CH E 410 Final Project

David Belias Cryogenic DistillationMike McEldrew Gas Separation MembranesDavid Kozak MDEA AbsorptionAustin Goewert Water Absorption

4/25/2014

ContentsExecutive Summary3Introduction3Distillation Analysis6Gas Separation Membranes16Model 1:17Model 2:18Model 3:21Model 4:23Absorption using MDEA25Introduction25Calculations and Equations26Discussion27Conclusion31Absorption using Water33Introduction33Calculations35Discussion36Conclusion40Recommendation41Appendix A43Appendix B46Appendix B146Appendix B247Appendix B348Appendix B449Appendix C:50Appendix C150Appendix C250Appendix C352References53

Executive SummaryThis report provides an analysis and evaluation of four separation unit operations. Cryogenic distillation, gas separation membranes, and absorption using water and MDEA were explored. Analysis for distillation utilized Aspen HYSYS, while the other three analyses utilized Wolfram Mathematica. Current market values for all prices were used in the cost analysis to find operational costs and revenues. All calculations can be found in the following discussions. The investigation found that absorption was the most profitable operation due to the highest purity product being sold. Specifically, absorption using water is the recommended option because it produced the greatest profit with the least uncertainty. Distillation had, by far, the greatest costs due to refrigeration and equipment prices. Gas separation membranes had much lower costs, but they were still triple those of absorption. The assumptions used in the analysis of absorption need to be explored further in subsequent examinations to more accurately examine the revenues and costs. In the future, changes in market prices and innovations in industry may yield different results in the capabilities of each unit operation. IntroductionThe separation of methane and carbon dioxide is a recurring industrial process that can be completed using numerous unit operations. In this analysis, Cryogenic distillation, gas separation membranes, and absorption using both water and methyl diethanolamine (MDEA) were investigated in great detail. The feed stream originated from a natural gas well and its properties are outlined in Table A below.Pressure (psia)Temperature (F)Methane Concentration (mol%)Carbon Dioxide Concentration (mol%)Feed Flow (MMSCFD)

494.777861435

Table A. Properties of the feedstock from the natural gas well.

The feed flow was converted to a molar flow using the ideal gas law at standard temperature and pressure (14.7 psia, 459.67 R). Equation A below shows how the molar flow was calculated.

Gases with varying energy levels could be sold for different prices, which are outlined in Table B below.ProductMethane Concentration (mol%)Price ($/MMBtu)Specifications

Waste Gas> H/kx), the liquid composition is approximately uniform horizontally. Liquid composition is approximately 0.005 at the top of the column and 0.1 at the bottom. By using tabulated partial pressures, vapor composition and thereby H can be determined at the top and bottom of the column. Htop and Hbottom were calculated for all operating conditions tested. Since Htop/Hbottom is approximately one for all operating conditions(Table 6), it is valid to assume H is constant throughout the column.

Table 6 :Comparison of Henrys Law Constant Values at Top and Bottom of Column9,10T (K)P (psi)Htop/Hbottom

298480.9903

298520.9903

298590.9903

298660.9903

2734801.0022

Note: See Appendix C1 for H values

Table 7: Solubility of Carbon Dioxide in Water at Various Temperatures and Pressures9,10

The solubility of a gas in a liquid depends on temperature, the partial pressure of the gas, the nature of the solvent, and the nature of the vapor. Lower temperatures and higher pressures increase solubility, therefore decreasing H. Particles at lower temperatures have less energy and thus are more inclined to the lower energy liquid phase. Higher pressures tend to force particles into the liquid phase in order to relieve the applied pressure. Equation 4 is used to calculate the effect of these changes on the liquid mole fraction of CO2, which in turn is used to calculate a new Henrys Law constant.

Table 8: Henrys Law Constants at Various Operating ConditionsT (K)P (psi)H

2984801.20236

2985200.831172

2985900.73256

2986980.554863

2734800.430802

At this point, the solubility of methane in water must be considered. Numerous experimental sources show the Henrys law constant for methane in water is high compared to that of carbon dioxide11 (Hmethane 20). Therefore, 100% methane recovery is assumed.CalculationsThe calculations for each system were similar and proceeded as follows: 1. Assume equilibrium at bottom of column. Use Henrys law constant to calculate xout2. Use CO2 species balance to calculate approximate Lmin3. Generate table of Lin and column volume over range of Lmin 2.5Lmin4. Calculate annual profit and capital cost for each value of L - - - * - - - *** See introduction for revenue calculations. Revenue values are constant due to 100% recovery.**4 Cpw = 4.183 Jg-1k-1 CpCO2= .846 Jg-1k-1 CpCH4=2.203 Jg-1k-1 CpFeed=0.86(CpCO2) +0 .14(CpCH4)= 2.0328 Jg-1k-1 12,13

DiscussionThe inlet feed of 86% methane leaves only three product options: sell the feed as high energy gas (70-95%), purify to pipeline quality gas (95%), or purify to liquefied natural gas (99.995%). Operating conditions of T=298K and P=480psi were chosen for the initial calculations since they require no change to the vapor feed.Annual profits were calculated over a range of liquid flow rates for both purities. Since the feed is high in methane concentration, the associated costs are minute in comparison to the revenue. As a result, profit values are approximately equal to revenue; profits therefore are quite consistent across all liquid flow rates. Average values of costs and profits are shown below in Figure 23.Figure 23

Variations in liquid flow rate have minimal impact on profit because the revenue outweighs all associated costs. High energy gas and pipeline quality gas products will be discarded at this point since the liquefied natural gas profit is clearly the highest.As discussed earlier, increasing pressure increases the solubility of carbon dioxide in water. Higher solubility will decrease both capital and water costs; however compression costs will increase. The liquefied gas product was examined at increased pressures, specifically 520 psi, 590 psi, and 698 psi. The pressure of 698 psi was chosen because the product stream will exit the column at 600 psi, eliminating the need for compression after the column. Annual profit and costs were determined for each pressure over a range of liquid flow rates. The average costs and revenue are displayed below in Figure 24. Again, costs have minimal impact on profit. In order to determine the optimal pressure for the column, capital costs were plotted against annual profit. It is clear in Figure 25 below that increasing pressure has a negative financial impact. It is concluded that the optimal pressure is the feed pressure of 480 psi.Figure 24

Figure 25Note: See Appendix C2 for exact profit values.

The next variable considered is decreased temperature. As discussed above, lowering temperature increases the solubility of carbon dioxide in water. This will decrease the capital cost and liquid flow rate; however an additional water stream is required to cool the gas. The most efficient method for this cooling stream is a countercurrent flow along the inlet stream. Assuming the cooling water is at 273 K, countercurrent over a long distance will decrease the inlet stream temperature to 273 K. Similarly, the temperature of the water on the other end will increase to 298 K. i.e. Tw= Tfeed.5 The liquid flow rate required for this heat exchange is calculated assuming all heat leaving the vapor goes into the water. The calculation is described below. (The feed saturation temperature at 480 psi was calculated in HYSYS as 188 K.)

Lw=250 mol/s is arbitrarily chosen to account for some heat loss to the surroundings. Assuming the temperature of the liquid flow into the column is also 273 K, the operating conditions for the process are T=273 K , P=480 psi. The decreased temperature increases solubility, resulting in a smaller H value (0.43). The liquid flow rates and corresponding column volumes at 273 K are noticeably smaller than those at 298 K. (The exact values can be seen in APPENDIX Iii). Figure 26

Figure 26 compares average costs associated with both temperatures. Despite the addition of a cooling stream, water costs are less at 273 K due to smaller liquid inlet requirements. Both liquid and vapor stream compression costs decrease at 273 K as liquid compression is proportional to liquid flow rate and vapor compression is proportional to temperature. Lastly, capital costs decrease due to higher solubility at lower temperatures.

Figure 27

Capital costs are plotted against annual profit across the range of liquid flow rates at both temperatures. It is apparent that higher profits are generated at a lower operating temperature.Note: See Appendix C3 for exact capital and liquid flow rate values

Figure 28

In order to determine the optimal liquid flow rate for the process, a long term profit analysis is conducted. 30 year profit is calculated and plotted against liquid flow rate. Since the Raschig rings require replacement every 30 years, a 50 year profit analysis is also conducted. The long term profit results are shown here.

ConclusionIt is apparent that operating conditions of T=273 K and P= 480 psi generate the highest profit for the absorption process. Short term profits are maximized due to relatively low capital costs. Low temperature and inexpensive cooling maximize long term profits. Both 50 and 30 year analyses(Figure 28) display liquid flow rate maxima in the range of 350-400 mol/s. It is therefore recommended to run the absorption column at T=273 K, P=480 psi, Lin = 375 mol/s, and Lcooling = 250 mol/s. Relaxation of cooling assumptions will likely require a higher cooling liquid flow rate. RecommendationAfter completion of the analysis of the four unit operations, absorption is clearly the best method. One of the main reasons for the higher profit is the ease with which liquefied natural gas is achieved. Distillation and gas separation membranes required immense operational costs when producing the liquefied natural gas. The increased revenue generated by producing the liquefied natural gas as opposed to pipeline quality made the absorption columns a much more profitable operation. In Figure 23, below, it is easy to see that not only was the net profit much greater in each of the absorption options, but the operational costs were also much lower than that of gas separation membranes and especially distillation. Gas separation membranes failed in producing liquefied natural gas, because the polysulfone membrane permeability coefficients of methane and carbon dioxide are not drastically different. The amount of membrane area needed to produce the required purity would be extremely high. For distillation, the operational costs are dominated by refrigeration and equipment costs. The cost of refrigeration was between $50 and $70 per million Btu. Each plate in the distillation column was $442,000. The refrigeration costs depended upon the reflux ratio, which depended upon the number of stages. When trying to produce the higher purity gas products, the number of stages required was very large, driving the operational costs way up. Even though both the distillate and bottoms streams were able to be sold, the operational costs greatly outweighed the revenue generated.Figure 23: Comparison of net profit and operational costs between each of the analyzed unit operations. The values presented in this graph are taken from the optimal design for each unit operation.

It can be seen in Figure 23, that the net profit generated from absorption using water slightly exceeds that of absorption using MDEA. Therefore, absorption using water is the suggested process. In order to affirm this suggestion further, the assumptions made during the MDEA absorption analysis must be revisited. In the MDEA absorption analysis, it was assumed that there was no cost involved with the regeneration of the MDEA after each day. This assumption is most likely not entirely true, and would need to be investigated further. This assumption also meant that the amount of MDEA needed for this absorption process would only be one days worth. It is reasonable to imply that the MDEA regeneration is not perfect, and that additional MDEA would most likely need to be purchased. When considering these uncertainties, absorption using water can be confidently suggested over absorption using MDEA. Absorption using water does not come without reservation as well. The calculations for both types of absorption were done assuming that methane was entirely insoluble in water. This assumption allowed methane recovery to be 100%. Obviously, methane is not entirely insoluble in water, and some of the water will absorb methane. In order to confidently assert the absorption process as the best, calculations would need to be completed without this assumption. Another hesitation involved with absorption using water is its dependence on the market for methane. Because the carbon dioxide leaves as waste in absorption processes, there is no revenue generated by carbon dioxide. This leaves the entire net profit dependent upon the revenue generated by the methane rich stream. In distillation and gas separation membranes, there is additional revenue generated by carbon dioxide rich outlet streams. This extra income diversifies the market for the feedstock, which could be very advantageous. Still, these doubts in absorption using water do not alter the final recommendation. Absorption will almost certainly have the least operational costs associated with it. Even if methane recovery cannot be assumed to be 100%, the revenue generated from the liquefied natural gas stream will exceed that of the pipeline quality gas by around 20%.

Appendix A

Figure A1. Effect of temperature level on cost of refrigeration for cooler and condenser.

Figure A2. Plots of a) Number of Stages vs. Reflux Ratio and b) Total Cost vs. Reflux Ratio for producing pipeline quality gas with high purity carbon dioxide bottoms with a condenser pressure of 605 psia.

Figure A3. Plots of a) Number of Stages vs. Reflux Ratio and b) Total Cost vs. Reflux Ratio for producing pipeline quality gas with high purity carbon dioxide bottoms with a condenser pressure of 480 psia.

Figure A4. Plots of a) Number of Stages vs. Reflux Ratio and b) Total Cost vs. Reflux Ratio for producing pipeline quality gas with low energy gas bottoms with a condenser pressure of 480 psia.

Figure A5. Plots of a) Number of Stages vs. Reflux Ratio and b) Total Cost vs. Reflux Ratio for producing liquefied natural gas with high purity carbon dioxide bottoms with a condenser pressure of 480 psia.

Figure A6. Plots of a) Number of Stages vs. Reflux Ratio and b) Total Cost vs. Reflux Ratio for producing liquefied natural gas with low energy gas bottoms with a condenser pressure of 480 psia.

Profit ($M/yr)Refrigeration Cost ($M/yr)Compression Cost ($M/yr)Equipment Cost ($M/yr)Heating Cost ($M/yr)

Feed35.380000

600 Psia Pipeline CO232.18.110.3252.650.144

480 Psia Pipeline CO231.529.830.02691.770.1799

480 Psia Pipeline Low Energy29.89.350.02740.8840.192

480 Psia Liquefied CO219.2512.480.0189911.490.0843

480 Psia Liquefied Low Energy16.2512.320.0189911.490.0763

Table A1. Profit and different costs in millions of dollars per year for the different product streams explored.

Appendix B: Gas Separation Membrane Additional InformationAppendix B1: Single Stage Gas Separation Membrane:Area of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Stream purityWaste Stream Flow Rate (mol/s)

00.8600547.640.00000.00

10000000.8620546.260.07001.38

30000000.8658543.610.07304.02

50000000.8695541.100.07506.54

80000000.8746537.560.078010.07

100000000.8779535.340.080012.29

500000000.9205505.960.124541.68

800000000.9374493.390.155654.24

1000000000.9452487.010.175860.62

1155600000.9500482.730.190764.91

3000000000.9754449.040.334598.60

5000000000.9806435.190.3931112.44

10000000000.9900362.410.6020185.22

Table B11: Table of operational variables with respect to changing membrane area, for the single stage gas separation membrane process model.Table A3: Table of operational variables changing across a domain of reflux ratios for the two stage gas separation process model

Area of Membrane (cm2)Waste Gas Value ($/year)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Value ($/year)Profit $/year

00.000.000.0035336084.8435336084.84

10000000.000.003229.0935329204.3935325975.29

30000000.000.009687.2835313063.6835303376.40

50000000.000.0016145.4735300031.9735283886.50

80000000.000.0025832.7635273238.6235247405.87

1000000052691.750.0032290.9535261799.7235282200.52

50000000278159.840.00161454.7334943344.1935060049.30

80000000452272.180.00258327.5734701632.8634895577.47

100000000571116.040.00322909.4634536542.5934784749.17

115560000663335.81193871.28373154.1739322771.9539419082.31

3000000001767555.90180341.55968728.3837555965.2338174451.20

5000000002368842.65174781.151614547.3036592621.2337172135.43

10000000005975778.56145550.953229094.5930765026.5233366159.53

Table B12: Table of operational costs and product stream revenues with respect to changing membrane area, for the single stage gas separation membrane process model.

Appendix B2: Two Stage Gas Separation Membrane Model:Reflux Ratio (Fraction of Feed Recycled)Flow Rate of Recycle Stream (mol/s)Area of Second Membrane (cm2)Total Area of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Stream purityWaste Stream Flow Rate (mol/s)

0.020010.953339797001495397000.949492.8050.058554.830

0.040021.905111105001266705000.944498.0000.013549.425

0.047125.81093402001249002000.942499.6350.010048.000

0.060032.85875683901231283900.937502.1040.006845.531

0.080043.81160979701216579700.931505.8660.004541.769

0.100054.76451650701207250700.924509.6180.003338.017

0.120065.71644452101200052100.917513.3880.002634.247

0.140076.66938296301193896300.911517.1850.002230.450

0.160087.62232717801188317800.904521.0120.001926.623

0.180098.57427843001183443000.897524.8720.001622.763

0.2000109.52722467001178067000.891528.7660.001418.869

0.2200120.48017588801173188800.884532.6960.001314.940

0.2400131.43212800401168400400.878536.6610.001110.974

0.2600142.3858069231163669230.871540.6630.00106.972

0.2800153.3383372451158972450.865544.7020.00102.933

0.2944161.23001155600000.860547.6350.00000.000

Table B21: Table of operational variables with respect to changing reflux ratio, for the two stage gas separation membrane process model.

Reflux Ratio (Fraction of Feed Recycled)Compression Cost ($/year)Membrane Cost ($/year)Waste Stream Value ($/year)Product Stream Value ($/year)Net Profit ($/year)

0.0200481372.15482877.840.0035095620.3134131370.32

0.0400521964.21409031.030.0035271255.3434340260.10

0.0471540109.61403314.562684256.6135299973.0537040805.49

0.0600573617.52397593.222546190.1735312872.7236887852.15

0.0800626238.22392845.092335827.4635322057.0036638801.15

0.1000678926.23389832.672125979.2435326558.2636383778.59

0.1200729050.17387508.171915157.9635329277.2036127876.82

0.1400783851.50385520.411702854.7535331128.8535864611.69

0.1600835996.55383719.061488834.7235332417.2235601536.33

0.1800887900.13382144.941272974.8535333365.4035336295.19

0.2000939547.58380408.981055196.8535334058.5135069298.81

0.2200990938.92378833.76835450.3935334687.6334800365.34

0.24001042066.83377287.54613690.7235335164.7734529501.12

0.26001092931.31375759.80389898.2935335559.9434256767.12

0.28001143525.03374243.17164041.2035335890.6333982163.62

0.2944Table B22: Table of operational costs and product stream revenues with respect to changing reflux ratio, for the two stage gas separation membrane process model.

1179812.90373154.170.0035336084.8433783117.77

Appendix B3: Three Stage Gas Separation Model:Table B31: Table of operational variables with respect to changing reflux ratio of the second recycle stream, for the three stage gas separation membrane model.

Reflux Ratio for The Second Recycle StreamArea of each of the First 2 Membranes (cm2)Area of the third Membrane (cm2)Total Area of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Stream purityWaste Stream Flow Rate (mol/s)

0.001058112500532499001694749000.95490.0480.094157.587

0.002058152700484277001647331000.95490.5640.086457.071

0.003058192800436056001599912000.95491.080.078556.555

0.004058232900387836001552494000.95491.5970.070556.038

0.005058272800339618001505074000.95492.1130.062355.522

0.006058312700291400001457654000.95492.630.054055.006

0.007058352500243184001410234000.95493.1460.045554.489

0.008058392200194969001362813000.95493.6630.036853.972

0.009058431900146755001315393000.95494.180.028053.455

0.01005847140098543401267971400.95494.6970.019052.938

0.01105851000051446901221646900.95495.2020.010052.433

0.01105850000050332701220332700.95495.2140.001651.968

0.0120585503002123711173129710.95495.7310.000451.904

Reflux Ratio for The Second Recycle StreamWaste Stream Value ($/year)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Value ($/year)Profit $/year

0.0010.00861073.41547250.4839398155.0537989831

0.0020.00861677.25531938.7639439639.6538046024

0.0030.00862279.64516626.7239481124.2638102218

0.0040.00862880.96501315.0039522689.2638158493

0.0050.00863481.88486002.6339564173.8638214689

0.0060.00864081.01470690.2639605738.8738270967

0.0070.00864678.27455377.9039647223.4738327167

0.0080.00865275.20440065.2139688788.4738383448

0.0090.00865871.40424752.8439730353.4838439729

0.0100.00866465.41409439.9639771918.4838496013

0.0112932176.70867045.81394481.3439812518.7241483168

0.0112906144.89867059.41394056.9739813483.4841458512

0.0122902588.24867651.22378814.6839855048.4841511171

Table B32: Table of operational costs and product stream revenues with respect to changing reflux ratio for the second recycle stream, for the three stage gas separation membrane model.

Appendix B4: Four Stage Gas Separation Model:Reflux Ratio for The Third Recycle StreamArea of each of the First Three Membranes (cm2)Area of the Fourth Membrane (cm2)Total Area of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Stream PurityWaste Stream Flow Rate (mol/s)

0.010048466000162536001616516000.95494.4840.022753.151

0.017850181800101919001607373000.95495.2020.010052.433

0.02005071780094985201616519200.95495.2840.008552.351

0.03005312710079251001673064000.95495.4700.005252.165

0.04005547460072697701736935700.95495.5480.003852.087

0.05005773970069123901801314900.95495.5900.003052.045

0.06005992380066870501864584500.95495.6170.002552.018

0.07006203250065315401926290400.95495.6350.002252.000

0.08006407190064174201986331200.95495.6490.001951.986

0.09006604770063298702044729700.95495.6590.001751.976

0.10006796510062604002101557000.95495.6670.001651.968

Table B41: Table of operational variables with respect to changing reflux ratio of the third recycle stream, for the four stage gas separation membrane model.

Reflux Ratio for The Third Recycle StreamWaste Stream Value ($/year)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Value ($/year)Profit ($/year)

0.01000.001155984.67521988.3139754794.0238076821

0.01782932176.701205166.89519035.9539812518.7241020493

0.02002927585.481220839.67521989.3439819111.2441003868

0.03002917167.171292772.25540248.1939834064.9940918212

0.04002912827.601365180.26560872.9739840335.9240827110

0.05002910462.091437194.04581661.6239843712.5740735319

0.06002908968.971508635.40602091.9739845883.2840644125

0.07002907940.001579481.17622017.3939847330.4240553772

0.08002907185.051649750.16641405.1339848455.9740464486

0.09002906603.461719471.66660262.5639849259.9340376129

0.10002906144.891788680.12678612.6339849903.1040288755

Table B42: Table of operational costs and product stream revenues with respect to changing reflux ratio of the third recycle stream, for the three stage gas separation membrane model.

Appendix C: Absorption using Water Additional InformationAppendix C1: Henrys Law constant values at top and bottom of column for various operating conditions T (K)P (psi)HtopHbottom

2984801.873341.85521

2985201.729231.71250

2985901.524071.50932

2986601.362431.34924

2734800.403980.40488

Appendix C2:Consistency of profit values over different operating conditions and flow rates T=298 K P=480 psi T=298 K P =520 psi T=298 K P=590 psiLiquid Flow Rate (mol/s)Annual Profit ($/year)Liquid Flow Rate (mol/s)Annual Profit ($/year)Liquid Flow Rate (mol/s)Annual Profit ($/year)

655

675

700

725

750

775

800

825

850

875

900

925

950

975

1000

1025

1050

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1100

1150

52120750

52120391

52119941

52119492

52119043

52118593

52118144

52117695

52117245

52116796

52116347

52115897

52115448

52114999

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52113651

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52087512

52086169

52084402

52082635

52080868

52079100

52077333

52075566

52073799

52072032

52070264

52068497

52066730

52064963

52063196

52061428

52059661

52057894

52056127

52052592

404

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52051729

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52048189

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52042418

52040495

52038571

52036647

52034724

52032800

52030876

52028953

52027029

52025105

52023182

52021258

52013563

52005868

51990479

T=298 K P =698 psi T=273 K P=480 psiLiquid Flow Rate (mol/s)Annual Profit ($/year)Liquid Flow Rate (mol/s)Annual Profit ($/year)

359

375

400

425

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52040194

52038766

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52029841

52027609

52025378

52023146

52020915

52018683

52016452

52014221

52011989

52009758

52007526

52005295

52003063

52000832

51996369

236

250

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52138611

52137680

52136017

52134354

52132691

52131028

52129365

52127702

52126039

52124377

52122714

52121051

52119388

52117725

52116062

52114399

52112736

52111074

52109411

52107748

Appendix C3: Comparison of liquid flow rate and capital cost between 298 K and 273 K T=298 K T=273 KLiquid Flow Rate (mol/s)Capital Cost ($)Liquid Flow Rate (mol/s)Capital Cost ($)

(Lmin)236

250

275

300

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1719271

1453857

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650344

625890

605218

587514

572182

558775

546951

536446

527051

518597

510952

497661

486502

477000

(Lmin)655

675

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725

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850

875

900

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975

1000

1025

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1100

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1200

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3317951

2725738

2253525

1939419

1715381

1547516

1417046

1312734

1227422

1156356

1096235

1044721

1000085

961029.8

926583.3

895963.6

868566.6

843915.7

821616.7

806507

750263.8

722523.6

698610

References1. Combustion Values Fuel Gases. The Engineering ToolBox. Web. 18 April 2014. www.engineeringtoolbox.com/fuel-gases-combustion-values-d_510.html. 2. Hestermans, P. White, D. The Vapor Pressure, Heat of Vaporization and Heat Capacity of Methane from the Boiling Point to the Critical Temperature. J. Chem. Phys. 1961, 65, 362-365. Retrieved from webbook.nist.gov.3. Giauque, W.F.; Egan, C.J., Carbon Dioxide. The Heat Capacity and Vapor Pressure of the Solid.The Heat of Sublimation. Thermodynamic and Spectroscopic Values of the Entropy, J. Chem .Phys. 1937, 5, 45-54. Retrieved from webbook.nist.gov. 4. Vrachnos, A. Kontogeorgis, G. Voutsas, E. Thermodynamic Modeling of Acidic Gas Solubility in Aqueous Solutions in MEA, MDEA and MEA-MDEA Blends. Ind. Eng. Chem. Res. 2006, 45, 5148-5154. 5. Subramanian, R.S. Thermal Analysis of a Steady State Heat Exchanger. Clarkson University. Web. 24 April 2014. http://web2.clarkson.edu/projects/subramanian/ch330/notes/Thermal%20Analysis%20of%20a%20Steady%20State%20Heat%20Exchanger.pdf.6. Chiu, Li-Feng. Li, Meng-Hui. Heat Capacity of Alkanolamine Aqueous Solutions. Chem. Eng. Data, 1999, 44 (6), 1396-1401. //pubs.acs.org on November 19, 2008.7. Methyl Diethanolamine. Wikipedia, the Free Encyclopedia. Wikimedia Foundation, Inc. 28 February 2013. Web. 24 April 2014. http://en.wikipedia.org/wiki/Methyl_diethanolamine.8. Henrys Law. Wikispaces: ChemEngineering. Wikimedia Foundation, Inc. Web. 24 April 2014. http://chemengineering.wikispaces.com/Henry's+law.9. Carroll, J. J., Slupsky, J. D., and Mather, A. E., J. Phys. Chem. Ref. Data, 20, 1201, 199110. Fernandez-Prini, R. and Crovetto, R., J. Phys. Chem. Ref. Data, 18, 1231, 198911. Lide and Frederikse,1995CRC Handbook of Chemistry and Physics, 76th Edition, D. R. Lide and H. P. R. Frederikse, ed(s)., CRC Press, Inc., Boca Raton, FL, 1995.12. Specific heat of Methane Gas. The Engineering Toolbox, Web. 24 April 2014.http://www.engineeringtoolbox.com/methane-d_980.html.13. Specific heat of Carbon Dioxide Gas. The Engineering Toolbox, Web. 24 April 2014.http://www.engineeringtoolbox.com/carbon-dioxide-d_974.html.

2Chart137.98983115538.046023633638.102217898638.15849329938.214689350438.27096759238.327167302238.383448061938.439729230538.49601311141.483168268641.458511988641.5111708183

Reflux Ratio of the Third StageMillions of Dollars per YearNet Annual Profit Vs. Reflux Ratio of the Third Stage

Process Flow Diagram

FeedVr1, Product StreamVr2, Recycle Stream 1Vp1Vr3, Recycle Stream 2Vp2Vr4, Recycle Stream 3Vp3Vp4, Waste Stream

New Process Flow Diagram

Vr1, CH4 Rich StreamVr2, First Recycle StreamVr3, Second Recycle StreamVr4, Third Recycle StreamVp2Vf, Feed StreamVp1Vp3Vp4, CO2 Rich Stream

Optimizing Cost for 1 StageArea of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream Value ($/year)Profit $/year00.86547.635000009964220.169165973.534874770.592080934874770.592080910000000.862546.2580.071.37675003229.0945929962279.98950893.534867979.963281134864750.868689130000000.8658543.6120.0734.02009687.2837769957728.564653043.534852049.976285734842362.692509750000000.8695541.0990.0756.5360016145.472969954053.827907913.534839188.397677734823042.924717780000000.87456537.560.07810.07460025832.7567369946498.524510213.534812744.835785734786912.0790497100000000.877897535.3430.0812.2952691.7491147058032290.945929943272.932902813.534801455.265159934821856.0683546500000000.9205505.9550.12452841.6799278159.8393563260161454.72969853473.48342693.534487157.191994234603862.3017505800000000.937405493.3940.155589254.24452272.1796534240258327.567369785314.688358673.534248601.409255334442546.02154881000000000.945173487.0110.17578360.6243571116.0359462460322909.45929738761.829560053.534085666.403460234333872.98020641155600000.95482.7250.19068764.91663335.806328951193871.276988869373154.171051529702352.8277356438809411.310942438905721.6692313000000000.975385449.0370.33450898.59751767555.89961265180341.553897666968728.37769266417.58432102437065670.337284137684156.30539915000000000.9806435.1920.3931112.4432368842.64818611174781.1461501681614547.2969028725.70897311436114902.835892436694417.041928410000000000.99362.4110.602185.2245975778.55562388145550.9521255643229094.5927590846.9118485430363387.64739432964520.6588923CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)385856.60370000.12

Optimizing Cost for 1 Stage

Membrane Area (cm^2)Net Profit ($ per year)Net Profit vs Membrane Area

Cost Analysis for adding Stages

Waste Gas Value vs Membrane Area

3 Stages

Product Stream Value vs Membrane Area

4 StagesReflux Ratio (Fraction of Feed Recycled)Flow Rate of Recycle Stream (mol/s)Area of Second Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.0210.9527339797001495397000.949181492.8050.0584654.8303065.783481372.150638225482877.83655930310027320.08829133.535095620.309019534131370.32182190.0421.9054111105001266705000.943984980.013465449.4248071.3302521964.212326204409031.02651593610077501.52562713.535271255.339694834340260.10085270.0471325.8100375593402001249002000.941657499.6350.0147.99982684256.6070420373.8099540109.607366528403314.56035971910085706.58694013.535299973.054290237040805.4936060.0632.858175683901231283900.937369502.1040.0067924445.53092546190.1747417778.389573617.523013237397593.21827066710089392.20503233.535312872.717613136887852.1510710.0843.810860979701216579700.93064505.8660.0044872241.76922335827.4632573585.58626238.217345199392845.09300069810092016.28552183.535322056.999326136638801.15223760.154.763551650701207250700.923906509.6180.0033332438.01672125979.2364329692.7802678926.233383163389832.67065582210093302.36009573.535326558.260334936383778.59272890.1265.716244452101200052100.917192513.3880.0026423634.24681915157.9625341699.63729050.170531692387508.17462282410094079.20085533.535329277.202993636127876.82037330.1476.668938296301193896300.910506517.1850.0021828830.45041702854.74912547107.119783851.502731952385520.40857388110094608.24303733.535331128.850630535864611.68845010.1687.621632717801188317800.903851521.0120.0018553726.62331488834.72277514114.245835996.554575862383719.05815573410094976.34789673.535332417.217638535601536.3276820.1898.574327843001183443000.897228524.8720.00160222.76331272974.85454273121.338887900.126387378382144.93912402610095247.25817313.535333365.403605835336295.19263720.2109.52722467001178067000.890638528.7660.0014198218.8691055196.85328431128.396939547.58301302380408.97787136610095445.28937233.535334058.51280335069298.8052030.22120.479717588801173188800.884083532.6960.0012677414.9395835450.388978797135.419990938.924452788378833.76094749710095625.03854963.535334687.634923634800365.33850210.24131.432412800401168400400.877563536.6610.0011434710.974613690.723829667142.4061042066.83312994377287.54129306410095761.36344473.535335164.772056334529501.12146290.26142.38518069231163669230.871077540.6630.001040056.97215389898.28505094149.3571092931.30904448375759.80174698110095874.2693013.535335559.942553634256767.1168130.28153.33783372451158972450.864626544.7020.000952632.93338164041.196962591156.2711143525.03461967374243.16705719910095968.75004463.535335890.625156133982163.62044180.2944117855161.23019815230.00690874115560000.0069090.86547.635000161.231179812.89766963373154.17107382910096024.24033013.535336084.841155433783117.772412Area of First Gas Membrane (cm2)Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)115560000547.635385856.60370000.12

4 Stages

Net Annual Profit Vs Second Membrane Area

Stage Cost Analysis

Net Annual Profit Vs. Reflux Ratio

Second Membrane Area Vs. Reflux Ratio

Reflux Ratio for The Second Recycle StreamArea of each of the First 2 Membranes (cm2)Area of the third Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Vp2 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.00158112500532499001694749000.95490.0480.094125357.5869032.641658.1345861073.406900759547250.4830697419849538.76125367439398155.045014737.9898311550.00258152700484277001647331000.95490.5640.086386457.0708032.664258.1661861677.254691677531938.7623333959859909.91265273439439639.650610938.04602363360.00358192800436056001599912000.95491.080.078504456.5547032.686758.1976862279.638967248516626.7186875919870281.06405179439481124.256207238.10221789860.00458232900387836001552494000.95491.5970.070475356.0384032.709258.2289862880.961345943501314.9979512459880672.31458147439522689.258325938.1584932990.00558272800339618001505074000.95492.1130.06229555.522032.731758.2602863481.882106166486002.6313959819891043.46598053439564173.863922138.21468935040.00658312700291400001457654000.95492.630.053959355.0055032.754158.2913864081.009211839470690.2648407179901434.71651021439605738.866040838.2709675920.00758352500243184001410234000.95493.1460.045463554.4888032.776458.3223864678.271183692455377.8982854539911805.86790927439647223.471637138.32716730220.00858392200194969001362813000.95493.6630.036803253.9721032.798758.3532865275.203016344440065.208820739922197.11843895439688788.473755838.38344806190.00958431900146755001315393000.95494.180.027973553.4552032.82158.384865871.403091321424752.8422654669932588.36896863439730353.475874538.43972923050.015847140098543401267971400.95494.6970.018969452.9383032.843258.4146866465.407893277409439.9590550679942979.61949831439771918.477993238.4960131110.010976895851000051446901221646900.95495.2020.0152.43312932176.6987090732.864958.4445867045.812181479394481.3398123579953129.68046057439812518.721842341.48316826860.0115850000050332701220332700.95495.2140.001579251.96762906144.8933561732.865458.4452867059.412695233394056.9722010769953370.87002799439813483.480111941.45851198860.012585503002123711173129710.95495.7310.00041705951.9042902588.2385324532.887558.4756867651.222224167378814.6802275539963762.12055767439855048.482230741.5111708183Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)547.635385856.60370000.12

Total Area of Membrane (cm2)Millions of Dollars per yearNet Annual Profit Vs. Total Area of Gas Membrane

Reflux Ratio of the Third StageMillions of Dollars per YearNet Annual Profit Vs. Reflux Ratio of the Third Stage

Reflux Ratio for The Third Recycle StreamArea of each of the First Three Membranes (cm2)Area of the Fourth Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Vp2 Flowrate (mol/s)Vp3 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.0148466000162536001616516000.95494.4840.022694553.1509027.223444.983758.62731155984.67073739521988.3073481479938698.5046766439754794.018706438076821.04062090.0177661550181800101919001607373000.95495.2020.0152.43312932176.6987090728.18747.166662.16251205166.88529908519035.9461626829953129.68046057439812518.721842341020492.58908960.025071780094985201616519200.95495.2840.0085257452.3512927585.4823407128.488147.861663.30371220839.67477861521989.3406584179954777.80917127439819111.236685141003867.70358880.035312710079251001673064000.95495.470.0051631352.16472917167.1679749829.841351.038268.59381292772.24763622540248.1914469899958516.24746628439834064.989865140918211.71875690.045547460072697701736935700.95495.5480.003755552.08712912827.6017120731.159954.211773.99251365180.26188964560872.9675521749960083.97965451439840335.918618140827110.29088830.055773970069123901801314900.95495.590.002986152.04482910462.0907208232.432257.344279.42661437194.0356453581661.6202079029960928.14314048439843712.572561940735319.00742950.065992380066870501864584500.95495.6170.0025003152.01812908968.966761833.65960.429384.87621508635.40468426602091.9725277039961470.81966718439845883.278668740644124.86821850.076203250065315401926290400.95495.6350.0021647851.99972907939.9974417334.843463.467590.33421579481.16719876622017.3913261529961832.60401831439847330.416073240553771.854990.086407190064174201986331200.95495.6490.0019184151.98622907185.0471253735.98966.461195.7971649750.16170767641405.1335840879962113.99184696439848455.967387940464485.71922150.096604770063298702044729700.95495.6590.001729351.97582906603.4557705537.098869.4127101.2631719471.65851795660262.5616371789962314.98315315439849259.932612640376129.1682280.16796510062604002101557000.95495.6670.001579251.96762906144.8933561738.175872.3251106.7311788680.12171953678612.6343479759962475.77619809439849903.104792440288755.242081Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)547.635385856.60370000.12

In the previous sections it can be seen that the most profit occurs when the CH4 purity is 0.95. In this spread sheet there will be various attampts using new recycle strategies to attain 0.95 CH4 purity, the cost will then be analyzed.

Net Annual Profit Vs. Reflux Ratio of the Third Recycle Stream

# of StagesCh4 purityMolar Flow rate of Product Stream (mol/s)Compression Cost ($/year)Membrane AreaMembrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Co2 Waste Stream ValueProfit $/year00.86547.6700842835.710773533.52949924.9877073610.95482.725193871.276988869115560000373154.17105152820632.89482801542715506.1312716720.94547.67219954.3886653770921239.0327059513.53004382.2258054530.96547.67219954.3886653770940839.86318905743543405.0640908540.97547.67219954.3886653770950640.27843060943582606.7250570650.98547.67219954.3886653770960440.69367216243621808.38602327CH4 Energy of Combustion (BTU/lbmol)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)3221070000.12

Chart137.98983115538.046023633638.102217898638.15849329938.214689350438.27096759238.327167302238.383448061938.439729230538.49601311141.483168268641.458511988641.5111708183

Total Area of Membrane (cm2)Millions of Dollars per yearNet Annual Profit Vs. Total Area of Gas Membrane

Process Flow Diagram

FeedVr1, Product StreamVr2, Recycle Stream 1Vp1Vr3, Recycle Stream 2Vp2Vr4, Recycle Stream 3Vp3Vp4, Waste Stream

New Process Flow Diagram

Vr1, CH4 Rich StreamVr2, First Recycle StreamVr3, Second Recycle StreamVr4, Third Recycle StreamVp2Vf, Feed StreamVp1Vp3Vp4, CO2 Rich Stream

Optimizing Cost for 1 StageArea of Membrane (cm2)Product Stream PurityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream Value ($/year)Profit $/year00.86547.635000009964220.169165973.534874770.592080934874770.592080910000000.862546.2580.071.37675003229.0945929962279.98950893.534867979.963281134864750.868689130000000.8658543.6120.0734.02009687.2837769957728.564653043.534852049.976285734842362.692509750000000.8695541.0990.0756.5360016145.472969954053.827907913.534839188.397677734823042.924717780000000.87456537.560.07810.07460025832.7567369946498.524510213.534812744.835785734786912.0790497100000000.877897535.3430.0812.2952691.7491147058032290.945929943272.932902813.534801455.265159934821856.0683546500000000.9205505.9550.12452841.6799278159.8393563260161454.72969853473.48342693.534487157.191994234603862.3017505800000000.937405493.3940.155589254.24452272.1796534240258327.567369785314.688358673.534248601.409255334442546.02154881000000000.945173487.0110.17578360.6243571116.0359462460322909.45929738761.829560053.534085666.403460234333872.98020641155600000.95482.7250.19068764.91663335.806328951193871.276988869373154.171051529702352.8277356438809411.310942438905721.6692313000000000.975385449.0370.33450898.59751767555.89961265180341.553897666968728.37769266417.58432102437065670.337284137684156.30539915000000000.9806435.1920.3931112.4432368842.64818611174781.1461501681614547.2969028725.70897311436114902.835892436694417.041928410000000000.99362.4110.602185.2245975778.55562388145550.9521255643229094.5927590846.9118485430363387.64739432964520.6588923CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)385856.60370000.12

Optimizing Cost for 1 Stage

Membrane Area (cm^2)Net Profit ($ per year)Net Profit vs Membrane Area

Cost Analysis for adding Stages

Waste Gas Value vs Membrane Area

3 Stages

Product Stream Value vs Membrane Area

4 StagesReflux Ratio (Fraction of Feed Recycled)Flow Rate of Recycle Stream (mol/s)Area of Second Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.0210.9527339797001495397000.949181492.8050.0584654.8303065.783481372.150638225482877.83655930310027320.08829133.535095620.309019534131370.32182190.0421.9054111105001266705000.943984980.013465449.4248071.3302521964.212326204409031.02651593610077501.52562713.535271255.339694834340260.10085270.0471325.8100375593402001249002000.941657499.6350.0147.99982684256.6070420373.8099540109.607366528403314.56035971910085706.58694013.535299973.054290237040805.4936060.0632.858175683901231283900.937369502.1040.0067924445.53092546190.1747417778.389573617.523013237397593.21827066710089392.20503233.535312872.717613136887852.1510710.0843.810860979701216579700.93064505.8660.0044872241.76922335827.4632573585.58626238.217345199392845.09300069810092016.28552183.535322056.999326136638801.15223760.154.763551650701207250700.923906509.6180.0033332438.01672125979.2364329692.7802678926.233383163389832.67065582210093302.36009573.535326558.260334936383778.59272890.1265.716244452101200052100.917192513.3880.0026423634.24681915157.9625341699.63729050.170531692387508.17462282410094079.20085533.535329277.202993636127876.82037330.1476.668938296301193896300.910506517.1850.0021828830.45041702854.74912547107.119783851.502731952385520.40857388110094608.24303733.535331128.850630535864611.68845010.1687.621632717801188317800.903851521.0120.0018553726.62331488834.72277514114.245835996.554575862383719.05815573410094976.34789673.535332417.217638535601536.3276820.1898.574327843001183443000.897228524.8720.00160222.76331272974.85454273121.338887900.126387378382144.93912402610095247.25817313.535333365.403605835336295.19263720.2109.52722467001178067000.890638528.7660.0014198218.8691055196.85328431128.396939547.58301302380408.97787136610095445.28937233.535334058.51280335069298.8052030.22120.479717588801173188800.884083532.6960.0012677414.9395835450.388978797135.419990938.924452788378833.76094749710095625.03854963.535334687.634923634800365.33850210.24131.432412800401168400400.877563536.6610.0011434710.974613690.723829667142.4061042066.83312994377287.54129306410095761.36344473.535335164.772056334529501.12146290.26142.38518069231163669230.871077540.6630.001040056.97215389898.28505094149.3571092931.30904448375759.80174698110095874.2693013.535335559.942553634256767.1168130.28153.33783372451158972450.864626544.7020.000952632.93338164041.196962591156.2711143525.03461967374243.16705719910095968.75004463.535335890.625156133982163.62044180.2944117855161.23019815230.00690874115560000.0069090.86547.635000161.231179812.89766963373154.17107382910096024.24033013.535336084.841155433783117.772412Area of First Gas Membrane (cm2)Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)115560000547.635385856.60370000.12

4 Stages

Net Annual Profit Vs Second Membrane Area

Stage Cost Analysis

Net Annual Profit Vs. Reflux Ratio

Second Membrane Area Vs. Reflux Ratio

Reflux Ratio for The Second Recycle StreamArea of each of the First 2 Membranes (cm2)Area of the third Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Vp2 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.00158112500532499001694749000.95490.0480.094125357.5869032.641658.1345861073.406900759547250.4830697419849538.76125367439398155.045014737.9898311550.00258152700484277001647331000.95490.5640.086386457.0708032.664258.1661861677.254691677531938.7623333959859909.91265273439439639.650610938.04602363360.00358192800436056001599912000.95491.080.078504456.5547032.686758.1976862279.638967248516626.7186875919870281.06405179439481124.256207238.10221789860.00458232900387836001552494000.95491.5970.070475356.0384032.709258.2289862880.961345943501314.9979512459880672.31458147439522689.258325938.1584932990.00558272800339618001505074000.95492.1130.06229555.522032.731758.2602863481.882106166486002.6313959819891043.46598053439564173.863922138.21468935040.00658312700291400001457654000.95492.630.053959355.0055032.754158.2913864081.009211839470690.2648407179901434.71651021439605738.866040838.2709675920.00758352500243184001410234000.95493.1460.045463554.4888032.776458.3223864678.271183692455377.8982854539911805.86790927439647223.471637138.32716730220.00858392200194969001362813000.95493.6630.036803253.9721032.798758.3532865275.203016344440065.208820739922197.11843895439688788.473755838.38344806190.00958431900146755001315393000.95494.180.027973553.4552032.82158.384865871.403091321424752.8422654669932588.36896863439730353.475874538.43972923050.015847140098543401267971400.95494.6970.018969452.9383032.843258.4146866465.407893277409439.9590550679942979.61949831439771918.477993238.4960131110.010976895851000051446901221646900.95495.2020.0152.43312932176.6987090732.864958.4445867045.812181479394481.3398123579953129.68046057439812518.721842341.48316826860.0115850000050332701220332700.95495.2140.001579251.96762906144.8933561732.865458.4452867059.412695233394056.9722010769953370.87002799439813483.480111941.45851198860.012585503002123711173129710.95495.7310.00041705951.9042902588.2385324532.887558.4756867651.222224167378814.6802275539963762.12055767439855048.482230741.5111708183Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)547.635385856.60370000.12

Total Area of Membrane (cm2)Millions of Dollars per yearNet Annual Profit Vs. Total Area of Gas Membrane

Reflux Ratio for The Third Recycle StreamArea of each of the First Three Membranes (cm2)Area of the Fourth Membrane (cm2)Total Area of Membrane (cm2)Ch4 purityMolar Flow rate of Product Stream (mol/s)Waste Gas purityWaste Gas Flow Rate (mol/s)Waste Gas Value ($/year)Vp1 Flowrate (mol/s)Vp2 Flowrate (mol/s)Vp3 Flowrate (mol/s)Compression Cost ($/year)Membrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Product Stream ValueProfit $/year0.0148466000162536001616516000.95494.4840.022694553.1509027.223444.983758.62731155984.67073739521988.3073481479938698.5046766439754794.018706438076821.04062090.0177661550181800101919001607373000.95495.2020.0152.43312932176.6987090728.18747.166662.16251205166.88529908519035.9461626829953129.68046057439812518.721842341020492.58908960.025071780094985201616519200.95495.2840.0085257452.3512927585.4823407128.488147.861663.30371220839.67477861521989.3406584179954777.80917127439819111.236685141003867.70358880.035312710079251001673064000.95495.470.0051631352.16472917167.1679749829.841351.038268.59381292772.24763622540248.1914469899958516.24746628439834064.989865140918211.71875690.045547460072697701736935700.95495.5480.003755552.08712912827.6017120731.159954.211773.99251365180.26188964560872.9675521749960083.97965451439840335.918618140827110.29088830.055773970069123901801314900.95495.590.002986152.04482910462.0907208232.432257.344279.42661437194.0356453581661.6202079029960928.14314048439843712.572561940735319.00742950.065992380066870501864584500.95495.6170.0025003152.01812908968.966761833.65960.429384.87621508635.40468426602091.9725277039961470.81966718439845883.278668740644124.86821850.076203250065315401926290400.95495.6350.0021647851.99972907939.9974417334.843463.467590.33421579481.16719876622017.3913261529961832.60401831439847330.416073240553771.854990.086407190064174201986331200.95495.6490.0019184151.98622907185.0471253735.98966.461195.7971649750.16170767641405.1335840879962113.99184696439848455.967387940464485.71922150.096604770063298702044729700.95495.6590.001729351.97582906603.4557705537.098869.4127101.2631719471.65851795660262.5616371789962314.98315315439849259.932612640376129.1682280.16796510062604002101557000.95495.6670.001579251.96762906144.8933561738.175872.3251106.7311788680.12171953678612.6343479759962475.77619809439849903.104792440288755.242081Feed Flowrate (mol/s)CH4 Energy of Combustion (BTU/lbmol-CH4)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)547.635385856.60370000.12

In the previous sections it can be seen that the most profit occurs when the CH4 purity is 0.95. In this spread sheet there will be various attampts using new recycle strategies to attain 0.95 CH4 purity, the cost will then be analyzed.

Net Annual Profit Vs. Reflux Ratio of the Third Recycle Stream

# of StagesCh4 purityMolar Flow rate of Product Stream (mol/s)Compression Cost ($/year)Membrane AreaMembrane Cost ($/year)Product Stream Energy (MMBTU/year)Product Stream Energy Value ($/MMBtu)Co2 Waste Stream ValueProfit $/year00.86547.6700842835.710773533.52949924.9877073610.95482.725193871.276988869115560000373154.17105152820632.89482801542715506.1312716720.94547.67219954.3886653770921239.0327059513.53004382.2258054530.96547.67219954.3886653770940839.86318905743543405.0640908540.97547.67219954.3886653770950640.27843060943582606.7250570650.98547.67219954.3886653770960440.69367216243621808.38602327CH4 Energy of Combustion (BTU/lbmol)Operating Time per year (Hrs/year)Electric Cost ($/kilowatt-hr)3221070000.12