The qualitative effect of CO₂, H₂S and N₂ on the phase envelope of a rich gas or oil is shown in Figure 4.9 on page 100 in reference [1]. As shown in Figure 4.9 a and b, both CO₂ and H₂S lower the cricondenbar of the mixture. If sufficient quantities of the CO₂ and H₂S components are added to a reservoir fluid and the reservoir pressure is kept above the phase envelope, a single dense fluid phase exists. Although the actual mechanism is more complex, it is this solubility that is the primary driving force behind miscible flood enhanced oil recovery projects. NGL components such as ethane, propane and butane have a similar effect. With the increasing environmental concerns associated with acid gas (CO₂ and/or H₂S) injection into the reservoir and enhanced oil recovery, a  good understanding of the impact on phase behavior is essential.

Nitrogen, on the other hand, raises the cricondenbar and decreases miscibility. It is sometimes used for pressure maintenance. There are also a few nitrogen miscible floods.

In this TOTM, we will study the impact of CO₂, H₂S and N₂ on the phase behavior of different reservoir fluids such as black oil, volatile oil, and a rich gas. Computer simulated phase envelopes showing the quantitative effect are presented and discussed.

The Peng-Robinson (PR) [2] equation of state (EOS) option of ProMax [3] was used to perform all of the calculations in this study. In dealing with high content acid gases or nitrogen, care should be taken to verify the accuracy of an equation of state for handling these constituents. In general it is wise to assume the equations of state are inaccurate for modeling the thermodynamic properties and the phase behavior of systems containing high concentrations of non-hydrocarbon components like acid gases and nitrogen. Verification with experimental data is recommended before accepting results from equations of state.

Case Studies:

Volatile Oil: Figures 1, 2 and 3 present the impact of CO₂ and H₂S and their mixture on the phase behavior of a volatile oil. The compositions of the light oil and the acid gas used to generate these two figures are shown in Table 1. For the properties (average normal boiling point, molecular weight and relative density of single carbon number (SCN), see Table 3.3 on page 64 of reference [1].  Both CO₂ and H₂S lower the cricondenbar of the volatile oil. These quantitative behaviors agree well with the qualitative ones shown in Figure 4.9 a and b. Figure 3 presents the impact of equal molar mixtures of CO₂ and H₂S on the volatile oil phase envelope. The net effect is almost midway of the effect of CO₂ and H₂S. In all three figures, the critical point of mixture shifts considerably to the left. The cricondentherm point also shifts to the left as the concentration of acid gases increase. The net effect is enhancing miscibility, shrinkage of the two phase region and expanding the liquid phase region. These are all desirable for enhanced oil recovery.

Figure 1. The impact of CO₂ concentration on the volatile oil phase envelope

Rich Gas: The compositions of the rich gas and the non-hydrocarbons used to generate Figures 4, 5 and 6 are shown in Table 2. Figures 4, 5 and 6 present the impact of N₂, CO₂ and H₂S on the phase behavior of the rich gas, respectively. As shown in Figure 4, N₂ raises the cricondenbar of the rich gas. This quantitative behavior agrees well with the qualitative one shown in Figure 4.9 c. Nitrogen raises the cricondenbar, shifts the critical point to the left and decreases miscibility; therefore, it is best used for pressure maintenance. Miscibility can be attained only at very high pressures. Note for the case of 60 mole % in Figure 3, the bubble point curve and the critical point look abnormal which indicates that the equation of state and/or the binary interaction parameters used are incapable of handling high concentrations of N₂

Figure 2. The impact of H₂S concentration on the volatile oil phase envelope

Figure 3. The impact of acid gas (equal mole H₂S and CO₂) concentration on the volatile oil phase envelope.

 Figure 5 presents the impact of CO₂ concentration on the rich gas phase envelope. Like the case of the volatile oil,  CO₂ lowers the cricondenbar,  shifts the cricondentherm to the right but shifts the critical point to the left.

Figure 6 presents the impact of H₂S concentration on the rich gas phase envelope. Both the critical and cricondentherm points shift to the right as H₂S increases but the cricondenbar does not lower as it did for CO₂.

Black Oil: Figures 7 and 8 present the impact of CO₂ and H₂S on the phase behavior of black oil. The compositions of the black oil and the acid gas used to generate these two figures are shown in Table 3.

As shown in Figure 7, contrary to the case of the volatile oil, the cricondenbar raises as the CO₂ content increases but both the critical and cricondentherm points shift to the left. Compared to Figure 1 for the volatile oil, the impact of CO₂ on the black oil phase envelope is much less.

            Table 1. Composition of the volatile oil used to generate Figures 1, 2, and 3.

* Acid Gas = H₂S, CO₂, or equal molar mixture of H₂S, CO₂.

The impact of H₂S on this black oil is similar to its impact on the volatile oil (Figure 2). As shown in Figure 8, H₂S lowers the cricondenbar of this black oil. The critical point shifts considerably to the left. The cricondentherm point also shifts to the left as the concentration of H₂S increases. The net effect is enhancing miscibility, shrinkage of the two-phase region and expanding the liquid phase region. The impact of H₂S on the black oil is less compared to the volatile oil shown in Figure 2.

Figure 4. The impact of N₂ concentration on the rich gas phase envelope

Figure 5. The impact of CO₂ concentration on the rich gas phase envelope

Figure 6. The impact of H₂S concentration on the rich gas phase envelope

            Table 2. Composition of the rich gas used to generate Figure 4, 5, and 6.

* Non-Hydrocarbons = N₂, H₂S, or CO₂,.

Figure 7. The impact of CO₂ concentration on the black oil phase envelope

Figure 8. The impact of H₂S concentration on the black oil phase envelope

             Table 3. Composition of the black oil used to generate Figures 7 and 8.

^* For properties (average normal boiling point, molecular weight and relative density of single carbon number (SCN), see Table 3.3 page 64 of reference [1].

Conclusions:

The analysis of Figures 1 through 8 indicates that the impact of non-hydrocarbons on any reservoir fluids depends on the type/nature and composition of the reservoir fluid. The type of non-hydrocarbon as well as its concentration also plays an important role. The injection of acid gases into a reservoir fluid changes the phase behavior and the thermodynamic properties of the reservoir fluids. Even though not discussed in this TOTM, CO₂ injection for the purpose of enhanced oil recovery may cause asphaltene deposition and blockage in the reservoir formation and the surface facilities. Depending on compositions, pressures and temperatures, much more complex phase behavior is possible. Multiple liquid phases (in addition to aqueous phase) and/or solids may be present.

It is important to use the right tools and an accurate equation of state within simulation software to generate the correct phase envelope. It is recommended to check the accuracy of the thermodynamic models against field/experimental data before generating any phase envelope. The equation of state should be tuned to match the laboratory measured vapor-liquid-equilibria data for a sample of the reservoir fluid before undertaking any practical study/decision. The results shown in this TOTM are specific to the cases studied and have not been validated with actual data. These results should be used only as a guideline.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), P81 (CO₂ Surface Facilities), and PF4 (Oil Production and Processing Facilities) courses.

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. For more information about services offered by JMCC, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Reference:

1. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
2. Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., Vol. 15, p. 59, 1976.
3. ProMax 3.2, Bryan Research and Engineering, Inc., Bryan, Texas, 2011.

While dry ice has many good features and applications, its formation can plug up equipment and cause severe operational problems in gas processing plants. Therefore, accurate predictions of conditions for dry ice formation are required. In order to prevent dry ice formation, a good knowledge and understanding of phase behavior of systems containing carbon dioxide are essential in cryogenic gas processing as in turboexpander plants for deep natural gas liquid (NGL) recovery. Thermodynamic modeling based on the equality of chemical potentials for each component in all phases and application of an equation of state with tuned parameters is normally used for accurate prediction of dry ice formation conditions.

In this tip of the month (TOTM), we will study the phase behavior of gas mixtures containing carbon dioxide. A description of phase behavior at different conditions of pressure and temperature is presented.

The Peng-Robinson (PR) [5] equation of state (EOS) option of ProMax [6] was used to perform all of the calculations in this study. In dealing with dry ice, reference [7] discusses the importance of using the right tools in process simulation software. The same reference also demonstrates the accuracy of ProMax against experimental data, including GPA RR 10 experimental data [8], for prediction of dry ice formation at different conditions.

Case Studies:

The composition of the two mixtures containing CO₂ considered in this study is shown in Table 1. Figure 1 also presents a simplified process flow diagram that was used to study dry ice formation in this study.  The feed gas (stream 1) enters Sep-100 from which the vapor stream (stream 2) is cooled in HEX-100. The stream leaving this cooler is passed through Sep-101 for separation of gas and liquid.

Figure 2 presents a complete phase envelope for mixture A (see Table 1) in which the state of each region has been identified.

The feed gas (stream 1) enters Sep-100 at -96˚F and 300 psia (-71.1˚F and 2069 kPa) which is point “A” on Figure 2. At this condition, it is all vapor and all of the feed leaves the separator as vapor. In the HEX-100, the vapor stream (stream 2) is cooled at constant pressure to -160˚F (-106.7˚C), which is represented by point “E” (stream 4). The horizontal dotted straight line identifies the cooling path. During the cooling process when point “B”, the dew point, on Figure 2 is reached, the first drop of liquid is formed. Between points “B and C”, mixture of liquid + vapor coexist at equilibrium. At point C, the incipient point of dry ice, solid phase will also form. Between points “C and D”, three phases of solid + liquid + vapor will coexist at equilibrium. Further cooling to point “E” results in a mixture of solid + liquid at equilibrium. Finally, the stream leaving this cooler is passed through Sep-101 for separation of any gas from and liquid.

Table 1. The composition of the two mixture studies

Figure 1. A simplified process diagram for the case study

 If mixture A enters the cooler at a pressure less than 167 psia (1152 kPa) and cools down, it will form dry ice without forming any liquid. As an example, let’s  assume the mixture is at     -100˚F and 100 psia (-73˚C and 690 kPa), point “x” on Figure 2. If this gas is cooled at constant pressure of 100 psia (690 kPa), it forms dry ice at a temperature of about -133˚F (-92˚C). Further cooling below about -137˚F (-94˚C) will form solid + liquid + vapor at equilibrium. Finally, cooling below -200 ˚F (-129˚F) results in a mixture of solid + liquid in equilibrium.

Figure 2. Complete phase envelope for mixture A.

At a pressure of 300 psia (2069 kPa), starting at -90°F (-68°C) (Point “A”), the fluid is 100% vapor.  Cooling at constant pressure results in liquid formation when the temperature reaches about -113°F (-81°C) at Point “B”.  Further cooling results in dry ice formation at Point “C” and the temperature is approximately -119°F (-84°).  The last vapor bubble would disappear at Point “D” (about -156°F, -104°C).  Below this point, the fluid exists as dry ice and liquid.

For the cooling process described above for a constant pressure of 300 psia,  the cooling temperature and vapor fraction of mixture as a function of heat removed from the process fluid (mixture A) in HEX-100 are shown in Figures 3A (Field Units) and 3B (SI Units).

Figure 3A. Temperature and vapor fraction of mixture A as it passes through HEX-100 (Field Units).

Figure 3B. Temperature and vapor fraction of mixture A as it passes through HEX-100 (SI Units).

Each mixture has a unique phase envelope and dry ice formation curve. As the mixture composition changes, the shape of the phase envelope and the dry ice curve will change. Similarly, a complete phase envelope for mixture B with the cooling path is shown in Figures 4, 5A, and 5B.

Figure 4. Complete phase envelope for mixture B.

Conclusions:

In cryogenic processes such as turboexpander plants for deep NGL recovery, accurate prediction of dry ice formation conditions is important. A good knowledge of phase behavior and thorough understanding of dry ice formation can prevent severe operational problems. On the phase envelope, any operating condition that lies on, to the left or below the dry ice curve (the dotted black curves on Figures 2 and 4) will form a solid phase and may cause severe operational problems, damage the equipment and lead to human casualty.

It is important to use the right tools and an accurate equation of state within simulation software to generate the correct phase envelope and dry ice curve. It is recommended to check the accuracy of the thermodynamic models against experimental data before generating any phase envelope or performing process simulation.

Figure 5A. Temperature and vapor fraction of mixture B as it passes through HEX-100 (Field Units).

To learn more about similar cases and how to minimize operational problems, we suggest attending our G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), PF81 (CO₂ Surface Facilities), and PF4 (Oil Production and Processing Facilities) courses.

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. For more information about services offered by JMCC, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Figure 5B. Temperature and vapor fraction of mixture B as it passes through HEX-100 (SI Units).

Reference:

1. http://en.wikipedia.org/wiki/Dry_ice
2. Yaws, C. Matheson gas data book (7th ed.). McGraw-Hill Professional. p. 982, 2001
3. Häring, H-W. Industrial Gases Processing. Christine Ahner. Wiley-VCH, 2008
4. Treloar, R., Plumbing Encyclopedia (3rd ed.). Wiley-Blackwell, 2003.
5. Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., Vol. 15, p. 59, 1976.
6. ProMax 3.2, Bryan Research and Engineering, Inc, Bryan, Texas, 2011.
7. Hlavinka, M. W., Hernandez, V. N., and McCartney, D., “Proper Interpretation of  Freezing and  Hydrate  Prediction Results From Process Simulation,” Proceedings of the Eighty-Fifth GPA Annual Convention. Grapevine, TX: Gas  Processors Association, 1999:121-127 GPA 2006.
8. Kurata, F., “Solubility of Solid Carbon Dioxide in Pure Light Hydrocarbons and Mixtures of Light Hydrocarbons,” GPA Research Report RR-10, Gas Processors Association, 1974

For a pure compound above critical pressure and critical temperature, the system is often referred to as a “dense fluid” or “super critical fluid” to distinguish it from normal vapor and liquid (see Figure 1 for carbon dioxide in December 2009 TOTM [1]).

Calculation Procedure:

The same step-by-step calculation procedure described in the February 2012 TOTM [2] was used to determine the pressure and temperature profiles in a pipeline considering the Joule-Thompson expansion effect and heat transfer between the pipeline and surroundings.

In the following section we will illustrate the pressure drop calculations for transporting CO₂ in dense phase using the gas phase pressure drop equations. For details of pressure drop equations in the gas and liquid phases refer to the January 2012 TOTM [3].

Case Study:

For the purpose of illustration, we considered a case study [also described in reference 2] for transporting 160 MMSCFD (4.519×10⁶ Sm³/d) CO₂ using a 100 miles (160.9 km) long pipeline with an inside diameter of 15.551 in (395 mm). The inlet conditions were 2030 psia (14 MPa) and 104˚F (40˚C). The following assumptions were made:

1. CO₂, with nitrogen impurities of 0, 1, 5, 10, and 15 mole %.
2. Horizontal pipeline, no elevation change.
3. Inside surface relative roughness’s (roughness factor), ε/D, of 0.00013.
4. The ambient/surrounding temperature,Ts, is 55 ˚F and (12.8 ˚C)
5. Overall heat transfer coefficients of 0.5 Btu/hr-ft²-˚F (2839 W/m²-˚C).

Properties: The dense phase behavior and properties were calculated using the Peng-Robinson equation of state (PR EOS) [4] in ProMax [5] software. ProMax was also used to determine pressure and temperature profiles along the pipeline.

Results and Discussions:

Figures 1 through 4 present the phase envelope, dry ice (CO₂ freeze out) curve, and pipeline pressure and temperature profile for 1, 5, 10, and 15 mole % N₂ impurities, respectively, the relative roughness (ε/D) of 0.00013, and the overall heat transfer coefficient (U) of 0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C).

Figure 1. Phase envelop and dense phase pipeline pressure-temperature profile for 99 mole % CO₂ + 1 mole % N₂, ε/D=0.00013, and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C).

Figure 2. Phase envelop and dense phase pipeline pressure-temperature profile for 95 mole % CO₂ + 5 mole % N₂, ε/D=0.00013, and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C).

Figure 3. Phase envelop and dense phase pipeline pressure-temperature profile for 90 mole % CO₂ + 10 mole % N₂, ε/D=0.00013, and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C).

Figure 4. Phase envelop and dense phase pipeline pressure-temperature profile for 85 mole % CO₂ + 15 mole % N₂, ε/D=0.00013, and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C).

The effect of N₂ impurities on the line temperature profile is shown in Figure 5. This figure indicates that N₂ impurities have negligible effect on the pipeline temperature profile.

Figure 6 presents the effect of N₂ impurities on the pipeline pressure profile. This figure indicates that as the N₂ impurities increases the pressure drop increases. This can be explained by the fact as the N₂ impurities increase, the mixture density decreases, consequently the velocity increases. Note the pressure drop is proportional to square of velocity and inverse of density. While viscosity decreases with increase in N₂ impurities, its effect is not as large as the density effect. Table 1 presents variation of the mixture density and viscosity as a function of N₂ mole %.

Table 1. Effect of N₂ impurities on density (ρ) and viscosity (µ) of mixture at the inlet condition of 2030 psia (14 MPa) and 104˚F (40˚C)

Conclusions: 

Analyzing Table 1 and Figures 1 through 6, the following conclusions can be made:

1. For the range 0 to 15 mole % N₂, the effect of the N₂ impurities on the pipeline temperature profile is negligible.
2. As the N₂ impurities increase, the pipeline pressure drop increases due to the change in thermophysical properties of mixture.
3. Care should be taken to use accurate thermophysical properties and the phase envelope should be plotted to avoid any operating problem.

Figure 5. Variation of the pipeline temperature profile with the N₂ impurities and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C)

Figure 6. Variation of the pipeline pressure profile with the N₂ impurities and U=0.5 Btu/hr-˚F-ft² (2.839 W/m²-˚C)

To learn more about similar cases and how to minimize operational problems, we suggest attending our G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), P81 (CO₂ Surface Facilities), and PF4 (Oil Production and Processing Facilities) courses.

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. For more information about services offered by JMCC, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Reference:

1. Bothamley, M.E. and Moshfeghian, M., “Variation of properties in the dese phase region; Part 1 – Pure compounds,” TOTM, http://www.jmcampbell.com/tip-of-the-month/2009/12/variation-of-properties-in-the-dense-phase-region-part-1-pure-compounds/, Dec 2009.
2. Moshfeghian, M., ”Transportation of CO₂ in the Dense Phase,” TOTM, http://www.jmcampbell.com/tip-of-the-month/2012/02/ , Feb 2012
3. Moshfeghian, M., ”Transportation of CO₂ in the Dense Phase,” TOTM, http://www.jmcampbell.com/tip-of-the-month/2012/01/, Jan 2012
4. Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., Vol. 15, p. 59, 1976.

ProMax 3.2, Bryan Research and Engineering

For a pure compound, above critical pressure and critical temperature, the system is oftentimes referred to as a “dense fluid” or “super critical fluid” to distinguish it from normal vapor and liquid (see Figure 1 for carbon dioxide in December 2009 TOTM [1]).

Calculation Procedure:

The following step-by-step calculation procedure may be used to determine the pressure and temperature profiles in a pipeline considering the Joule-Thompson expansion effect and heat transfer between the pipeline and surroundings.

1. Divide the pipeline into n segments. The segments may be different lengths, but should be carefully chosen to provide the information sought through the calculations to be made. The more segments, the longer the calculation time. Time, however, is a relatively small investment compared to the importance of adequate representation of the line profile.
2. Assume an outlet pressure for each segment by use of a linear interpolation along the length of the line. Note that the outlet pressure of the first segment automatically becomes the inlet pressure to the second segment.
3. For the first iteration calculation, assume the flow in the segment is isothermal.
4. Calculate the average temperature, T_avg= (T_out + T_in)/2, and pressure, P_avg= (P_out + P_in)/2, for the first segment in the line. For the first iteration the inlet and outlet temperatures for the segment will be the same since isothermal flow is assumed.
5. Using the EOS, determine the state of the flow at T_avg and P_avg to establish whether or not the flow is in the dense phase.
6. Using the gas phase or liquid phase equations, calculate the segment pressure drop.
7. Compare the calculated pressure at the end of a segment with the pressure that was assumed in step 2. If the difference between these pressures is sufficiently small, proceed to step 8. If the difference between the assumed and calculated pressure at the end of segment is too large (1 psi or 6.9 kPa), replace the assumed outlet pressure with the calculated value of the outlet pressure and repeat steps 4 through 7 as many times as necessary to calculate s suitable segment outlet pressure.
8. Calculate the enthalpy at the end of the segment by writing an energy balance around the segment using the following procedure:
   H_out = H_in+ Q                        (1)
   Where:
   Q = UA (T_avg-T_s)                     (2)
   H_out= Enthalpy of the fluid at the outlet of the segment
   H_in= Enthalpy of the fluid at the inlet of the segmentQ = The overall heat transfer to or from the segment
   U = The overall heat transfer coefficient between the external surface of the pipe and its surroundings
   A = The external surface area of the segment of pipe
   T_avg = The average temperature of the segment
   T_s = The temperature of material surrounding the pipe
9. Using the EOS, determine the segment outlet temperature based on the calculated H_out and P_out.
10. If the temperature calculated in step 9 is the same as the assumed value in step 3, the calculations proceed to the next segment of the line. If the temperature is different from that assumed in step 3, calculations revert to step 4 using the newly calculated value for segment outlet temperature.

When conditions at the outlet end of the last segment of the line have been calculated to a satisfactory small difference (less than 1 psi or 6.9 kPa for pressure and less than 0.1 ˚F or 0.05 ˚C for temperature), calculations for flow conditions in the pipeline are complete.

In the following section we will illustrate the pressure drop calculations for transporting CO₂ in dense phase using the gas phase pressure drop equations. For details of pressure drop equations in the gas and liquid phases refer to the January 2012 TOTM [2].

Case Study:

For the purpose of illustration, we considered a case study [also described in reference 2] for transporting 160 MMSCFD (4.519×10⁶ Sm³/d) CO₂ using a 100 miles (160.9 km) long pipeline with an inside diameter of 15.551 in (395 mm). The corresponding mass flow rate is 214.7 lb_m/sec (97.39 kg/s). The inlet conditions were 2030 psia (14 MPa) and 104˚F (40˚C). The following assumptions were made:

1. Pure CO₂, ignored any impurities such as N₂.
2. Horizontal pipeline, no elevation change.
3. Five different inside surface relative roughness’s (roughness factor), ε/D, were studied (0.00004, 0.00013, 0.0002, 0.0004, and 0.001).
4. The ambient/surrounding temperature,Ts, is 55 ˚F and (12.8 ˚C)
5. Six different overall heat transfer coefficients ranging from 0 to 1 Btu/hr-ft²-˚F (0 to 5.678 W/m²-˚C) were studied.

Properties: The dense phase behavior and properties were calculated using the Span and Wagner CO₂  EOS [3] in ProMax [4] software. ProMax was also used to determine pressure and temperature profiles along the pipeline.

Results and Discussions:

Figure 1 presents the pressure drop per unit length as a function of relative roughness (ε/D) and the overall heat transfer coefficient (U). In this figure, the values of U₁ through U₆ are 0, 0.125, 0.25, 0.5, 0.75, and 1.0 Btu/hr-˚F-ft² (0, 0.71, 1.42, 2.839, 4.259, and 5.678 W/m²-˚C), respectively.

Figure 1. Variation of pressure drop with the relative roughness and the overall heat transfer coefficient.

            Figure 1 indicates that as the overall heat transfer coefficient increases, pressure drop decreases. This is because the line temperature drops more quickly at higher overall heat transfer coefficients. Note that as the U approaches 1.0 Btu/hr-˚F-ft² (5.678 W/m²-˚C) its effect vanishes.

As an example, Tables 1 and 2 present the impact of relative roughness on the pressure drop for an overall heat transfer coefficient of 0 and 0.50 Btu/hr-˚F-ft² (0 and 2.839 W/m²-˚C), respectively. These tables also present the line outlet temperatures.

Table 1. Impact of relative roughness on pressure drop (Number of segments=10).

Table 2. Impact of relative roughness on pressure drop (Number of segments=10).

These two tables and Figure 2 indicate that while the relative roughness has great impact on the pressure drop, its effect on temperature is small. On the other hand, the effect of overall heat transfer coefficient on the outlet temperature is more significant. The impact of U on the line temperature profile is shown in Figure 3. This figure also indicates that U has great impact on the line temperature profile. Figure 4 also indicates that the effect of relative roughness on the line temperature is negligible. Figure 5 presents the effect of the overall heat transfer confident on the line pressure profile. As can be seen in this figure, the increase in the overall heat transfer coefficient results in lower pressure drop. This is because the line temperature drops more quickly at the higher values of overall heat transfer coefficients.

Figure 2. Variation of the outlet temperature with the relative roughness and the overall heat transfer coefficient.

Figure 3. Variation of temperature profile with the overall heat transfer coefficient

Figure 4. Variation of the temperature profile with the pipe relative roughness

Figure 5. Variation of the line pressure profile with the overall heat transfer coefficient

Conclusions:

Analyzing Tables 1 and 2 and Figures 1 through 5, the following conclusions can be made:

1. The effect of the overall heat transfer coefficient on the pipeline temperature is significant.
2. As the overall heat transfer coefficient increases, the outlet temperature decreases.
3. As the overall heat transfer coefficient increases, the outlet pressure increase (line pressure drop decreases).
4. As the value of the heat transfer coefficient approaches 1.0 Btu/hr-˚F-ft² (5.678 W/m²-˚C) its effect on the pipeline pressure drop vanishes.
5. While pipeline roughness factor has great impact on the pressure drop, it has little effect on the pipeline temperature profile.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), P81 (CO₂ Surface Facilities), and PF4 (Oil Production and Processing Facilities) courses.

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. For more information about services offered by JMCC, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Reference:

1. Bothamley, M.E. and Moshfeghian, M., “Variation of properties in the dese phase region; Part 1 – Pure compounds,” http://www.jmcampbell.com/tip-of-the-month/2009/12/variation-of-properties-in-the-dense-phase-region-part-1-pure-compounds/, December 2009.
2. Moshfeghian, M., ”Transportation of CO₂ in the Dense Phase,” http://www.jmcampbell.com/tip-of-the-month/
3. Span, R.; Wagner, W. – Equations of State for Technical Applications. I. Simultaneously Optimized Functional Forms for Nonpolar and Polar Fluids. Int. J. Thermophys. 2003,24(1), 1-39
4. ProMax 3.2, Bryan Research and Engineering, Inc, Bryan, Texas, 2011.

When a pure compound, in gaseous or liquid state, is heated and compressed above the critical temperature and pressure, it becomes a dense, highly compressible fluid that demonstrates properties of both liquid and gas. For a pure compound, above critical pressure and critical temperature, the system is oftentimes referred to as a “dense fluid” or “super critical fluid” to distinguish it from normal vapor and liquid (see Figure 1 for carbon dioxide in December 2009 TOTM [1]). Dense phase is a fourth (Solid, Liquid, Gas, Dense) phase that cannot be described by the senses. The word “fluid” refers to anything that will flow and applies equally well to gas and liquid. Pure compounds in the dense phase or supercritical fluid state normally have better dissolving ability than do the same substances in the liquid state. The dense phase has a viscosity similar to that of a gas, but a density closer to that of a liquid. Because of its unique properties, dense phase has become attractive for transportation of CO₂ and natural gas, enhanced oil recovery, food processing and pharmaceutical processing products.

The low viscosity of dense phase, super critical carbon dioxide (compared with familiar liquid solvents), makes it attractive for enhanced oil recovery (EOR) since it can penetrate through porous media (reservoir formation). As carbon dioxide dissolves in oil, it reduces viscosity and oil-water interfacial tension, swells the oil and can provide highly efficient displacement if miscibility is achieved. Additionally, substances disperse throughout the dense phase rapidly, due to high diffusion coefficients. Carbon dioxide is of particular interest in dense-fluid technology because it is inexpensive, non-flammable, non-toxic, and odorless. Pipelines have been built to transport CO₂ and natural gas in the dense phase region due to its higher density, and this also provides the added benefit of no liquids formation in the pipeline.

In the following section we will illustrate the pressure drop calculations for transporting CO₂ in dense phase using liquid phase and vapor phase pressure drop equations.

Case Study:

For the purpose of illustration, we considered a case study for transporting 160 MMSCFD (4.519×10⁶ Sm³/d) CO₂ using a 100 miles (160.9 km) long pipeline with an inside diameter of 15.551 in (395 mm). The corresponding mass flow rate is 214.7 lb_m/sec (97.39 kg/s). The inlet conditions were 2030 psia (14 MPa) and 104˚F (40˚C). The following assumptions were made:

1. Pure CO₂, ignored any impurities such as N₂.
2. Horizontal pipeline, no elevation change.
3. Inside surface relative roughness (roughness factor), ε/D, is 0.00004.
4. Isothermal transportation of CO₂.

Properties: Dense phase behavior is unique and has special features. The thermophysical properties in this phase may vary abnormally. Care should be taken when equations of state are used to predict thermophysical properties in dense phase. Evaluation of equations of state should be performed in advance to assure their accuracy in this region. Many simulators offer the option to use liquid-based algorithms (e.g. COSTALD [2]) for this region. Dense phase is a highly compressible fluid that demonstrates properties of both liquid and gas. The dense phase has a viscosity similar to that of a gas, but a density closer to that of a liquid. This is a favorable condition for transporting CO₂ and natural gas in dense phase as well as carbon dioxide injection into crude oil reservoir for enhanced oil recovery.

Figures 1 and 2 present variation of density and viscosity of CO₂ with pressure at constant temperature of 104 ˚F (40 ˚C) calculated by the SRK EOS and COSTALD liquid density option in ProMax [3] and the Span and Wagner CO₂  EOS in REFPROP [4] software. Note, ProMax also has the Span and Wagner CO₂  EOS option which produced practically the same results as the REFPPROP.

Figure 1. Density-Pressure diagram for CO₂ at 104˚F (40˚C) by the SRK EOS and COSTALD liquid in ProMax and Span and Wagner CO₂  EOS in REFPROP

Figure 2. Viscosity-Pressure diagram for CO₂ at 104˚F (40˚C) by the SRK EOS and COSTALD liquid in ProMax and Span and Wagner CO₂  EOS in REFPROP

For the sake of easier calculation steps, these diagrams were fitted to the following 3^rd degree polynomials for density and viscosity, respectively:

In these equations, ρ is density (kg/m³), µ is viscosity (cP) and P_avg is the average pipeline segment pressure calculated by:

The fitted coefficients for equations 1 and 2 are presented in Table 1.

Table 1. The fitted coefficients for CO₂ density and viscosity (Equations 1 & 2) at 104˚F (40˚C)

Figures 1 and 2 clearly indicate that there are large differences between predicted properties using two different sources. In the following section, we will illustrate the impact of these differences on pressure drop calculations.

Liquid Phase Pressure Drop Equations: The pressure drop for a liquid phase is calculated as follows.

Where:

Vapor Phase Pressure Drop Equations: In addition to Equations 5 through 8, which are also valid and used for the gas pipeline, the following equations are also used.

Where:

Results and Discussions:

The pressure drop calculations were performed using the liquid phase and vapor phase equations. First, the pipeline cross sectional area was calculated with Equation 8 and the gas density at the standard condition was calculated with equation 10.  In each case the calculation was trial and error and the following step-by-step procedure was followed:

1. The line was divided into n segments (e.g. n = 1, 10, 20, or 100).
2. For segment 1, an outlet pressure was guessed.
3. Segment average pressure was calculated with Equation 3.
4. CO₂ density and viscosity were calculated using Equations 1 and 2, respectively.
5. CO₂ velocity was calculated with Equation 7.
6. Reynolds number was calculated with Equation 6.
7. Friction factor was calculated with Equation 5 (this is also trial and error).
8. Liquid phase pressure drop was calculated with equation 4.
9. Calculate average gas compressibility factor with equation 11.
10. Calculate segment gas outlet pressure by Equation 9 and segment pressure drop with Equation 12.
11. If the calculated outlet pressure is not the same as the guessed outlet pressure in step 2, replace the guessed outlet pressure with the calculated outlet pressure and repeat steps 3 through 10 until the calculated outlet pressure becomes equal to the guessed value.
12. Use the calculated outlet pressure of segment “1” for the inlet of segment “2” and repeat the above steps for each segment till the end of line is reached.

Table 2 summarizes the pressure drop calculation results for four cases in which the pipeline was divided into 1, 10, 20, and 100 segments. Table 2 indicates that for the cases of 10 segments and higher no change in pressure drop is observed.

Table 2. Summary of pressure drop calculation results for different number of segments and different sources of properties.

For all cases tested, both the liquid phase and the vapor phase pressure drop equations gave exactly the same pressure drop. Note that there is at least 100 psi (690 kPa) difference in pressure drops calculation using REFPROP (Span and Wagner CO₂ EOS) or ProMax (SRK EOS and COSTALD liquid density) because the EOS options were different. However, the Span and Wagner CO₂ EOS in both software would result in the same pressure drop. A sample calculation in MathCad format is attached: Dense Phase CO2 Pipeline 1 Segment ProMax.

Table 3 presents the impact of relative roughness on pressure drop. Typical / generally accepted numbers for relative roughness are (and these are regarded as conservative) for steel pipes are:  new or clean service  =  0.00004, mildly corroded  =   0.0002, corroded / dirty service =  0.0004.

Table 3. Impact of relative roughness on pressure drop (Number of segments=10).

Conclusions:

As discussed in December 2009, dense phase behavior is unique and has special features. The thermophysical properties in this phase may vary abnormally. Care should be taken when equations of state are used to predict thermophysical properties in dense phase. Evaluation of equations of state should be performed in advance to assure their accuracy in this region. Many simulators offer the option to use liquid-based algorithms (e.g. COSTALD) for this region. It is very important to use the most appropriate option.

Dense phase is a highly compressible fluid that demonstrates properties of both liquid and gas. The dense phase has a viscosity similar to that of a gas, but a density closer to that of a liquid. This is a favorable condition for transporting CO₂ and natural gas in dense phase. It was also found that either the liquid phase or vapor phase pressure drop equations can be used to calculate CO₂ pressure drop in the dense phase. Both set of equations gave exactly the same pressure drop. Due to high density of CO₂ in the dense phase, pressure drop due to elevation change should not be ignored.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), P81 (CO₂ Surface Facilities), and PF4 (Oil Production and Processing Facilities) courses.

By: Dr. Mahmood Moshfeghian

Reference:

1. Bothamley, M.E. and Moshfeghian, M., “Variation of properties in the dese phase region; Part 1 – Pure compounds,” http://www.jmcampbell.com/tip-of-the-month/2009/12/variation-of-properties-in-the-dense-phase-region-part-1-pure-compounds/, December 2009.
2. Hankinson, R. W., Thomson, G. H., AIChE J., Vol. 25, no. 4, pp. 653-663, 1979.
3. ProMax 3.2, Bryan Research and Engineering, Inc, Bryan, Texas, 2011.
4. NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP): Version 9.0, 2011.