CH E 410 Final Project

David Belias – Cryogenic Distillation

Mike McEldrew – Gas Separation Membranes

David Kozak – MDEA Absorption

Austin Goewert – Water Absorption

4/25/2014

Executive Summary

This 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)

494.7 77 86 14 35

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.

A ¿ n=P VRT

=(14.7 psia )∗( 35×106 ft3day

× 1day24h )

(10.73 psia∗ft3

lb−mol∗° R )∗(459.67 ° R )=4346.4 lb−mol

h=547.638 gmol

s

Gases with varying energy levels could be sold for different prices, which are outlined in Table B below.

Product Methane Concentration (mol%)

Price ($/MMBtu) Specifications

Waste Gas <10% - -Low Energy Gas 10-40% 2.50 -

Medium Energy Gas 40-70% 3.00 -

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

High Energy Gas 70-95% 3.50 -Pipeline Quality Gas 95% 4.00 600 psia

Liquefied Natural Gas 99.995% 5.20 600 psiaHigh Purity Carbon

Dioxide1% 0.003/SCF -

Since the feed was already a high energy gas, pipeline quality gas and liquefied natural gas were explored as possible product streams. The revenue generated from selling the feedstock, pipeline quality gas, and liquefied natural gas were calculated using Equations B, C, and D. Selling the high purity carbon dioxide was also investigated for some unit operations. Calculating the revenue for this stream is outlined in equation E below. The operating time for this analysis was 7,000 hours per year.

B ¿Feedstock Reve nue( $yr )=0.86× Feed Flow ( lb−mol )hr

× OperationTime (hr )yr

× CombustionValue (MMBtu )lb−mol

× $ 3.50MMBtu

C ¿ Pipeline Revenue ( $yr )=0.95×∏ .Flow (lb−mol )hr ×

Operation Time (hr )yr ×

CombustionValue (MMBtu )lb−mol × $4.00

MMBtu

D ¿ Liq. NGRevenue( $yr )=0.99995×∏ . Flow (lb−mol )hr ×

OperationTime (hr )yr ×

CombustionValue (MMBtu )lb−mol × $5.20

MMBtu

E ¿CO2 Revenue( $yr )=∏ . Flow (SCF )hr ×

OperationTime (hr )yr × $0.003SCF

The combustion value of methane was found in Btu per standard cubic feet and converted to MMBtu per pound mole using Equation F.1 Equation A was used to calculate the number of moles in one standard cubic foot.

F ¿CombustionValue(MMBtulbmol )= 1150BtuSCF× SCFlbmol

× MMBtu106 Btu

=0.3859 MMBtulbmol

In order to calculate the high purity carbon dioxide flow rate used in Equation E, the ideal gas law was employed at standard temperature and pressure.

There were also operational costs to consider, before calculating the net profit of a given system. Each of the aforementioned unit operations requires the pressurization of gas or liquid streams. The cost associated with this compression can be seen in Equations G and H.

3

Table B. Product stream market prices based on purity.

G ¿ LiquidCompressionCost ( $yr )= Liquid Flow Rat e(m3)s

×(P2−P1)(Pa)×J

Pa∗m3× kJ1000 J

× 1kW

1 kJs

× 7000hyr

× $ 0.12kW−hr

H ¿GasCompressionCost ( $yr )=Gas Flow Rate(mol)s× 8.314 Jmol∗K

×T (K )× ln (P2P1

)× kJ1000 J

× 1kW

1 kJs

× 7000hyr

× $0.12kW−hr

Each unit operation has its own unique operational costs, which will be discussed further in the subsequent sections. The net profit was calculated by subtracting the total operational costs from the revenue generated from the product and waste streams.

Distillation was the first operation considered for this separation. The simulations were performed using Aspen HYSYS with the Peng-Robinson fluid package. The main factors investigated were number of stages, reflux ratio, column pressure, feed quality, and product streams. Costs for running the column included refrigeration, compression, heating, and equipment.

The next unit operation examined was gas separation membranes. The primary elements explored were number of stages, recycling strategy, membrane area, feed entry stage, and outlet stream purity. The main costs associated with gas separation membranes are the cost of membranes, and the cost of gas compression. The calculations were performed using Wolfram Mathematica.

The third operation that was investigated was MDEA absorption. The main variables of concern for the absorption involved Henry’s Law constant, liquid flow rate, volume of the column, pressure of the column, and temperature of the column. The more substantial costs included the capital for building the column and the pressurization of the feed as well as heating and cooling the two feed streams. These calculations were performed in both Excel and Wolfram Mathematica.

4

Absorption using Water

IntroductionThe separation of carbon dioxide from methane can be accomplished by absorption of carbon dioxide into water. Several key equations are necessary to perform this analysis:

1. Volume of column: Vol=−V '

k0a∫y¿

yout dy(1− y )2 ( y−Hx )

- k o−1=( 1

k y+ Hk x

)

- a=constant ¿

- k y=0.56molm2 s

- k x=8.6molm2 s

2. x [ y ]=¿- V '=V ¿ (1− y¿)- L'=L¿

3. Henry’s Law constant : H=y∫¿

x∫¿¿¿

- y∫¿ ¿ : vapor mole fraction at interface

- x∫¿¿: liquid mole fraction at interface

4. Henry’s Law variation with8 T: kH=kH' exp[−C ( 1T −

1T ' )]

- kH=Pgas

x∫¿¿

- C : constant8 (=2400 Kelvin for CO2)

It is essential to derive an equation for the volume of the absorption column in order to calculate the capital cost for this process. Equation 1 is derived from a material balance within the column. Since liquid concentration varies throughout the column, equation 2 is necessary to evaluate the integral.

5

The final step in solving for the volume of the column is the evaluation of H using solubility data for carbon dioxide in methane. Since the process is gas phase dominated (1/ky >> 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. H top 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 Henry’s Law Constant Values at Top and Bottom of Column9,10

T (K) P (psi) Htop/Hbottom

298 480 .9903298 520 .9903298 590 .9903298 660 .9903273 480 1.0022

Note: See Appendix C1 for H values

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

6

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 Henry’s Law constant.

Table 8: Henry’s Law Constants at Various Operating Conditions

T (K) P (psi) H298 480 1.20236298 520 0.831172298 590 0.73256298 698 0.554863273 480 0.430802

At this point, the solubility of methane in water must be considered. Numerous experimental sources show the Henry’s law constant for methane in water is high compared to that of carbon dioxide11

(Hmethane 20). Therefore, 100% methane recovery is assumed.

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CalculationsThe calculations for each system were similar and proceeded as follows:

1. Assume equilibrium at bottom of column. Use Henry’s law constant to calculate xout

2. Use CO2 species balance to calculate approximate Lmin

3. Generate table of Lin and column volume over range of Lmin 2.5Lmin

4. Calculate annual profit and capital cost for each value of L

- CapitalCost=$63566m3

∗Volume (m3)

- Profit=Revenue−Compression−Cooling−Water

- Revenue (high energy gas )=$3.5 x106

- Revenue ( pipelinequality gas )=$ 4.0 x106

- Revenue (liquified natural gas )=$5.2 x106 *

- Compression : seeintroduction

- Water=L¿( galy )x $0.151000 gal

- Vapor cooling−discussed below **

* 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.

8

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.

9

Figure 23

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.

10

Figure 24

Figure 25

Note: See Appendix C2 for exact profit values.

ΔTw= ΔTfeed.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.)

Cpw ΔTw=CpFeed ΔT Feed

Lw=CpFeedCpw

xMW w

MW FeedxV Feed=233.9055

mols

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 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.

11

Figure 26

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

12

Figure 27

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, L in = 375 mol/s, and Lcooling = 250 mol/s. Relaxation of cooling assumptions will likely require a higher cooling liquid flow rate.

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Figure 28

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.

Distillation Gas Separation MDEA Absorption Water Absorption

32.1

41.5

52 52.1

11.23

1.246 0.4335 0.3955

Maximum Profit and Total Costs for Different Operations

Maximum Profit ($M/yr) Operational Costs ($M/yr)

14

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 day’s 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%.

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Appendix C: Absorption using Water Additional Information

Appendix C1: Henry’s Law constant values at top and bottom of column for various operating conditions

T (K) P (psi) Htop Hbottom

298 480 1.87334 1.85521298 520 1.72923 1.71250298 590 1.52407 1.50932298 660 1.36243 1.34924273 480 0.40398 0.40488

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 psi

Liquid Flow Rate (mol/s)

Annual Profit ($/year)

Liquid Flow Rate (mol/s)

Annual Profit ($/year)

Liquid Flow Rate (mol/s)

Annual Profit ($/year)

655675700725750775800825850875900925950975

100010251050107511001150

52120750

52120391

52119941

52119492

52119043

52118593

52118144

52117695

52117245

52116796

52116347

52115897

52115448

52114999

456475500525550575600625650675700725750775800825850875900950

52087512

52086169

52084402

52082635

52080868

52079100

52077333

52075566

52073799

52072032

52070264

52068497

52066730

52064963

404425450475500525550575600625650675700725750775800900

10001200

52051729

52050113

52048189

52046266

52044342

52042418

52040495

52038571

52036647

52034724

52032800

52030876

52028953

52027029

16

52114549

52114100

52113651

52113201

52112752

52111853

52063196

52061428

52059661

52057894

52056127

52052592

52025105

52023182

52021258

52013563

52005868

51990479

T=298 K P =698 psi T=273 K P=480 psi

Liquid Flow Rate (mol/s)

Annual Profit ($/year)

Liquid Flow Rate (mol/s)

Annual Profit ($/year)

359375400425450475500525550575600625650675700725750775800850

52040194

52038766

52036535

52034303

52032072

52029841

52027609

52025378

52023146

52020915

52018683

52016452

236250275300325350375400425450475500525550575600625650675700

52138611

52137680

52136017

52134354

52132691

52131028

52129365

52127702

52126039

52124377

52122714

52121051

17

52014221

52011989

52009758

52007526

52005295

52003063

52000832

51996369

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 K

Liquid Flow Rate (mol/s) Capital Cost ($) Liquid Flow Rate (mol/s) Capital Cost ($)

(Lmin)236

250

1719271

145385

(Lmin)655

675

3317951

272573

18

275300325350375400425450475500525550575600625650675700750800850

7117216

4100621

3896662818877760771715709679730650344625890605218587514572182558775546951536446527051518597510952497661486502477000

700725750775800825850875900925950975

100010251050107511001150120012501300

8225352

5193941

9171538

1154751

6141704

6131273

4122742

2115635

6109623

5104472

1100008

5961029.

8926583.

3895963.

6868566.

6843915.

7821616.

7806507

750263.8

722523.6

698610

19

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