]. From Equations (1) and (2), the equilibrium constant for the SR1 reaction and WGS reaction at the respective temperature can be calculated. It is considered that equilibrium conversion and chemical equilibrium of the reactions depends on the thermodynamic properties of the gaseous mixture and catalyst characteristics.
To properly monitor and evaluate the catalyst performance it is necessary to compare DCS readings of the gas chromatography analysis data with predicted gas composition and how the pressure drop DCS readings data compare to the theoretically predicted values. Besides that, the temperature rise across the tube is required to indicate the kinds of adjustment that can be justified. The key components in the exit dry gas analyses are methane and, in addition, the carbon oxides (CO and CO2), while hydrogen composition is then adjusted to give a total dry gas composition of 100%.
The accuracy of the pressure drop calculation is such that the actual value should be within 10%
of the theoretical value. Actual pressure drops greatly exceeding the theoretical value would indicate
some problem has or is occurring. Examples of such problems would be carbon formation catalyst breakage, faulty loading such as over-vibrating the tubes and/or failure to clean the tubes, pigtails, support plates, etc.
The calculations inside the developed model involve the solution of material and energy balance equations along with reaction kinetic expressions for the catalysts according to the literature findings [15–25]. The model calculates the material balance,ATECH4, gas radial temperature gradient, pressure drop, heat duty, molar fluxes, and reaction rates. The analytical expressions used in the one-dimensional heterogeneous model are shown in Figure3. The calculation procedure is performed in Matlab (Version 2019b, The MathWorks, Inc., Natick, US, MA, 2019) file which is fairly easy to use.
Figure 3.The analytical expressions used in the one-dimensional heterogeneous model according to literature findings [9,10,15–25].
The basic input requirements consist of two parts, one which must be manually filled in by the operator and another one which is automatically exchanged between DCS data and memory block by compiling with system-function. In Table2a list of all necessary variables needed for monitoring and evaluation of the SMR catalyst is shown.
The model converts the total wet feed flow to mole fractions of carbon, hydrogen, and oxygen with a base of the inlet dry gas as 100%. By using the mass balance and the equilibrium Equations (1) and (2), one can derive a quadratic equation:
a2(1−KWGS) +φa−KWGS(φ−4d)(B−2d) =0 (3) Solving foragive following expression:
a=−φ±
φ2+4(1−KWGS)(θ−4d)(B−2d)KWGS
1/2
2(1−KWGS) (4)
whereΦandθpresent intermediate calculation parameters as follows:
φ=C+HKWGS+3d(1−2KWGS)−θ(1−KWGS) (5)
θ=2C+H−2O or a+b+4d (6)
whereC,H, andOdenote total molar quantities of carbon, hydrogen, and oxygen in compounds in the system (in kmol), whilea,b,c, anddrepresent molar quantities of H2, CO, CO2, and CH4in reformed gas (in kmol), respectively.
Pressure (in bar or atm) in the tubes is calculated according to p=C+H−2d+i
a
KSR1d(H−a−2d) a(θ−a−4d)
1/2
(7) whereidenotes molar quantity of inert gases (Ar+He) in reformed gas (in kmol).
By using Equations (4) and (7) the model solves reforming calculations by assuming a methane content of the reformed gas (d), solving the corresponding hydrogen content (a) and pressure (p).
The Newton–Raphson technique was used to get a rapid convergence in order to obtain the reformed gas composition. The technique uses previous values of the methane outlet molar concentration (dn−2 and dn−1) to predict the value for the next calculation:
dn−1=dn− (pn−p)
(pn−pn−1)(dn−dn−1) (8) where thenthand (n−1)thresults are used to predict the value ofdto use in the (n+1)thcalculation.
The activity multiplier will default to the standard values if there is no input (preferred values are in range from 0.25 to 0.65). The model minimizes the function which is the sum of the appropriately weighted squares of the difference between DCS readings and corresponding values from the simulation.
Using input data, the model will converge in 30 s or less to give final results. Logic flow diagram for this model is shown in Figure4.
Figure 4.Model logic flow diagram.
For the purpose of synchronization between the model and any DCS system the C++programming language was used for development of system-function and compiled with the MATLAB Compiler (MEX) (Version 2019b, The MathWorks, Inc. Natick, US, MA, 2019) [26]. The programming procedure
which contained the basic functionality for SIMULINK shared memory block is shown as a logic flow diagram in Figure5.
Figure 5.Logic flow diagram of developed system-function and shared memory block.
Characteristic process data of the top-fired SMR designed by Kellogg Inc. which is used in developed model for data reconciliation are given in Table3.
Limitations of developed model are the following:
1. impossibility to evaluate carbon forming potential with higher hydrocarbon feed streams, due to the reason that the model converts all of these compounds to an equivalent methane before any tube integrations take place. However, it is believed that from about 30% tube level down, all higher hydrocarbons have been broken down. Carbon forming predictions from this point in the tube to the bottom are accurate;
2. the model does not provide any information about tube hot band problems. The model with the heat flux profile does show the region of the highest heat transfer, but nothing more as to hot band formation;
3. all of the reformer tubes within the furnace are assumed to be identical. Of course, this is not true in real conditions due to reason that tubes close to the refractory brick wall are under different heat fluxes in comparison with the tubes in the middle part of the furnace. In order to compensate this nonuniformity sets of simulations were performed and results are adjusted against real process data.
Table2.ListofvariablesformonitoringandevaluationoftheSMRcatalyst. No.VariableUnitInputbyVariableUnitInputby 1.Reformertubelengthmm Operator
Tubefeedgasvolumeflowm3/h DCS synchronization memoryblockby encodingS-function
2.IDofreformertubemmTubesteammassflowt/h 3.ODofreformertubemmTubeinlettemperature◦C 4.NumberofreformertubespcsTubeoutlettemperature◦C 5.ThermalconductivityofreformertubematerialkJ/m2·hr·KTubeinletpressurebar 6.FiredlengthmmTubeoutletpressurebar 7.CatalystparticleheightmmTubepressuredropbar 8.CatalystparticleholediametermmCH4contentinreformed gasMol% 9.No.ofholes-Furnacefuelgasvolume flowm3/h 10.Catalystbulkdensitykg/m3Fuelgastemperature◦C 11.Activitymultiplier-Furnaceairvolumeflowm3/h 12.Tubewalltemperature◦CFurnaceairtemperature◦C 13.HeattransfercoefficientkJ/m2·hr·KCH4contentinreformed gasdrymol% 14.CH4contentinfeedgasdrymol%COcontentinreformedgasdrymol% 15.C2H6contentinfeedgasdrymol%CO2contentinreformed gasdrymol% 16.C3H8contentinfeedgasdrymol%H2contentinreformedgasdrymol% 17.C4H10contentinfeedgasdrymol%N2contentinreformedgasdrymol% 18.C5H12contentinfeedgasdrymol%Ar+Hecontentin reformedgasdrymol% 19.C6H12andC6+contentinfeedgasdrymol% 20.COcontentinfeedgasdrymol% 21.CO2contentinfeedgasdrymol% 22.H2contentinfeedgasdrymol% 23.N2contentinfeedgasdrymol% 24.H2Scontentinfeedgasdrymol% 25.Ar+Hecontentinfeedgasdrymol%
Table3.Summaryofprocessdataofthetop-firedSMR. ReformerTubesValue/UnitCatalystPelletsValue/Unit Heatedlengthofreformertubes10.00mShapeRaschigringswith12holes Insidediameterofreformertubes0.085mDimensions19×12mm/30%;19×16mm/70%; Outsidediameterofreformertubes0.110mBulkdensity800kg/m3 Numberofreformertubes520Porosity0.51963 ConstructionmaterialofreformertubesMANAURITEXMand900Tortuosity2.74 Numberofrows10Meanporeradius80Å Numberofarchburners198Catalystcharacteristiclength0.001948cm Heatdutyofreformer204.80MWhCatalystmaterialNiO+CaAl12O19 Skintemperature840◦CCatalystquantity32.0tons ProcessGasFlowRateand CompositionValue/UnitFuelCharacteristicsValue/Unit Molarflowrate1530kmol/hMolarflowrate792kmol/h;3%ofO2excessairat 503K Compositionmol%,drybasisCompositionmol%,drybasis C2H60.00C2H61.11 C3H80.00C3H80.00 i-C4H100.00i-C4H100.00 H21.43H21.43 CO20.95CO20.95 N20.95N20.95 Ar+He0.01Ar+He0.01 InletConditionsValue/UnitOutletConditionsValue/Unit Temperature773KTemperature800◦C Pressure30.5barPressure30.0bar S/Cratio3.60S/Cratio3.60 Maximumallowableoutlettemperature900◦C Ammoniaproductioncapacity1360MTPD