Efficiency Comparison of Valve and Sieve Trays in Distillation Columns Robert H. Anderson,’ Gavln Garrett,’ and Matthew Van Winkle’ The University of Texas at Austin, Austin, Texas 78772
The purpose of this study was to compare Murphree efficiencies of various valve trays to those of sieve trays, for 18-in. and overall efficiency for larger diameter columns. Within the accuracy of the available basic data, effects of component surface tension differences and component molar latent heat of vaporization differences were observed. The valve tray types studied exhibited a higher average operating efficiency and greater turndown ratio than the sieve tray studied. The binary system which demonstrated a positive deviation from neutrality by both Zuiderweg’s definition of surface tension effects and Todd’s definition of molar latent heat of vaporization effects exhibited a higher operating efficiency than did the negative binary system. Efficiency plots determined for all the valve trays studied were quite similar. The only major difference in these plots was a slight shift in average efficiency between the different valve trays.
Introduction Over the past several years fractionation devices have changed greatly in design to obtain better efficiencies and lower pressure drops as well as to correct certain other deficiencies frequently encountered in commercial operation. Two general designs of trays or contacting devices and their modifications represent the majority of tray types in new applications a t the present time. These are the sieve tray and the valve tray and each has its specific advantages and disadvantages. Many studies of efficiency and pressure drop have been conducted on the two tray types in academic and industrial laboratories and most of the studies on proprietary trays have been conducted by Fractionation Research Incorporated (FRI). Most of the FRI material is available only to its members, who only may release the information pertaining to their own devices. The industrial results are in most cases unavailable. Further, most academic distillation research is done on equipment far too small in size to be of value for industrial application. Experimental Equipment These considerations served as a basis for the present work as well as that of Todd (1971) and Garrett (1975). All data taken during this research were taken on the 18-in. diameter distillation column. Details of the column design are shown in Table 111. The column has two 18 X 24 in. glass sections to allow visual observation of the tray action. The tray package was a standard 18-in. diameter package supplied by the Wyatt Corporation. It had adjustable downcomer escape clearances and weir heights. It was modified by our shop to be very similar in basic design to that used by Todd (1971). This modified package design did, however, have replaceable trays so that different tray types could be tested. The experimental equipment described in detail by Todd consisted of three plates on 18-in. tray spacing. All trays were equipped with vapor and liquid sampling devices as well as thermocouples and pressure measuring devices (DP cells) so that a number of compositions and conditions could be measured simultaneously. The test plate was the center plate and was located in the column so that operating conditions on the plate could be observed as well as measured by instrumentation. The dual thermosyphon Cosden Oil and Chemical Co., Big Spring, Tx. 96
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
reboilers had a heat input capacity of 1.5 X lo6 B t u h r . Two banks of water cooled condensers, two in series, two in parallel, were used. The large heating capacity was provided to reach flooding conditions for any system contemplated for study. The entire experimental equipment was provided with automatic instrumentation for control. All measurement and control instruments and the same control loops and measurements points used in this study were the same as those used by Todd (1971) and Garrett (1975). Table I shows the points where column temperatures were measured and Table I1 shows the points where samples were removed for the column. Table I11 lists pertinent information about the tray packages used in this study and that used by Todd while Table IV includes column information related to the literature data used here for comparison. Experimental Procedure The experimental work consisted of running two binary mixtures in an 18-in. diameter distillation column and measuring tray efficiency and hydraulic data. For each binary, a 100% of flood sample, including all necessary data, was taken for each tray type. Data were taken at 15,30,45, 60, 75, 90, and 97.5% of the column flood points in each case. These data points were selected so that the operation of the tray could be studied over a wide range of operating conditions. Binary Systems. Two systems were studied in this research, l-propanol-toluene and benzene-l-propanol binaries. By the definition given by Zuiderweg and Harmens (1958) for surface tension effects, the l-propanol-toluene system exhibits a negative deviation from neutrality, while the l-propanol-benzene system is positive over the concentration range at 3OoC. Because the actual temperature increase in the column from top to bottom had a greater effect on the liquid surface tension than the concentration effect, both systems were slightly negative. By the Todd (1972) definition based on latent heat effects, the l-propanol-toluene system showed positive deviations while the benzene-l-propanol system exhibited negative deviations. Positive deviation is defined as follows. (1) For surface tension effects, the surface tension of the internal reflux liquid increases from the top to the bottom of the column because the surface tension of the higher boiling component is greater than that of the lower boiling component.
Table I. List of Experimental Temperature Measurement Points ~~~~
Table 111. Experimental Column Information Tray type
~
1. Vapor space above tray 2,
'1, of the distance from the
downcomer inlet t o the outlet weir 2. Vapor space above tray 2, ' I 2of the distance from the downcomer inlet to the outlet weir 3. Vapor space above tray 2, 'I4of the distance from the downcomer inlet to the outlet weir 4. Liquid in the downcomer from tray 1 5. Liquid on tray 2, ' I , of the distance from the downcomer inlet t o the outlet weir of the distance from the down6. Liquid on tray 2, comer inlet to the outlet weir 7. Vapor space above tray 3, 'I4of the distance from the downcomer inlet t o the outlet weir 8. Vapor space above tray 3, ' I 2of the distance from the downcomer inlet to the outlet weir 9. Vapor space above tray 3, '1, of the distance from the downcomer inlet to the outlet weir 10. Liquid in the downcomer from tray 2 11. Liquid in the downcomer from tray 3 12. Liquid in the column bottoms 13. Liquid on tray 1, '1' of the distance from the inlet skirt to the outlet weir 14. Liquid on tray 1, '/, of the distance from the inlet skirt to the outlet weir 15. Overhead vapor from column 16. Reboiler return line 1 7 . Condensate entering the reflux drum 18. Condensate leaving the reflux drum 19. Inlet cooling heater 20. Intermediate cooling water 21. Outlet cooling water 22. Room temperature 23. Condensate leaving the reboiler 24. Vapor space below tray 3
Column diameter, in. Column cross-sectional area, ft2 Tray spacing, in. Active or bubbling area per tray, ft2 Net area per tray, ft2 Segmental downcomer area, top & bottom, ft2 Weir height, in. Downcomer escape clearance, in. Slot or hole area, % active area Sieve tray hole size, in.
Nutter
Wyatt
Sieve
18.0
18.0
1.8.0
1.68 18.0
1.68 18.0
1.68 18.0
1.06 1.45
1.24 1.35
1.24 1.35
0.102 2.0
0.107 2.0
0.107 2.0
0.75
0.75
0.75
12.5
12.8
-
12.8 0.25
Glitsch
Nutter
Koch
47.75 12.44 24.0 9.3
48.0 12.56 24.0
48.0
1.04 1.38 2.0
0.95 1.44
-
Table IV. Four-Foot Column Information
Column diameter, in. Column cross-sectional area, ft2 Tray spacing, in. Bubbling area, ft2 Area of downcomer at bottom, PLO A"
Area of downcomer at top, ft2 Downcomer skirt clearance, in. Outlet weir height, in.
2.0
__
-
-
24.0
-
-
3.0
Table 11. List of the Sample Collection Points 1. Vapor above tray 2, ' I , of the distance from the down-
2. 3. 4. 5.
6. 7. 8. 9. 10. 11.
12. 13. 14.
comer inlet to the outlet weir Vapor above tray 2, ' I , of the distance from the downcomer inlet to the outlet weir Vapor above tray 2, 'I., of the distance from the downcomer inlet t o the outlet weir Vapor above tray 3, '/., of the distance from the downcomer inlet to the outlet weir Vapor above tray 3, ' I , of the distance from the downcomer inlet t o the outlet weir Vapor above tray 3, ' I I , of the distance from the downcomer inlet to the outlet weir Liquid on tray 2, '1, of the distance from the downcomer inlet to the outlet weir Liquid on tray 2, '//, of the distance from the downcomer inlet to the outlet weir Liquid in downcomer from tray 1 Liquid in downcomer from tray 2 Liquid in downcomer from tray 3 Bottoms product Overhead product Vapor below tray 3
(2) For molar latent heat of vaporization effects, the molar latent heat of the lower boiling component is greater than that of the higher boiling component. Negative deviation represents the opposite behavior, while neutral systems have either the same surface tensions or the same latent heats of vaporization. Thus it was hoped by using a common component, 1-propanol, the effects of surface tension and unequal molal latent heats of vaporization on efficiency could be demonstrated. These particular binaries were selected so that relatively large separation factors for the components (large a's were utilized) could be obtained with only three contact stages, while using util-
Table V. Source of Experimental Dataa Col.
Valve trays
Investigator
diameWhere ter, in.
Reference
18 Todd(1972) Todd UT FRI 48 FRI (1964) FRI FRI 48 Koch(1968) FRI FRI 48 Glitsch (1967) FRI UT 18 This work Anderson Garrett UT 18 Thiswork Perforated Anderson UT 18 This work This work tray Garrett UT 18 a All systems considered were binary systems. Those studied at The University of Texas were benzene-l-propano1 and 1-propanol-toluene. The system reported for the FRI studies was cyclohexane-n-heptane. Nutter Nutter Koch Glitsch Wyatt
ity water in the condensers and 100 psig steam in the reboilers.
Source of Data The data used in this study (see Table V) were obtained from the following sources: vapor-liquid equilibrium data for the benzene-1-propanol binary were reported by Prabhu and Van Winkle (1963); the vapor-liquid equilibrium data for the toluene-1-propanol binary were reported by Lu (1957). All physical properties of the binary systems were computed as outlined in the API Technical Data Book (1966). This is the same source of data and binary systems used by Todd in previous work done with this column. Data Analysis. The raw data collected (temperature, pressures, and compositions) were analyzed by a computer Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
97
program originally written by Todd (1971), but was modified for this work by Anderson and Garrett. All the column flow properties were determined by material and energy balances around the bottom of the column including the reboiler. Also, all efficiency data reported have been corrected for the effect of heat transfer through the downcomer walls on the composition of the phases leaving the tray. This correction was recommended by Ellis and Shelton (1960) and Todd (1971). The experimental and analysis procedure used in this work is the same as that used by Todd (1971). Error Analysis. Estimation of the size of errors in an experimental study aids in determining the validity of the research results. Errors were considered to result from three main sources: instrument accuracy, operating technique, and raw data analysis. Temperatures could be measured within 0.5'F. Column pressure and pressure drops could be measured within 0.1 in. of water. Samples could be analyzed within 0.16 wt % and the column flow rates could be measured within 1.6%. Errors occurring in the data analysis from these sources are considered negligible. From experimental techniques one source of error is maintaining essentially steady-state conditions in the column when samples are taken. The column was run for a minimum of 30 min without any noticeable change occurring in any of the temperature, pressure, or flow rate recorders. Another error source is the sampling technique. Before the final sample was taken, a t least 30 cm3 of fluid was removed from the sample line to assure the sample was fresh material from the column. The lines were also voided with nitrogen before the samples were taken. The samples were immediately cooled in the sample lines and samples from the lines were immediately sealed to prevent evaporation. Liquid samples removed from the downcomers could be nonrepresentative because of liquid bypass across the tray. This was corrected by recalculating liquid data by material and energy balances around the bottom of the column including the reboilers. Analysis of the data by computer yielded Murphree plate (1925) efficiency data on the tray packages. The efficiency data calculated showed a standard deviation of 5.6 on the reproducibility of these results. The greatest error occurred a t the lowest and highest percent of flood rates studied (15% and 98% of flood), where the greatest error would be expected. This error in the reproducibility of the efficiency values resulted in a standard deviation of 10.4. (u, standard deviation indicates the data scatter which is a measure of accuracy.) Results This study provided data for the determination of Murphree tray efficiency vs. column loading for two different tray types in the same column so that their performance could be directly compared. Also, the data gathered by Todd (1972) on a different tray design could be compared to these data because they were taken on a closely similar column. All the data reported are for total reflux runs. Tables VI and VI1 show the results of these experiments. The percent of flood listed in Tables VI, VII, and VI11 was determined as a linear fraction of the steam rate required to flood the column. The column flood point was determined by slowly increasing the steam rate (to the column) by increments until the level control in the overhead accumulator became erratic and the controller failed to function. At the same time that the level control function of the overhead accumulator became erratic, a large rise in the total column pressure drop was also observed. The data taken from the literature for comparison are 98
Ind. Eng. Chem., Process
Des. Dev., Vol. 15, No. 1, 1976
Table VI. Eighteen-Inch Column 1-Propanol-Toluene Binary Fs
0.32 0.64 0.87 1.18 1.44 1.71 1.82 0.23 0.43 0.63 0.92 1.24 1.44 1.53 0.41 0.69 0.86 1.13 1.39 1.65 1.73
% Flood
5%
E,,C
APT (in. of H,O)
Nutter Valve Tray 75.1 32.2 75.3 44.3 70.6 60.7 69.6 75.2 69.6 90.8 72.9 97.3 71.2 Wyatt Perfavalve Tray 15.4 64.9 27.6 72.8 42.3 72.6 58.5 72.6 74.7 76.7 90.0 61.1 96.0 45.2 Sieve Tray 15.7 15.0 29.6 50.2 43.6 61.2 60.2 63.0 74.7 57.8 89.8 57.0 97.8 52.8 16.1
1.0 1.4 1.3 1.6 2.1 3.0 3.9
1.3 1.2 1.2 1.6 2.2 3.9 4.4 0.02 0.51 0.85 0.89 1.10
1.40 2.30
Table VII. Eighteen-Iqch Column Benzene-1-Propanol Binary Fs
0.29 0.32 0.64 0.65 0.97 0.98 1.28 1.55 1.58 1.83 1.85 1.94 1.98 0.20 0.33 0.51 0.78 0.99 1.30 1.50 1.60 0.46 0.53 0.84 1.10
1.40 1.61 1.69
% Flood
% E,,c
Nutter Valve Tray 13.1 61.7 15.2 56.3 29.2 63.4 29.6 63.8 44.4 57.2 45.3 55.5 59.2 55.3 72.9 56.0 74.6 57.2 88.9 54.9 91.1 56.6 96.4 59.9 97.6 58.2 Wyatt Perfavalve Tray 12.1 43.1 16.0 52.2 30.6 51.8 44.4 55.5 56.6 50.8 75.1 52.4 90.0 35.9 96.0 34.3 Sieve Tray
APT (in.of H,O) 1.09 1.08 1.42 1.44 1.40 1.40 1.72 2.38 2.38 3.13 3.10 3.65 3.75 1.20 1.05 1.20 1.32 1.64 2.41 3.39 3.94
15.1
11.3
0.01
29.4 45.1 59.7 75.0 90.0 96.6
39.6 52.2 52.6 51.1 46.1 58.6
0.42 0.82 0.99 1.12 1.36 1.80
listed in Table VIII. Most of these data are from work done by Fractionation Research Institute (FRI). The FRI reported efficiencies are higher than those reported here because the FRI data were reported as overall efficiency rather than as Murphree vapor efficiency. The FRI data are reported as overall efficiency here because there were insufficient data in the FRI reports to calculate Murphree vapor efficiencies from them. The data reported on the Koch valve tray (Koch Engineering Co., Inc., 1968) are assumed to be FRI data since they were gathered on the same size
100
Table VIII. Four-Foot Column Cyclohexane-1-Heptane Binary Fs -
0.26 0.27 0.47 0.48 0.93 0.95 1.41 1.44 1.83 1.84 1.85 2.05 2.07 2.15 2.16 2.24 2.24 0.24 0.47 0.94 1.40 1.86 2.10 2.21 2.30 0.30 0.42 0.42 0.51 0.72 0.90 1.15 1.39 1.86 2.00
% Flood
Eo
I
I
2.3 2.2 2.8 2.9 3.2 3.4 4.1 4.4 5.7 5.5 6.0 7.2 7.7 8.4 9.0 9.9 10.5
... ...
I
I
i
I
I
i
I
IO
0 0 2 0 4 0 6 0 8 I O 1 2 14 1 6 18 2 0 2 2 2 4
-
F, F A C T O R
V,
pv)O
Figure 1. Efficiency study results on 18-in. diameter column 1propanol-toluene binary.
2.5 2.9 3.2 3.7 4.9 6.2 7.3 9.0
... ... ... ... ... ... ...
i
n - P r o p a n o l - toluene b i n a r y Atmospheric P r e s s u r e 18 in Diameter Calumn I E in Tray Spacing
APT (in. of hot liquid)
Glitsch Valve Tray 82.3 75.0 20 91.6 21 97.0. 41 90.0 42 92.5 62 91.5 63 92.2 80 82.0 80 87.1 82 85.2 90 76.5 92 78.8 95 74.0 96 72.3 100 60.6 100 61.3 Nutter Valve Tray 10 83.6 20 96.0 40 91.8 60 86.1 80 82.0 90 71.5 95 61.1 100 50.0 Koch Valve Tray ... 71.9 ... 93.2 ... 88.2 ... 84.9 ... 93.8 ... 85.5 ... 84.7 ... 83.0 ... 80.6 ... 72.3 11 11
I
Benzene -n-propanol binary Atmospheric Pressure l E i n Oiameter Column 18 in T r a y S p a c i n g
2 EO :70 60
- Nuller Valve ,Type o - Wyatt P e r f a Valve 0 - 1/4 in S i e v e Troy
0
20IO
-
01 0
I
I
I
I
I
I
1
I
1
-
B
I
I
I
14 16 18 2 0 2 2 2 4
0 2 0 4 0 6 08 I O 12 Fr F A C T O R - V ,
( pv)05
Figure 2. Efficiency study results on 18-in. diameter column benzene-1-propanol binary.
...
1001
1
1
.
1
I
I
1
1
I
I
I
I
I
90 -
column and with the same binary system and same standard FRI pressure, but the report does not specify where the data were obtained. The Glitsch valve (Fritz W. Glitsch and Sons, Inc.) and Nutter valve (FRI, 1964) data are specified as reported by FRI. All the data reported are for total reflux runs. Since the results obtained on this experimental column and the literature data have a common tray type (Nutter valves), a valid comparison can be made between these data. All of the valve tray types tested in the FRI tests produced nearly the same average efficiency and turndown ratio. They all produced the same shape of curve with only a very slight shift in average efficiency value at any given loading point. The data reported on the four foot diameter column for bubble trays showed approximately a 20% lower efficiency and approximately 40% narrower range of operation. Figure 3 shows these results. The data from the studies on the 18-in. column agreed with those from the 4-ft column. The average efficiency of the two valve trays was approximately the same, while the average efficiency of the sieve tray was approximately 20% less for the toluene-1-propanol binary. For the benzene-lpropanol binary, the average efficiency was the same for the valve tray and the sieve tray over their respective operating ranges. The range of operation of the Nutter valve tray was approximately 40% more than that of the sieve tray. Figures 1 and 2 show the results for the two aromaticalcohol binaries tested. Figure 1 shows toluene-1-propanol which is slightly negative based on surface tension and positive based on latent
%
80-
5
70-
u
/
Z 60w
=
50-
0
Z 40-
0 In
30-
G l i t s c h V a l v e s , Type V - l N u l t e r Valves, Type B 0 - Koch V a l v e s , Type T F _-_A v e r a g e B u b b l e Tray Oat0 o -
0-
C y c l o h e x a n e - n - h e p t a n e binary 24 prig 4 f t Diameter Column 24 in Tray Spacing
0
0 2 0 4 0 6 O B I O 12
14 16
I 8 20 2 2 2 4
F, F A C T O R - V, I p V ) O
Figure 3. Efficiency study results on 4-ft inside diameter column.
5 0 I E in D i a m e t e r Column 18 in T r a y S p a c i n g
0 0 2 0 4 0 6 08 I O 1 2 14 16 I 8 20 FI F A C T O R
-
V, Lpr)O5
Figure 4. Pressure drop results on the 18-in. inside diameter column.
Ind. Eng. Chem., Process Des. Dev.. Vol. 15,No. 1, 1976
99
10.01
, , , , , , , , ,
l Y ,
,
Cyclohexane-n- heptane binary 24psig 4 f t D i a m e t e r Column 24 in. T r o y S p a c i n g
Literature Cited
Y
cc
v) 3
9
20-
P
0
o 0
-Glitsch Valve, Type V-I - Nutter Valve, Type E
0 2 0 4 0 6 0 8 I O 12
FI F A C T O R
Figure 5. umn.
of hot liquid. Both figures show the same shape for the valve trays studied: a large region a t low loading where the pressure drop is fairly constant and then a fast increase in pressure drop with column loading as the flooding point is approached. The sieve tray shows a similar trend, but it has a 50-7096 lower pressure drop through its operating range than the valve trays.
Pressure drop results
- Vr
14 16 I S 2 0 2 2 2 4 lpV)O
on the 4-ft inside diameter col-
heat effects exhibits a higher efficiency than that shown in Figure 2 (benzene-1-propanol). The benzene-1-propanol system is slightly negative based on surface tension effects and negative based on latent heat effects. Hydraulic data in terms of single tray pressure drops are reported in Tables VI, VII, and VIII. These data are also shown in Figures 4 and 5. The data for the 18.-in. diameter column are reported as inches of water while the data for the 4-ft diameter column, Figure 5, are reported as inches
American Petroleum Institute, Division of Refining, “Technical Data Book-Ps troleum Reflning,” New York, N.Y., 1966. Ellis, S. R., Shelton, J. T., “International Symposium on Distillation,” Institution of Chemical Engineering, pp 171-176, London, May 1960. Fractionation Research, Inc., “Report of Tests of Nutter Type B Float Valve Trays,” Alhambra, Calif., July 2, 1964. Fritz W. Glltsch and Sons, Inc., “Glitsch V-1 Ballast Trav.” Bulletin No. 160. Dallas, Texas. Garrett, G. R., PH.D. Dissertation, The University of Texas, Austin, Texas, 1975. Koch Engineering Co., Inc., Bulletin No. 761, Wichita, Kansas, 1968. Lu. B. C. Y.. Can. J. Techno/.. 34. 468-472 119571. Murphree, E. V., I d . Eng. Chem.; 17, 747 (i925).’ Prabhu, P. S., Van Winkle, M., J. Chem. Eng. Data, 8, 210-214 (1963). Todd, W. G., Ph.D. Dissertation, The University of Texas, Aug 1971. Todd, W. G., Van Winkle, M., I d . Eng. Chem., Process Des. Dev., 11, 589 (1972a). Todd, W. G., Van Winkle, M., Ind. Eng. Chgm., Process Des. Dev., 11, 578 (1972b). Zuiderweg, F. J., Harmens, A., Chem. Eng. Scl, 8, 89 (1958).
Received for review February 19,1975 Accepted September 2,1975
Hydrogen Production from Water by Means of Chemical Cycles Eduardo D. Glandt and Alan L. Myers* Department of Chemicaland Biochemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19 I74
A thermochemical process uses heat instead of work to dissociate water into hydrogen and oxygen. The principle by which a reaction with an unfavorable AG can be driven by dividing it into several steps is discussed. Dozens of cycles that operate below 8OOOC have been proposed but none of them has been shown to work. Previous research indicates that no two-step cycle exists. A systematic study of three-step processes was performed by classifying them into standard patterns. The result of the study is that a three-step cycle probably does not exist.
Introduction The importance of hydrogen as a potential nonpolluting fuel is well known. I t will, however, be in short supply sooner as a chemical feedstock, since hydrogen is the basic raw material and major cost for fertilizer via nitrogen fixation by the Haber process, the crucial ingredient in coal liquefaction and petroleum desulfurization, as well as the limiting reactant in methanol synthesis for solvent uses and possible substitution for gasoline or liquid fuels. With these needs in mind, it is clear that new nonfossil sources of hydrogen should be studied, whatever the controversy about the role of hydrogen in a “hydrogen fuel economy” of the future. A closed-cycle thermochemical process is designed to split water into hydrogen and oxygen using only water and heat energy (at less than 8OOOC) but no other raw materials. The advantage over electrolysis is the potentially higher thermal efficiency (perhaps 50%) associated with the thermochemical method. 100
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
Key references which contain the most important thermochemical processes proposed to date can be found in six recent papers (Abraham and Schreiner, 1974; Chao, 1974; Euratom, 1973; I.G.T., 1972; Russell and Porter, 1974; Wentorf and Hanneman, 1973). Most of these processes appear to be unfeasible. Untested new processes continue to be proposed. The purpose of this work is to attempt to generate new processes in a systematic way, as a step toward identifying the optimum process. Any attempt to generate new processes and to determine the minimum number of reaction steps requires insight into the principles by which unfavorable reactions can be driven by heat instead of work. Thermodynamic Considerations Overcoming t h e F r e e Energy Barrier. The basis for comparing a thermochemical process for production of hydrogen with electrolysis is efficiency. Thermal efficiency is
