Abstract:
A novel thermochemical cycle for the decomposition of water is presented. Along with water, hydrogen, and oxygen, the cycle involves an alkali or alkali earth metal based process intermediate and a variety of reaction intermediates. The cycle is driven by renewable energy sources, and can have a maximum operating temperature below 1173 K (900° C.). The kinetics of the cycle are based on the reactant behavior as well as the separability characteristics of the chemicals involved.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims priority from, and is a 35 U.S.C. § 111(a) continuation of, co-pending PCT international application serial number PCT/US2005/045824, filed on Dec. 16, 2005, incorporated herein by reference in its entirety, which claims priority from U.S. provisional application Ser. No. 60/637,048, filed on Dec. 16, 2004, incorporated herein by reference in its entirety. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
       [0002]     Not Applicable  
       NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION  
       [0003]     A portion of the material in this patent document is subject to copyright protection under the copyright laws of the United States and of other countries. The owner of the copyright rights has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the United States Patent and Trademark Office publicly available file or records, but otherwise reserves all copyright rights whatsoever. The copyright owner does not hereby waive any of its rights to have this patent document maintained in secrecy, including without limitation its rights pursuant to 37 C.F.R. § 1.14.  
       BACKGROUND OF THE INVENTION  
       [0004]     1. Field of the Invention  
         [0005]     This invention pertains generally to the production of hydrogen from water, and more particularly to a thermochemical cycle using a renewable energy source that efficiently separates water into its components.  
         [0006]     2. Description of Related Art  
         [0007]     Hydrogen is mainly produced from natural gas through steam reforming and dry reforming of methane and other fossil fuels, and from coal through gasification. Hydrogen is also produced through electrolysis. These production methods consume fossil fuels, electricity, or both, and produce unwanted carbon dioxide as a byproduct. In addition, the hydrogen product usually requires separation from other by-products, such as carbon monoxide and carbon dioxide.  
         [0008]     Thermal decomposition of water typically requires temperatures greater than 2273 K (about 2000° C.).  
       BRIEF SUMMARY OF THE INVENTION  
       [0009]     The present invention provides a novel thermochemical cycle for the decomposition of water. Along with water, hydrogen, and oxygen, the cycle involves an alkali or alkali earth metal based catalyst and a variety of reaction intermediates. The cycle is driven by renewable energy sources, and can have a maximum operating temperature below 1173 K (900° C.). Alternatively, the cycle can operate at much higher temperatures. The kinetics of the cycle are based on the reactant behavior as well as the separability characteristics of the chemicals involved.  
         [0010]     An aspect of the invention is a method, comprising using an alkali metal based or alkali earth metal based process intermediate in a thermochemical cycle for water splitting. In one embodiment, the thermochemical cycle operates in the absence of solids. In another embodiment, the thermochemical cycle operates at temperatures at or below about 1173 K.  
         [0011]     Another aspect of the invention is a method for water splitting, comprising: introducing water into a system, introducing an alkali metal based or alkali earth metal based process intermediate into the system, separating the alkali metal based or alkali earth metal based process intermediate to produce reaction intermediates, reacting a subset of the reaction intermediates with water to produce hydrogen and hydroxide, combining a subset of the reaction intermediates with the hydroxide to produce water and oxygen, reforming the alkali metal based or alkali earth metal based process intermediate for continued use in the system, and removing the hydrogen and the oxygen from the system.  
         [0012]     One embodiment further comprises removing heat from the system, and generating power, electricity, or both from the heat. In another embodiment, the generating step uses fuel cells or turbines to generate the power, electricity, or both.  
         [0013]     A still further aspect of the invention is a system for water splitting, comprising: a plurality of interconnected reaction vessels, wherein the plurality of interconnected reaction vessels is configured to receive water from a source of water, wherein the plurality of interconnected reaction vessels is configured to admit an alkali metal based or alkali earth metal based process intermediate into the system, wherein water undergoes a series of thermochemical reactions with said alkali metal based or alkali earth metal based process intermediate, and wherein hydrogen and oxygen are recoverable from the system.  
         [0014]     In one embodiment, the alkali metal based or alkali earth metal based process intermediate is combined with a transition metal. In other embodiments, the alkali metal based or alkali earth metal based process intermediate comprises a carbonate or a hydroxide, or comprises more than one type of alkali metal or alkali earth metal. In another embodiment, the system is operated in a polytropic manner. In another embodiment, the system operates at temperatures at or below about 1300 K. In still another embodiment, the system operates in the absence of solids within the system.  
         [0015]     In yet another embodiment, heat generated by the series of thermochemical reactions is used to produce power, electricity, or both. In another embodiment, heat required for the series of thermochemical reactions is derived from solar or non-solar energy sources.  
         [0016]     Further aspects of the invention will be brought out in the following portions of the specification, wherein the detailed description is for the purpose of fully disclosing preferred embodiments of the invention without placing limitations thereon. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)  
       [0017]     The invention will be more fully understood by reference to the following drawings which are for illustrative purposes only:  
         [0018]      FIG. 1  is one embodiment of the thermochemical water splitting cycle according to the present invention.  
         [0019]      FIG. 2  is a second embodiment of the thermochemical water splitting cycle according to the present invention.  
         [0020]      FIG. 3  is a third embodiment of the thermochemical water splitting cycle according to the present invention.  
         [0021]      FIG. 4  is a thermochemical water splitting cycle associated with data in Tables 1-9.  
         [0022]      FIG. 5  is a steam cycle used in conjunction with the cycle of  FIG. 4  to produce power and/or electricity. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]     Referring more specifically to the drawings, for illustrative purposes the present invention is embodied in the system generally shown in  FIG. 1  through  FIG. 5 . It will be appreciated that the system may vary as to configuration and as to details of the parts, and that the method may vary as to the specific steps and sequence, without departing from the basic concepts as disclosed herein.  
         [0024]     The overall water decomposition reaction is given by the equation: 
 
2H 2 O→2H 2 +2O 2   (1) 
 
         [0025]     The present invention is a novel thermochemical cycle  10  that accomplishes the water decomposition reaction. The following examples detail various embodiments of the instant invention.  
         [0026]     In each embodiment, temperatures shown are shown by way of example, and are not intended to limit the invention. The maximum operating temperature can be less than or equal to 1173 K, but operating temperatures in the range of 298 K to 1300 K are within the scope of the invention. The choice of operating temperature is driven by several factors, including capital costs for the reactors and associated material movement equipment, operating cost for the cycle, and costs related to available high temperature energy sources.  
       Example 1  
       [0027]     One embodiment of the thermochemical cycle can involve sodium, sodium bicarbonate, sodium carbonate, sodium hydride, sodium hydroxide, sodium monoxide, and carbon dioxide as intermediates. 
 
2Na 2 CO 3 →4Na+2CO 2 +O 2   (2) 
 
4Na+4NaOH→4Na 2 O+2H 2   (3) 
 
4Na 2 O+4H 2 O→8NaOH  (4) 
 
4NaOH+2CO 2 →2Na 2 CO 3 +2H 2 O  (5) 
 
         [0028]     A process according to this embodiment is shown in  FIG. 1 .  
         [0029]     Sodium carbonate is first placed in vessel  22  and heated. The sodium carbonate decomposes to a gaseous mixture of sodium, oxygen, and carbon dioxide. The gas mixture is then cooled to liquefy the sodium. The mixture enters vessel  24 , where separation takes place. The sodium is sent to vessel  26 , where it reacts to completion with sodium hydroxide (molten) to produce sodium monoxide and hydrogen (gas). The sodium monoxide is sent to vessel  28 , where it is placed in contact with water to form sodium hydroxide.  
         [0030]     Some of the sodium hydroxide from vessel  28  is recycled back to vessel  26  to react with the sodium and to facilitate transport of both heat and sodium monoxide. Some sodium hydroxide is also sent to vessel  30 , where it is placed in contact with oxygen and carbon dioxide from vessel  24 . The carbon dioxide is adjusted so that the reaction proceeds to completion to form sodium carbonate (molten). The molten sodium carbonate is then fed to vessel  22 .  
         [0031]     The heat produced in vessels  26  and  28 , the heat from the exit streams containing hydrogen and oxygen, and the heat from the exit of reaction vessel  22  can be heat and power integrated with the heating needs of the system (e.g., heating of carbonate in and before vessel  22 , heating of inlet water), and outside hot utilities (e.g., solar, nuclear, fossil fuel based, geothermal, etc.) and cold utilities (e.g., cooling water) to produce electricity.  
       Example 2  
       [0032]     Another embodiment of the thermochemical cycle involves sodium, sodium carbonate, sodium hydroxide, and carbon dioxide as intermediates that help facilitate water decomposition. A process according to this embodiment is shown in  FIG. 2 . 
 
2Na 2 CO 3 →4Na+2CO 2 +O 2   (6) 
 
4Na+4H 2 O→4NaOH+2H 2   (7) 
 
4NaOH+2CO 2 →2Na 2 CO 3 +2H 2 O  (8) 
 
         [0033]     The reactions can be carried out at a variety of temperatures. Reaction (6) is endothermic and can typically be carried out around 1173 K, where all its products are gases. Kinetic rate information at 1173 K is given in Hughes et al., “Production of the Boranes and Related Research”, Academic Press, New York, 1967. Reaction (7) is exothermic and can be carried out at room temperature or even around 1133 K. Care must be taken to control the rate of reaction (7). This can be accomplished by running the reaction with excess steam. Reaction (8) is also exothermic and can also be carried out around 1133 K. The choice of operating temperature for these reactions depends on several factors including capital costs for the reactors and reactors and associated material moving equipment, operating cost for the cycle, as well as the available high temperature energy source. Stable operation requires efficient heat removal from reactions (7) and (8).  
         [0034]     Referring to  FIG. 2 , sodium carbonate is first placed in vessel  42  and heated. The sodium carbonate decomposes to a gaseous mixture of sodium, oxygen, and carbon dioxide. The gas mixture is then cooled to liquefy the sodium, and the mixture is sent to vessel  44 , where separation takes place. The sodium is sent to vessel  46 , where it reacts to completion with water (steam) to form sodium hydroxide (molten) and hydrogen (gas). Heat must be removed form vessel  46  to ensure stable operation. The sodium hydroxide is sent to vessel  48 , where it is placed in contact with the oxygen and carbon dioxide from vessel  44 . The carbon dioxide is adjusted so that the reaction proceeds to completion and forms sodium carbonate (molten). The molten sodium carbonate is then sent to vessel  42 .  
         [0035]     The heat from the reactions in vessels  46  and  48 , the heat from the exit streams containing hydrogen and oxygen, and the heat from the exit of reaction vessel  42  can be heat and power integrated with the heating needs of the system (e.g., heating of carbonate in and before vessel  42 , heating of inlet water), and outside hot utilities (e.g., solar, nuclear, fossil fuel based, geothermal, etc.) and cold utilities (e.g., cooling water) to produce electricity.  
       Example 3  
       [0036]     A third embodiment is given by the system of equations: 
 
2Na 2 CO 3 →4Na+2CO 2 +O 2   (9) 
 
4Na+4H 2 O→4NaOH+2H 2   (10) 
 
4NaOH+4CO 2 →4NaHCO 3   (11) 
 
4NaHCO 3 →2Na 2 CO 3 +2H 2 O+4CO 2   (12) 
 
         [0037]     Referring to  FIG. 3 , sodium carbonate is first placed in vessel  62  and heated. The sodium carbonate decomposes to a gaseous mixture of sodium, oxygen, and carbon dioxide. The gas mixture is then cooled to liquefy the sodium, and the mixture is sent to vessel  64 , where separation takes place. The sodium is cooled and sent to vessel  66 , where it reacts to completion with water to form sodium hydroxide and hydrogen. Although  FIG. 3  shows the reaction in vessel  66  with liquid water, the reaction can take place with liquid water or with steam. Heat must be removed from vessel  66  to ensure stable operation. The sodium hydroxide and some water are then sent to vessel  68 , where it is placed in contact with the oxygen and carbon dioxide from vessel  64 . The carbon dioxide is adjusted so that the hydroxide reacts to completion and forms sodium carbonate and sodium bicarbonate. The sodium bicarbonate and sodium carbonate solution is fed to vessel  70 , where the bicarbonate decomposes to carbonate, water, and carbon dioxide, the water is vaporized, and the carbonate melts. The carbon dioxide and water gases are then separated and recycled, while the sodium carbonate is sent to vessel  62 .  
         [0038]     In each example, heat integration is possible, but not shown. All reaction vessels shown can be operated in an adiabatic or in a polytropic manner throughout the applicable temperature range. In addition, the process can be operated in a manner that avoids the presence and/or movement of solids anywhere in the cycle. Finally, although temperature-based separations are disclosed, other types of separations can be utilized according to the present invention.  
       Example 4  
       [0039]      FIG. 4  shows a thermochemical cycle utilizing reactions (2) through (5), much like that in  FIG. 3 .  FIG. 5  is a standard reheat steam cycle associated with the cycle of  FIG. 4 . The data associated with the cycles shown in  FIG. 4  and  FIG. 5  are presented in Tables 1-9.  
         [0040]     Tables 1A-1B show the characteristics of each stream shown in  FIG. 4  and  FIG. 5 , including temperature, flow rate, and composition. Note that the composition of streams S 15 -S 20  is water only, as these streams comprise the steam cycle.  
         [0041]     Tables 2-4 provide thermodynamic data for the individual components at 1173 K, 1133 K, and 298 K, respectively.  
         [0042]     Tables 5A-5B provide the operating conditions for each heat exchanger H 1 -H 10 , turbine T 1 -T 2 , and pump P 1 .  
         [0043]     Table 6 indicates the heat load for the heat exchangers in the two systems, and Table 7 indicates the work load for the turbines and the pump.  
         [0044]     Tables 8 and 9 quantify the cost coefficients ($/GJ) and the utility cost ($/s), respectively, for the cycle shown in  FIG. 4  and  FIG. 5 . The value of the Hot Utility (HU) Cost for Groups 1-3 reflects the cost of natural gas. Fluctuations in the cost of natural gas will directly affect the cost efficiency of the cycle. For Group 4, the cost coefficient is zero, reflecting the use of solar power as the hot energy source. Note that the use of solar power realizes the greatest benefit in terms of cost. Table 9 also indicates the cost to produce hydrogen using the cycle of  FIG. 4 .  
         [0045]     In the cycle shown in  FIG. 4 , sodium carbonate enters reaction vessel V 1  as stream S 1 . In vessel V 1 , sodium carbonate is separated into sodium, oxygen, and carbon dioxide, which exits in stream S 2 . Stream S 2  enters vessel V 2 . Sodium in separated out into stream S 3 , and enters vessel V 3 . Meanwhile, the carbon dioxide and oxygen from vessel V 2  exit as stream S 4 , entering vessel V 4 .  
         [0046]     Water enters the system at stream S 12 , and is also recycled from vessel V 5 . Streams S 11 , S 13 , S 14  are composed of water, and are directed into vessel V 3  to combine with the sodium from stream S 3 . Hydrogen is produced in vessel V 3 , and exits the system in streams S 5 , S 6 . Vessel V 3  also produces sodium hydroxide, which enters vessel V 4  via stream S 7  and reacts with the carbon dioxide and oxygen from stream S 4 .  
         [0047]     The reaction in vessel V 4  produces sodium carbonate, which is routed back to vessel V 1  via stream S 1 . The reaction in vessel V 4  also produces water and oxygen, which enters vessel V 5  through stream S 9 . Oxygen exits the system through stream S 10 , and the water is recycled to vessel V 3  by way of streams S 11 , S 13 , S 14 .  
         [0048]      FIG. 5  shows a standard reheat steam cycle utilizing streams S 15 -S 20 , which generates power or electricity from a thermochemical cycle such as that shown in  FIG. 4 . Heat exchangers H 8  and H 10  pick up energy from heat exchangers H 2 , H 3 , H 4 , H 5 , H 6 , shown in  FIG. 4 , and utilize turbines T 1  and T 2  to generate power and/or electricity. Note that the heat load, shown in Table 6, for H 8 +H 10  is equal in magnitude to that of H 2 +H 3 +H 4 +H 5 +H 6 .  
         [0049]     The steam cycle shown in  FIG. 5  is intended only as an example, and other elements may be used to achieve similar or better results. For example, fuel cells can be utilized instead of turbines for energy generation.  
         [0050]      FIGS. 4 and 5 , and their associated data, represent one example of the use of the present invention and does not represent the maximum system efficiency possible. Other embodiments of the present invention could achieve efficiencies of 75-80%.  
         [0051]     Other systems of equations can be generated that involve the same intermediates. In addition, other alkali metals and alkali earth metals can be used in place of sodium. Finally, mixtures of these metals, their carbonates, and/or their hydroxides can be used according to the present invention, as can combinations of these materials with transition metals.  
         [0052]     Although the description above contains many details, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. Therefore, it will be appreciated that the scope of the present invention fully encompasses other embodiments which may become obvious to those skilled in the art, and that the scope of the present invention is accordingly to be limited by nothing other than the appended claims, in which reference to an element in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.” All structural, chemical, and functional equivalents to the elements of the above-described preferred embodiment that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Moreover, it is not necessary for a device or method to address each and every problem sought to be solved by the present invention, for it to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed under the provisions of 35 U.S.C. 112, sixth paragraph, unless the element is expressly recited using the phrase “means for.” 
                                                                                                                   TABLE 1-A                                       Stream #                1   2   3   4   5   6   7   8   9   10                        Flow (mol/s)   1   3.5   2   1.5   1   1   2   1.5   1.5   0.5       Pressure (kPa)   101.3   101.3   101.3   101.3   101.3   101.3   101.3   101.3   101.3   101.3       Temperature   1133   1173   1133   1133   1133   298   1133   1133   298   298       (° K)       H 2 O (mol/s)   0   0   0   0   0   0   0   1   1   0       H 2  (mol/s)   0   0   0   0   1   1   0   0   0   0       O 2  (mol/s)   0   0.5   0   0.5   0   0   0   0.5   0.5   0.5       Na (mol/s)   0   2   2   0   0   0   0   0   0   0       NaOH (mol/s)   0   0   0   0   0   0   2   0   0   0       Na 2 CO 3  (mol/s)   1   0   0   0   0   0   0   0   0   0       CO 2  (mol/s)   0   1   0   1   0   0   0   0   0   0       H (kJ/s)   100.9963   92.01492   32.6428   54.76664   25.16037   −0.00431   99.38876   33.44491   −12.1357   −0.00196       H (kJ/s) (Hysys)       Phase   Liquid   Vapor   Liquid   Vapor   Vapor   Vapor   Liquid   Vapor   Liquid/   Vapor                                           Vapor                  
 
         [0053]    
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1-B 
               
             
             
               
                   
                   
               
               
                   
                   
               
               
                   
                 Stream # 
               
             
          
           
               
                   
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
                   
               
             
          
           
               
                 Flow (mol/s) 
                 1 
                 1 
                 2 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Pressure (kPa) 
                 101.3 
                 101.3 
                 101.3 
                 101.3 
                 25330 
                 1818 
                 1818 
                 2.55 
                 2.55 
                 25330 
               
               
                 Temperature (°K) 
                 298 
                 298 
                 298 
                 1133 
                 873.15 
                 481.65 
                 1011.15 
                 295.2 
                 294.99 
                 295.26 
               
               
                 H 2 O (mol/s) 
                 1 
                 1 
                 2 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 H 2  (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 O 2  (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Na (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 NaOH (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Na 2 CO 3  (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 CO 2  (mol/s) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 H (kJ/s) 
                 −12.1338 
                 −12.1338 
                 −24.2676 
                 39.28542 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 H (kJ/s) (Hysys) 
                   
                   
                   
                   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Phase 
                 Liquid 
                 Liquid 
                 Liquid 
                 Vapor 
                 Vapor 
                 Vapor 
                 Vapor 
                 Vapor 
                 Liquid 
                 Liquid 
               
               
                   
               
             
          
         
       
     
         [0054]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   
               
               
                 T ° K (298.15-1300) 1173 
               
             
          
           
               
                   
                 CO 2   
                 H 2   
                 H 2 O 
                 O 2   
                 Na 
                 Na 2 CO 3   
                 NaOH 
                 CH 4   
               
               
                   
                   
               
             
          
           
               
                 Melting Point ° K 
                 216.55 
                 13.95 
                 273.15 
                 54.25 
                 371 
                 1127 
                 595 
                 90.65 
               
               
                 Boiling Point ° K 
                 194.65 
                 20.45 
                 373.15 
                 90.15 
                 1154.5 
                 1300 
                 1651 
                 111.75 
               
               
                 ΔH° f (kcal/mol) 
                 −94.052 
                 0 
                 −68.3174 
                 0 
                 0 
                 −269.46 
                 −101.96 
                 −17.889 
               
               
                 ΔG° f (kcal/mol) 
                 −94.26 
                 0 
                 −56.6899 
                 0 
                 0 
                 −249.55 
                 −90.06 
                 −12.14 
               
               
                 ΔH f  (cal/mol) 
                 1900 
                 28 
                 1436 
                 106 
                 630 
                 7000 
                 2000 
                 224 
               
               
                 ΔH v  (cal/mol) 
                 6030 
                 216 
                 9729 
                 1629 
                 23120 
                   
                   
                 2040 
               
               
                 Cps (cal/mol ° K) 
                   
                   
                   
                   
                 11.29728 
                 28.9 
                 14.22 
               
               
                 Cpl (cal/mol ° K) 
                   
                   
                 18 
                   
                 7.5 
                 28.9 
                 14.22 
               
               
                 Cpg (cal/mol ° K) 
                 13.41193 
                 7.57013 
                 11.82324 
                 8.436217 
                 4.97 
                   
                   
                 18.8295 
               
               
                 H (T) (kcal/mol) 
                 −83.7319 
                 6.312756 
                 −49.8732 
                 6.931505 
                 30.21382 
                 −237.177 
                 −87.5196 
                 −5.81685 
               
               
                   
               
             
          
         
       
     
         [0055]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                   
               
               
                 T ° K (298.15-1300) 1133 
               
             
          
           
               
                   
                 CO 2   
                 H 2   
                 H 2 O 
                 O 2   
                 Na 
                 Na 2 CO 3   
                 NaOH 
                 CH 4   
               
               
                   
                   
               
             
          
           
               
                 Melting Point ° K 
                 216.55 
                 13.95 
                 273.15 
                 54.25 
                 371 
                 1127 
                 595 
                 90.65 
               
               
                 Boiling Point ° K 
                 194.65 
                 20.45 
                 373.15 
                 90.15 
                 1154.5 
                 1300 
                 1651 
                 111.75 
               
               
                 ΔH° f (kcal/mol) 
                 −94.052 
                 0 
                 −68.3174 
                 0 
                 0 
                 −269.46 
                 −101.96 
                 −17.889 
               
               
                 ΔG° f (kcal/mol) 
                 −94.26 
                 0 
                 −56.6899 
                 0 
                 0 
                 −249.55 
                 −90.06 
                 −12.14 
               
               
                 ΔH f  (cal/mol) 
                 1900 
                 28 
                 1436 
                 106 
                 630 
                 7000 
                 2000 
                 224 
               
               
                 ΔH v  (cal/mol) 
                 6030 
                 216 
                 9729 
                 1629 
                 23120 
                   
                   
                 2040 
               
               
                 Cps (cal/mol ° K) 
                   
                   
                   
                   
                 11.08288 
                 28.9 
                 14.22 
               
               
                 Cpl (cal/mol ° K) 
                   
                   
                 18 
                   
                 7.5 
                 28.9 
                 14.22 
               
               
                 Cpg (cal/mol ° K) 
                 13.29212 
                 7.53773 
                 11.63964 
                 8.416095 
                 4.97 
                   
                   
                 18.3695 
               
               
                 H (T) (kcal/mol) 
                 −84.2659 
                 6.010599 
                 −50.2802 
                 6.594456 
                 6.840622 
                 −238.333 
                 −88.0884 
                 −6.56083 
               
               
                   
               
             
          
         
       
     
         [0056]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                   
               
               
                 T ° K (298.15-1300) 298 
               
             
          
           
               
                   
                 CO 2   
                 H 2   
                 H 2 O 
                 O 2   
                 Na 
                 Na 2 CO 3   
                 NaOH 
                 CH 4   
               
               
                   
                   
               
             
          
           
               
                 Melting Point ° K 
                 216.55 
                 13.95 
                 273.15 
                 54.25 
                 371 
                 1127 
                 595 
                 90.65 
               
               
                 Boiling Point ° K 
                 194.65 
                 20.45 
                 373.15 
                 90.15 
                 1154.5 
                 1300 
                 1651 
                 111.75 
               
               
                 ΔH° f (kcal/mol) 
                 −94.052 
                 0 
                 −68.3174 
                 0 
                 0 
                 −269.46 
                 −101.96 
                 −17.889 
               
               
                 ΔG° f (kcal/mol) 
                 −94.26 
                 0 
                 −56.6899 
                 0 
                 0 
                 −249.55 
                 −90.06 
                 −12.14 
               
               
                 ΔH f  (cal/mol) 
                 1900 
                 28 
                 1436 
                 106 
                 630 
                 7000 
                 2000 
                 224 
               
               
                 ΔH v  (cal/mol) 
                 6030 
                 216 
                 9729 
                 1629 
                 23120 
                   
                   
                 2040 
               
               
                 Cps (cal/mol ° K) 
                   
                   
                   
                   
                 6.60728 
                 28.9 
                 14.22 
               
               
                 Cpl (cal/mol ° K) 
                   
                   
                 18 
                   
                 7.5 
                 28.9 
                 14.22 
               
               
                 Cpg (cal/mol ° K) 
                 8.955043 
                 6.86138 
                 8.785997 
                 6.23324 
                 4.97 
                   
                   
                 8.767 
               
               
                 H (T) (kcal/mol) 
                 −94.0533 
                 −0.00103 
                 −68.3201 
                 −0.00094 
                 −0.00099 
                 −269.464 
                 −101.962 
                 −17.8903 
               
               
                   
               
             
          
         
       
     
         [0057]    
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 5-A 
               
             
             
               
                   
                   
               
               
                   
                   
               
               
                   
                 Unit 
               
             
          
           
               
                   
                 H1 
                 H2 
                 H3 
                 H4 
                 H5 
                 H6 
                 H7 
                 H8 
                 H9 
                 H10 
               
               
                   
                   
               
             
          
           
               
                 Temperature IN (° K) 
                 1173 
                 1133 
                 1133 
                 1133 
                 1133 
                 1133 
                 298 
                 481.65 
                 295.2 
                 295.26 
               
               
                 Temperature OUT 
                 1173 
                 1133 
                 1133 
                 1133 
                 298 
                 298 
                 1133 
                 1011.15 
                 294.99 
                 873.15 
               
               
                 (° K) 
               
               
                 Q (kJ/s) 
                 914.6174 
                 −198.622 
                 −348.64 
                 −117.92 
                 −25.1647 
                 −89.3193 
                 151.0303 
                 199.4494 
                 −426.574 
                 580.2165 
               
               
                 Q/ΔT (kJ/(° K*s)) 
                   
                   
                   
                   
                 0.030137 
                 0.106969 
                 0.180875 
                 0.376675 
                 2031.303 
                 1.004026 
               
               
                 W (kJ/s) 
               
               
                   
               
             
          
         
       
     
         [0058]    
       
         
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 5-B 
               
             
             
               
                   
                   
               
               
                   
                   
               
               
                   
                 Unit 
               
             
          
           
               
                 Properties 
                 T1 
                 T2 
                 P1 
               
               
                   
               
             
          
           
               
                 Temperature IN (° K) 
                 873.15 
                 1011.15 
                 294.99 
               
               
                 Temperature OUT (° K) 
                 481.65 
                 295.2 
                 295.26 
               
               
                 Q (kJ/s) 
               
               
                 Q/ΔT (kJ/(° K*s)) 
               
               
                 W (kJ/s) 
                 −105.928 
                 −251.936 
                 4.771517 
               
               
                   
               
             
          
         
       
     
         [0059]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                   
               
             
             
               
                   
                 Heat Loads (kJ/s) 
                 9.543035 
                           flow 
               
               
                   
                 H2 + H3 + H4 + H5 + H6 
                 −779.666 
               
               
                   
                 H1 + H7 
                 1065.648 
               
               
                   
                 H8 + H10 
                 779.666 
               
               
                   
                 H9 
                 −426.574 
               
               
                   
                   
               
             
          
         
       
     
         [0060]    
       
         
               
               
             
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                   
               
               
                   
                 Work Loads (kJ/s) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 T1 + T2 
                 −357.864 
               
               
                   
                 P1 
                 4.771517 
               
               
                   
                   
               
             
          
         
       
     
         [0061]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                   
               
               
                 Cost Coeffs ($/GJ) 
                 Group 1 
                 Group 2 
                 Group 3 
                 Group 4 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Hot Utility Cost ($/GJ) 
                 8.825 
                 8 
                 9.298 
                 0 
               
               
                 Cold Utility Cost ($/GJ) 
                 0.5 
                 0.5 
                 1.85 
                 1.85 
               
               
                 Electricity Cost ($/GJ) 
                 25.3 
                 26 
                 23.8889 
                 23.8889 
               
               
                   
               
             
          
         
       
     
         [0062]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                   
               
               
                 Utility Costs ($/s) 
                 Group 1 
                 Group 2 
                 Group 3 
                 Group 4 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HU Cost ($/s)*10{circumflex over ( )}3 
                 9.404341 
                 8.525182 
                 9.908393 
                 0 
               
               
                 CU Cost ($/s)*10{circumflex over ( )}3 
                 0.213287 
                 0.213287 
                 0.789161 
                 0.789161 
               
               
                 E Cost ($/s)*10{circumflex over ( )}3 
                 −8.93324 
                 −9.1804 
                 −8.43499 
                 −8.43499 
               
               
                 Total Cost ($/s)*10{circumflex over ( )}3 
                 0.684393 
                 −0.44193 
                 2.262567 
                 −7.64583 
               
               
                 H 2  Cost ($/kg H 2 ) 
                 0.342197 
                 −0.22097 
                 1.131284 
                 −3.82291