During the life cycle of a crude oil pipeline the properties of transported oil change, because in gathering systems the produced oils come from different wells. New wells may be added or some wells may go out of production for maintenance and repair. Production rates during the life of wells vary, too. In addition the properties of crude oil change during production. Due to seasonal variation, the average line temperature may also change. As it is shown in the proceeding sections, viscosity of crude oil is a strong function of API gravity and temperature.
In the March 2009 tip of the month (TOTM), procedures for calculation of friction losses in oil and gas pipelines were presented. The sensitivity of friction pressure drop with the wall roughness factor was also demonstrated.
In this TOTM, we will study crude oil °API and the pipeline average temperature and how they effect the pumping requirement. For a case study, we will consider a 160.9 km (100 miles) pipeline with an outside diameter of 406.4 mm (16 in) carrying crude oil with a flow rate of 0.313 m3/s (170,000 bbl/day). The pipeline design pressure is 8.963 MPa (1300 psia) with a maximum operating pressure of 8.067 MPa (1170 psia). The wall thickness was estimated to be 6.12 mm (0.24 in). The wall roughness is 51 microns (0.002 in) or a relative roughness (e/D) of 0.00013. The procedures outlined in the March 2009 TOTM were used to calculate the line pressure drop due to friction. Then assuming 75 % pumping efficiency, the required pumping power was calculated. Since the objective was to study the effect °API and the line average temperature have on the pumping power requirement, we will ignore elevation change. The change in pumping power requirements due to changes in crude oil °API and line average temperature for this case study will be demonstrated.
Case Study 1: Effect of Line Average Temperature (Seasonal Variation)
To study the effect of the line average temperature on the pumping power requirement, an in house computer program called OP&P (Oil Production and Processing) was used to perform the calculations as outlined in the March 2009 TOTM. For a 35 °API crude oil in the pipeline described in the preceding section, the required pumping power was calculated for the line average temperature ranging from 21.1 to 37.8 °C (70 to 100 °F). For each case, the required pumping power was compared with an arbitrary base case (85 °F or 29.4 °C) and the percentage change in the pumping power requirement was calculated, accordingly. Figure 1 presents the percent change in power requirement as a function of line average temperature. There is about 5% change in the pumping power requirement for the temperature range considered.
Note as the line average temperature increases, the power requirement decreases. This can be explained by referring to Figure 2 in which the oil viscosity decreases as the temperature increases. Lower viscosity results in higher Reynolds (i.e. Reynolds number is the ratio of inertia force to viscous force); therefore, the friction factor decreases (refer to the Moody friction factor diagram in the March 2009 TOTM).
Case Study 2: Effect of Variation of Crude Oil API
In this case, the effect of crude oil °API on the total pump power requirement for three different line average temperatures was studied. For each line average temperature, the crude oil °API was varied from 30 to 40 and the total pumping power requirement was calculated and compared to the base case (35 °API and average line temperature of 29.4°C=85°F).
For each case the percent change in total power requirement was calculated and is presented in Figure 3. As shown in this figure, when °API increases the total power requirement decreases. This also can be explained by referring to Figure 2 in which the crude oil viscosity decreases as ° API increases. The effect of viscosity is more pronounced at lower line average temperature (i.e. 21.1 °C or 70°F). Figure 3 also indicates that there is about 25 % change in total power requirement as °API varies from 30 to 40 °API. This is a big change and should be considered during design of crude oil pipelines.
Discussion and Conclusions
The analysis of Figure1-3 indicates that for the oil pipeline, the pumping power requirement varies as the crude oil °API changes. Increasing °API or line average temperature reduces the crude oil viscosity (see Figure 2). The reduction of viscosity results in higher Reynolds number, lower friction factor and in effect lower pumping power requirements.
In practical situations, an originating station takes crude out of storage and the midline stations taking suction from the upstream section of pipeline. In some parts of the world, the suction temperature to the originating pumps is +38 °C (+100 °F) but the temperature to the midline station is ground temperature (this assumes a buried line below the frost line) approximately 18 °C (65 °F). The originating station will always be more affected by temperature because storage will follow ambient – whereas the midline station will operate at notionally constant temperature +/- 5.5 °C (+/- 10 °F) in the lower 9 °C (48 °F). For the case studied in this TOTM, the number of pumping stations varied from 2.5 to 3.2.
In light of the above discussion, a sound pipeline design should consider expected variation in crude oil °API and the line average temperature.
The change in enthalpy for a fluid where no phase change occurs between Points (1) and (2) can be expressed as:
(1)
The second term on the right hand side of this equation is generally not convenient to solve manually. However, it is trivial or zero for the following cases: (1) ideal gases, (2) constant pressure, dP = 0, and (3) for a liquid considered incompressible. For all three cases enthalpy is a mathematical function only of temperature. Cp is commonly expressed by equations of the form:
(2)
Where A, B, and C are constants that depend on system composition and T is the absolute temperature. In most instances it is sufficiently accurate to find a Cp at the average temperature TAvg, where:
(3)
CPAvg is then found at this average temperature and
(4)
This approximate solution to the first integral, although not exact, is satisfactory for most applications. Heat capacity values for pure substances are readily available from many handbooks and similar reference material. As noted in Chapter 7 of Volume 1, Gas Conditioning and Processing [1], values of heat capacity can be found from the slope of hvs. T plots at a given pressure. The CP for hydrocarbon liquid mixtures may be estimated from the equations presented in Volume 1 [1].
For a non-ideal, compressible fluid like natural gas, the second term on the right hand side of Eq.(1) can’t be ignored. Therefore, in process simulation software, an equation of state like Soave-Redlich-Kwong (SRK) [2] or Peng-Robinson (PR) [3] is used to calculate h. For many calculations involving the heat capacity of natural gas, Figure 8.3 in Volume 1 is appropriate. Heat capacity at system pressure and average temperature is read off the graph and multiplied by gas mass flow rate and T to obtain the heat load, .
(5)
In this Tip of The Month (TOTM), the variation of heat capacity of natural gases with temperature, pressure, and relative density (composition) will be demonstrated. Then an empirical correlation will be presented to account for these variations. This correlation will be used to estimate natural gas heat capacity for wide ranges of pressure, temperature, and relative density. Finally, the accuracy of the proposed correlation will be discussed.
Development of a Generalized CP Correlation:
As mentioned earlier, CP can be defined from the slope of h vs. T plots at constant pressure. Mathematically, this is expressed by:
(6)
The derivative on the right hand side of Eq (6) may be obtained from an equation of state (EOS) but it is too tedious for hand calculations. Therefore, the PR EOS option in ProMax [4] was used to generate CP values for various values of pressure, temperature, and relative density. The total number of CP values calculated was 715. Table 1 presents the composition of five different natural gas mixtures used in this study.
Table 1. Gas compositions used for generating CP values
Figures 1 through 5 present variations of CP with pressure, temperature and gas relative density. The red highlighted regions in Figures 3, 4, and 5 identify the two phase region of gas and liquid where the CP concept is not valid. It should be noted that the isobar of 20 MPa represents a single phase even at low temperatures. However, at low temperature, the fluid is dense phase.
In order to correlate all the curves shown in Figures 1-5 by a single equation, the following expression is proposed.
(7)
Where T is temperature, P is pressure and CP is heat capacity. A non-linear regression algorithm was used to determine the optimum values of parameters “a” through “f”. First, CP values of each gas in Table 1 were used to determine “a” through “f”. Then all of the generated CP values were used to determine a set of generalized parameters. These parameters were tuned and rounded to best represent all five gases covering a wide range of relative density from 0.60 to 0.80. For each case, the parameters and the summary of statistical error analysis are presented in Table 2. Note that the CP values of the two phase region were not used for the regression process. The general range of this correlation is from 20 to 200 °C (68 to 392 °F) and from 0.10 to 20 MPa (14.5 to 2900 Psia).
Discussion and Conclusions
A single and relatively simple correlation has been developed to estimate heat capacity of natural gases as a function of pressure, temperature, and relative density (composition). This correlation covers wide ranges of pressure (0.10 to 20 MPa, 14.5 to 2900 Psia), temperature (20 to 200 °C, 68 to 392 °F), and relative density (0.60 to 0.80). A generalized set of parameters in addition to an individual set of parameters have been determined and reported in Table 2. The error analysis reported in Table 2 indicates that the accuracy of this equation is quite good and can be used for natural gas heat duty calculations. For the generalized set of parameters, the average absolute percentage error (AAPD) and the maximum absolute percent deviations (MAPD) for the total of 715 points are 4.34 and 23.61, respectively. The applicable ranges of the proposed correlation are shown in Table 2.
Table 2. Parameters for the proposed correlation; Eq. (7) in SI and FPS system
AAPD= Average Absolute Percent Deviation and
MAPD= Maximum Absolute Percent Deviation
NPT= Number of Points and
SG = Relative Density (Specific Gravity)
Note: Below the above the temperature ranges for pressures 2, 5, 7, and 10 MPa (14.5 to 1450 Psia), the gas mixture may be in two phase (gas and liquid) region.
It should be noted that the concept of heat capacity is valid only for the single phase region.
One of the most important physical properties of a gas is the ratio of specific heats. It is used in the design and evaluation of many processes. For compressors, it is used in the design of components and determination of the overall performance of the machine. Engineers are frequently asked to evaluate a compressor performance utilizing traditional equations of head, power and discharge temperature. While these simplified equations may not give exact results, they give useful information needed to troubleshoot a machine, predict operating conditions, or a long-term trend analysis. The accuracy of the performance information will depend on the proper selection of the ratio of specific heats. This Tip of the Month (TOTM) will investigate the application of the ratio of specific heats to compressors, its sensitivity to the determination of machine performance and give recommendations for improved accuracy.
Background of k-value
The ratio of specific heats is a physical property of pure gases and gas mixtures and is known by many other names including: adiabatic exponent, isentropic exponent, and k-value. It is used to define basic gas processes including adiabatic and polytropic compression. It also appears in many of the traditional equations commonly used to determine a compressor head, gas discharge temperature, gas power, and polytropic exponent. The k-value also influences the operating speed of a compressor, but we will simplify the present analysis by deleting speed from our evaluation. The following commonly used compressor performance equations show how the k-value is utilized in the design and evaluation of compressors.
Note: The actual Z-value will vary from the suction to discharge conditions. ZS is sometimes replaced with ZAVE to approximate the variations in compressibility value [1, 5]. See the nomenclature at the end of this TOTM.
The above equations are written in terms of the adiabatic process with the exception of Equation 5, which refers to the polytropic process. Both compression processes are similar and will give the same actual results. The adiabatic and polytropic methods are extensively used by manufacturers to design compressors, and make use of k-values to calculate their performance. However, as will be seen, the effect of the k-value and the calculated results will influence both compression processes alike. For simplicity, this Tip of the Month will use the adiabatic process.
It can be seen from Equations 1-5 that the k-value has an effect on a compressor head, temperature, power, and polytropic exponent. In order to determine how small changes in the k-value can influence a compressor performance, let us first define the k-value of a pure gas. The thermodynamic definition of a gas k-value is given by Equation 6. It shows the relationship to the specific heat at constant volume, CV and specific heat at constant pressure, CP. Both values vary with temperature and pressure.
For a pure gas there are many references that give CP and CV values at various conditions. One useful source is National Institute of Standards and Technology. Their website is http://webbook.nist.gov/chemistry/fluid/
The method of determining the k-value for gas mixtures is more complex. The major difference is that a gas mixture does not behave as any one of its components but as an “equivalent” gas. Therefore, to determine the k-value of the mixture, we must know the mole fraction of each component, Yi and the molar specific heat at constant pressure for each component, M CPi. Equation 7 can be used to determine the k-value of an ideal gas mixture [1, 5]. Real gases may deviate from the calculated value.
While Equations 1-7 are applicable for manual calculations methods, it is important to note that process simulation packages determine the compressor head and discharge temperature utilizing equations of state. The results are the same but the methods are very different.
K-value Sensitivity Analysis
In the compression process the temperature and pressure of the process gas both increase. Not knowing what k-value to select for evaluating the compression process can lead to errors. For example, a typical propane compressor may have a k-value at suction conditions of 1.195. At the compressor discharge conditions the k-value is 1.254. The difference in the two values varies by 4.94 percent and can have a significant influence in the performance evaluation. The following example illustrates how minor changes in the k-value can influence the calculated compressor head, temperature, power and the polytropic coefficient.
Example 1: A natural gas compressor is operating at the conditions given below. Only the k-value is varied from 1.20 to 1.28, all other given parameters remain constant. Figure 1 illustrates how the “apparent” performance of a compressor can change by varying the k-value.
It can be seen from Figure 1 that the discharge temperature deviated over 18.8 percent by only changing the k-value by 6.7 percent. In this case the k-value varied from a value of 1.20 to 1.28; which is the typical range for natural gas. Similarly, the power changed by 2.5 percent, polytropic exponent by 9.5 percent, and adiabatic head by 2.5 percent for the same variation of the k-value. The changes in compressor performance described in Figure 1 can be much larger depending on the gas composition and the operating temperature and pressure.
Corrected k-Value Recommendations
The k-value sensitivity for a single-stage machine is not nearly the problem as a multi-stage compressor. For a single-stage machine, the pressure ratio is typically lower and the temperature and pressure changes are less. As a result the changes in k-value are not as great and accurate results can be obtained by approximating the k-value at the suction conditions. However, for multi-stage machines, where the pressure and temperature ratios are higher, the k-value sensitivity is more of a factor in evaluating compressor performance. Most compressor manufacturers calculate the k-value for each stage of compression and avoid errors introduced by utilizing an overall k-value. Without their software, we are left with a corrected k-value by empirical methods.
There are many useful approximations that will correct for changes in the k-value as the process gas passes through the compressor. Normally the k-value will decrease during compression but not always. Utilizing the suction conditions to estimate the k-value will generally give higher values of temperature, heat, and power. The polytropic exponent generally decreases as the adiabatic exponent decreases. To avoid potential discrepancies, a k-value correct may be warranted. The following are six methods of determining the corrected k-value commonly used in industry.
At TS and PS: This method determines the k-value at suction conditions and is useful for single stage compressors or applications where there is little change in the k-value. The k-value is easy to determine and tends to overestimate results, especially if the temperature and pressure do not change significantly. For greater values of RP the results may become so conservative they become useless.k = ks at suction conditions
At TD and PD: This method determines the k-value at discharge conditions. The k-value is less conservative and tends to underestimate results. The k-value may be difficult to determine, especially if the discharge temperature is unknown. For gases with highly variable k-values, an iterative solution may be required to estimate the discharge temperature and corrected k-value.k = kD at discharge conditions
At TAVE and PSTD [5]: This method utilizes the average operating temperature at standard pressure and determines the k-value. Numerous reference books propose this method. Errors are introduced because the k-value at standard pressure may not accurately represent values at the operating pressure.k = at average operating temperature and standard pressure
At TAVE and PAVE: This method utilizes the k-value at the average operating temperature and pressure.k = at average operating temperature and pressure
Average value [1, 3]: This empirical method takes the average k-value at compressor inlet conditions and outlet conditions. Utilizing the average k-value will result in performance values that are closer to the actual performance of the compressor.
Weighted average value [4]: This empirical method takes the weighted average of the suction, mid-point and discharge conditions. Note that the mid-pressure is determined by equivalent pressure ratios, . The mid-temperature is estimated from the mid-pressure. This method considers the staged k-value to change with diverging isentropic and pressure lines shown on a Mollier chart.
Example 2 illustrates the various methods used to determine corrected k-values given above. It also compares the range of the resulting values.
Example 2: A propane compressor is operating at the given conditions shown below. Table 1 lists the k-values attributed to various operating and reference conditions [6].
Summary
This Tip of the Month has defined the physical property of process gases called the k-value or ratio of specific heats. It has shown that small changes in the k-value can have a significant effect on the calculated values of head, power, gas discharge temperature, and polytropic exponent. Recommendations were also given to improve the accuracy by utilizing different k-value methods.
The formation of hydrates in processing facilities and pipelines has been a problem to the natural gas industry. Whether the problem occurs in transportation or processing, hydrate formation can cause shutdowns and even destruction of valuable equipment. Because of these devastating and often costly consequences of hydrate formation, methods have been applied to prevent hydrate development in gas streams. The conditions that tend to promote hydrate formation include: low temperature, high pressure, and a gas at or below its water dew point temperature with “free” water present. The formation of hydrates can be prevented by using any of the following techniques; (a) adjusting the temperature above and pressure below the hydrate formation condition, which may not be practically possible due to economical and/or operational reasons, (b) dehydrating a gas stream with solid desiccant or glycol dehydration to prevent a free water phase, and (c) impeding hydrate formation in the free water phase by injection of an inhibitor. The most common inhibitors are methanol (MeOH), monoethylene glycol (MEG) and diethylene glycol (DEG). Typically, methanol is used in a non-regenerable system while MEG and DEG are used in regenerable processes. With the use of inhibitors, the injected inhibitor may distribute into three possible phases: (a) the vapor hydrocarbon phase, (b) the liquid hydrocarbon phase and (c) the aqueous phase in which the hydrate inhibition occurs and the inhibitor has an effect on hydrate formation inhibition. Therefore, calculating the inhibitor concentration in aqueous phase is important.
Several models have been developed for prediction of hydrate formation condition in the presence of an inhibitor. Hammerschmidt [1], Nielsen and Bucklin [2], Carroll [3] and Moshfeghian-Maddox [4] correlations are used to predict concentration of inhibitors in an aqueous solution and for lowering the hydrate formation temperature. Portability and simplicity are advantages of these correlations since they are applicable even with a simple calculator and the results are in good agreement with the experimental data [1-4]. It is to be noted that simulation packages such as ProMax® [5], HYSYS® [6] and GCAP [7] are available for predicting the effect of inhibitors on hydrate formation.
The injection rate is a function of feed gas temperature (FGT), pressure (FGP), relative density (SG), hydrate formation temperature depression (HFTD), and lean solution concentration. Recently, Moshfeghian and Taraf [8-10] proposed a shortcut/graphical method to predict the required MEG or MeOH weight percent and flowrate for a desired depression in hydrate temperature of natural gas mixtures.
In this tip of the month (TOTM), we will demonstrate how the diagrams presented by Moshfeghian and Taraf [10] can be used to determine the concentration of MeOH in the rich solution and the required total injection rate for a desired hydrate formation temperature.
Figures 1-4 are applicable for any wet natural gas mixture with specific gravity of 0.6. Note that the right hand y-axis represents the total injection rate of MeOH which may distribute into gas phase, liquid hydrocarbon phase and rich solution phase. In order to extend the application of these charts to gas mixtures with other specific gravities, two correction factors and W2 should be used. These correction factors are used to correct the inhibitor concentration in the rich solution for other relative densities (0.65-0.80) which are shown in Figure 5. is the correction factor due to the difference of inhibitor concentration in the rich solution in different hydrate formation temperature depression. This factor is applicable for gas with specific gravities greater than 0.6. W2 is the correction factor due to the difference in inhibitor concentration in the rich solution due to the difference in gas specific gravities. To determine W2, the S-factor is defined as follow:
By calculating the S-factor, W2 can be easily read from Figure 5. This correction factor is applicable for gas with specific gravities of 0.65 and greater.
Using W1 and W2, the obtained weight percent from Figures 1-4 (Wtfig) is corrected as follows:
The obtained flow rate from charts (Figures 1-4) should be corrected further using flow rate correction factor (FLC) presented in Figure 6. The correction factor can be applied as follow:
Considering the above correction factors, the charts are applicable for natural wet gases with specific gravities of 0.6-0.8 saturated, at temperature of 20, 30, 40 and 50 oC and pressures of 3, 5, 7 and 9 MPa.
As mentioned earlier, the inhibitor in the aqueous phase (rich solution) has an effect on hydrate formation inhibition and it is independent of the inhibitor weight percent in the lean solution. The same hydrate temperature depression is achieved when there is a similar inhibitor weight percent in the rich solution. However, the injection rate is a function of both lean and rich stream concentration.
Therefore, a simple material balance gives the following equation:
Case Study
To demonstrate the application of the proposed charts, example 6.6 in Volume 1 of “Gas Conditioning and Processing,” [11] is considered. In this example it is stated that 3.5 × 106 Sm3/d of natural gas leaves an offshore platform at 40 oC and 8000 kPa. The hydrate temperature of the gas is 17 oC. The gas arrives onshore at 5 oC and 6500 kPa. The associated condensate production is 60 m3/106 Sm3. The amount of methanol required to prevent hydrate formation in the pipeline is to be estimated.
It should be noted that in this example the composition (or relative density) of natural gas is not given; therefore, to demonstrate the use of these charts a relative density of 0.6 is assumed. The feed gas pressure is 8 MPa so a linear interpolation between 7MPa (Figure 3) and 9 MPa (Figure 4) is applied.
The summary of known data is:
FGT = 40 oC; HFT = 17 oC, FGP = 8 MPa, SG = 0.60, Inhibitor = 100 Wt % MeOH
Minimum Flowing Temperature (MFT) = 5 oC
HFTD = HFT – MFT = 17 – 5 = 12 oC
Due to the uncertainties involved in all inhibitor injection calculation methods, a safety factor is normally applied to the hydrate formation temperature depression. For example, this case has the HFTD set to the minimum flowing temperature. In practical situations, a design factor such as 5 deg oF (2.8 oC) below the minimum flowing temperature is used to ensure any errors in the estimation method are covered, and also to ensure that the minimum temperature includes any upset process condition.
As an example, the location of HFTD, required weight percent and injection rate of MeOH for pressure of 9 MPa for this example are shown in Figure 4. The results are tabulated in Table 1, and a comparison between the results of this work and those based on the Hammerschmidt [11] equation, ProMax [5], HYSYS [6], and GCAP [7] is shown in Table 2. As can be seen from Table 2, the agreement between the graphical method and ProMax is quite good. The methanol injection rates as estimated by HYSYS are significantly lower than the other methods, and caution should be applied if one is using HYSYS for inhibitor injection estimates. It is likely that the differences in the natural gas water dew point predictions are the result of this discrepancy. Also note for modeling methanol liquid systems in process simulators, a polar equation of state package for the vapor phase and a polar model for the liquid phases must be selected to obtain accurate results.
Conclusions
For determination of required methanol concentrations in the aqueous phase (rich solution) and its flowrate for a desired depression in hydrate formation temperature of a wet natural gas mixture, reference charts proposed by Moshfeghian and Taraf [10] can be used. These charts were generated for pressures 3, 5, 7, and 9 MPa based on ProMax and are generated for a natural gas mixture with relative density of 0.6 but are extended to gases with relative densities up to 0.8 by using two correction factors. A simple equation was also proposed to extend the charts’ usage to other lean MeOH concentrations.
The results obtained by these charts are compared with the results of the other methods for a practical case and good agreement is found. It is also suggested that linear interpolation can be used for pressures between 3, 5, 7, and 9 MPa.
To receive the full manuscript of Moshfeghian-Taraf’s paper, send an e-mail to info@jmcampbell.com
By: Dr. Mahmood Moshfeghian
Check it out, interesting conversation going on on process safety.
REFERENCES
Hammerschmidt, E.G., “Formation of gas hydrates in natural gas transmission lines”, Ind. & Eng. Chem., Vol: 26, p. 851, 1943.
Nielsen, R. B. and R.W. Bucklin, “Why not use methanol for hydrate control”, Hydrocarbon Processing, Vol: 62, No. 4, P 71, April 1983.
Carroll, J., “Natural Gas Hydrates, A Guide for Engineers”, Gulf Professional Publishing, 2003.
Moshfeghian, M. and R. N. Maddox, “Method predicts hydrates for high-pressure gas stream”, Oil and Gas J., August 1993.
ProMax®, Bryan Research & Engineering Inc, Version 2.0, Bryan, Texas, 2007
HYSYS® v 2006, Aspen Technology Inc., Cambridge, Massachusetts, 2006
GCAP®, 8th Ed., Facilities Analysis Software, John M. Campbell & Co., Norman, Oklahoma, 2009.
Moshfeghian, M. and Taraf, R., “New method yields MEG injection rate”. Oil and Gas J., September 2008.
Moshfeghian, M. and Taraf, R., “A new shortcut/graphical method to determine the required MEG injection rate for natural gas hydrate inhibition,” 87th Annual Gas Processor Association Convention March 2-5, in Grapevine, Texas, (2008).
Moshfeghian, M. and Taraf, R., “Generalized Graphical Method to Determine the Required MEG and Methanol Injection Rate for Natural-Gas Hydrate Inhibition,” 88th Annual Gas Processor Association Convention March 8-11, in San Antonio, Texas, (2009).
Campbell, J. M., “Gas Conditioning and Processing”, Vol. 1, The Basic Principles, 7th Ed., Second Printing, J. M. Campbell and Company, Norman, Oklahoma, 1994.
In the February 2007 tip of the month (TOTM), Joe Honeywell [1] presented a procedure for calculating fluid pressure drop for liquid in a piping system due to friction. Continuing Honeywell’s TOTM, we will outline procedures for calculation of friction losses in oil and gas pipelines. From an engineer’s point of view the question may arise “how sensitive is friction pressure drop with the wall roughness factor?” Of course the answer is “it depends”. To explain this answer quantitatively and qualitatively, we will study the effect of wall roughness factor for two case studies in this month’s TOTM. In the first case study, an oil pipeline with a flow rate of 0.313 m3/s (170,000 bbl/day) and in the second case, a natural gas pipeline with a flow rate of 22.913 Sm3/s (70 MMSCFD) will be studied and calculation results will be presented in tabular and graphical format.
Friction Factor
The Moody diagram in Figure 1 is a classical representation of the fluid behavior of Newtonian fluids and is used throughout industry to predict fluid flow losses. It graphically represents the various factors used to determine the friction factor. For example, for fluids with a Reynolds number of 2000 and less, the flow behavior is considered a stable laminar fluid and the friction factor is only dependent on the Reynolds number [2]. The friction factor, f, for the Laminar zone is represented by:
Where Re is the Reynolds number and is expressed as the ratio of inertia force to viscous force and mathematically presented as.
Fluids with a Reynolds number between 2000 and 4000 are considered unstable and can exhibit either laminar or turbulent behavior. This region is commonly referred to as the critical zone and the friction factor can be difficult to accurately predict. Judgment should be used if accurate predictions of fluid loss are required in this region. Either Equation 1 or 3 are commonly used in the critical zone. If the Reynolds number is beyond 4000, the fluid is considered turbulent and the friction factor is dependent on the Reynolds number and relative roughness. For Reynolds numbers beyond 4000, the Moody diagram identifies two regions, transition zone and completely turbulent zone. The friction factor represented in these regions is given by the Colebrook formula which is used throughout industry and accurately represents the transition and turbulent flow regions of the Moody diagram.
The Colebrook formula for Reynolds number over 4000 is given in equation 3.
The roughness factor is defined as the absolute roughness divided by the pipe diameter or . Typical values of absolute roughness are 5.9x10-4 in (0.0015 mm) for PVC, drawn tubing, glass and 0.0018 in (0.045 mm) for commercial steel/welded steel and wrought iron [3].
The Colebrook equation has two terms. The first term, ()/3.7, is dominate for gas flow where the Re is high. The second term, , is dominate for fluid flow where the relative roughness lines converge (smooth pipes). In the “Complete Turbulence” region, the lines are “flat”, meaning that they are independent of the Reynolds Number. In the “transition Zone”, the lines are dependent on Re and . When the lines converge in the “smooth zone” the fluid is independent of relative roughness.
Liquid (Incompressible) Flow
For liquid flow, equation 4 has been used by engineers for over 100 years to calculate the pressure drop in pipe due to friction. This equation relates the various parameters that contribute to the friction loss. This equation is the modified form of the Darcy-Weisbach formula which was derived by dimensional analysis.
The friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using an iterative method or a trial and error procedure.
Gas (Compressible) Flow
For gas flow, density is a strong function of pressure and temperature, and the gas density may vary considerably along the pipeline. Due to the variation of density, equation 5 should be used for calculation of friction pressure drop.
Again, the friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using a trial and error procedure. Actual volume flow rate is needed to calculate the velocity of gas in the line from which the Reynolds number is calculated. Equation 6 may be used to convert the volume flow rate at standard condition to the actual volume flow rate.
Case Study 1: Oil Pipeline
Consider a 16-inch (inside diameter of 395 mm) oil export line for transportation of 170,000 bbl/day (0.313 m3/s) of a 43 API crude oil (relative density of 0.81) from an offshore platform to the shore oil terminal. The total length of pipe is 55 km. The ambient temperature is 5 °C and the crude oil viscosity at the average pipe temperature is 0.001 cP. The pipe line inlet pressure is 14.9 MPa (absolute). Since the objective is to study the effect of roughness factor on friction pressure drop, we will ignore elevation change.
To study the effect of roughness factor on friction pressure drop, was varied from 1x10-6 to 1x10-3. The roughness factor of = 1x10-6 represents a very smooth pipe. The calculated friction pressure drop as a function of the roughness factor is plotted in Figure 2. For each value of roughness factor, the percent change in frictional pressure drop was calculated in comparison to a very smooth pipe (= 1x10-6) and the results are presented in Figure 3. The calculated results are also presented in Table 1.
Case Study 2: Gas Pipeline
Let’s consider an 8-inch (inside diameter of 190 mm) gas export line for transportation of 70 MMSCFD (22.913 Sm3/s) of natural gas with a molecular weight of 19.3 (relative density of 0.67) from an offshore platform to the shore. The total length of pipe is 43 km. The ambient temperature is 5°C and the gas viscosity at the average pipeline temperature is 1.1x10-6 cP. The gas inlet temperature is 35°C and pressure is 13.0 MPa (absolute). Since the objective is to study the effect of roughness factor on friction pressure drop, we will again ignore elevation change.
Similar to the oil pipeline, the roughness factor, was varied from 1×10-6 to 0.006. Note, for a roughness factor greater than 0.006, a higher inlet pressure, a larger diameter or lower flow rate was needed. The calculated friction pressure drop as a function of roughness factor is presented in Figure 2. For each value of roughness factor, the percent change in frictional pressure drop in comparison to a very smooth pipe (= 1×10-6) was calculated and the results are presented in Figure 3.
Discussion and Conclusions
The analysis of Figure 2 indicates that for the oil pipeline, the friction pressure drop is almost independent of the roughness factor in the range of 1×10-6< <1×10-4; however, for >1×10-4, it will increase with . For liquid lines, the Reynolds number is normally in the range of 5×104 to 1×106. For this range, the friction factor curves in Figure 1 approach close to each other so the values of friction factors become close to each other.
Contrary to the oil pipeline, the friction pressure drop for the gas pipeline is a strong function of . As can be seen in Figure 2, friction pressure drop increases very rapidly with the roughness factor. Figure 3 shows the comparison of percent change of friction pressure drop between oil and gas pipelines as a function of roughness factor. For the liquid pipeline, the maximum change is 20 % but for the gas pipeline the maximum change is more than 200 %. Again this can be explained by referring to Figure 1. For gas pipelines, the Reynolds number is higher than in the liquid line and the range is normally 5×106<Re<1×108. For this range, the friction factor curves in Figure 1 are apart from each other, so the friction factors are not close.
In summary, contrary to liquid pipelines the gas pipelines are very sensitive to wall roughness and using smooth pipe can reduce friction pressure drop considerably. This in turn lowers the OPEX. Therefore, regular pigging to clean the pipe surface is done to lower the roughness factor. The modern gas transmission companies will add a Fusion Bounded Epoxy (FBE) liner to gas pipelines because the pipe is sensitive to roughness. This lowers OPEX for the long term. It should be noted that the smoother the pipe, the higher the CAPEX, so as always, detailed total cost analysis should be performed for engineering applications.
Due to the sensitivity of gas pipelines to roughness factor and other operation parameters, there are numerous gas flow equations (e.g. Weymouth, Panhandle A and B, AGA) to best fit certain design conditions [1].
To learn more about similar cases and how to minimize operational problems, we suggest attending our ME44 (Overview of Pumps and Compressors in Oil and Gas Facilities), ME46 (Compressor Systems – Mechanical Design and Specification), PL4 (Fundamental Pipeline Engineering), G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), and PF4 (Oil Production and Processing Facilities) courses.
By: Dr. Mahmood Moshfeghian
Reference:
Honeywell, Joe, “Friction Pressure Drop Calculation,” Campbell Tip of the Month, Feb 2007
Campbell, J. M., “Gas Conditioning and Processing, Vol. 1, the Basic Principals, 8th Ed., Campbell Petroleum Series, Norman, Oklahoma, 2001
Menon, E.S, Piping Calculations Manual, McGraw-Hill, New York, 2005
In this tip of the month, we will discuss how miscalculations and incorrect analysis of potential process upsets can affect process safety. There are many aspects in facility design engineering and process safety engineering that should be considered when designing a new facility or debottlenecking an existing one. During these times of compressed schedules and budgets, it can become difficult to ensure all project deliverables receive the proper amount of checking and documentation. Mistakes in engineering design and operations of the following systems can result in serious safety incidents which must be avoided. Quality control, technical training, calculation checking and method verifications can aid in minimizing safety risks in these systems. This months’ tip will focus on Pressure Relief Systems.
A primary process system in oil and gas facilities requiring careful attention is the Pressure Relief System. The most common components in upstream pressure relief systems are:
Protected Equipment
Emergency Shut Down Valves
Depressurization Valves
Pressure Safety Valves (PSV)
Pressure Safety Valves Inlet and Discharge Piping
Flare Header
Flare Knock Out Drum
Flare Stack / Tip
The primary purpose of the pressure relief system is to ensure that the operation’s personnel and equipment are protected from overpressure conditions that happen during process upsets, power failures, and from external fires. In some locations and facilities, it is accepted practice to vent the pressure safety valves directly to atmosphere provided the process fluid is discharged at sufficient velocity to ensure good dispersion and that the fluids molecular weight is lighter than air. In this TOTM we will be discussing components in the pressure relief system in which detailed engineering calculations must be completed to select and install properly.
Pressure Safety Valves:
The purpose of a pressure safety valve is to protect equipment and / or piping from any possible overpressure scenario. There are multiple industry recommended practices and standards that govern the sizing, selection and installation of pressure safety valves. Many of these are referenced in this TOTM. A study that was conducted by Berwanger, et al. [1] determined that only 65% of upstream processing facility pressure safety valves meet the existing standards. Accurate pressure safety valve relieving requirements, scenario analysis and installation design is critical to ensure safety of the equipment and the operations staff during an upset condition. The American Institute of Chemical Engineering found that roughly 30% of process industry losses have been found to be partially attributed to deficient pressure relief systems [2]. If an upset process condition occurs with a system that has a pressure safety valve that is missing, undersized, or not properly installed, there is a potential that the equipment will not be protected and will mechanically fail. This could result in a significant loss of fluid containment and potential fatalities depending upon the fluids contained within the process.
On March 4, 1998, there was a major vessel failure at a Sonat Exploration facility in Pitkin Louisiana. The vessel failure and subsequent fire resulted in four deaths. A cause of the incident was failure of a low pressure vessel open to a high pressure gas source that was not provided with any pressure relief devices [3].
In determining the relevant relieving scenarios for a pressure relief valve, it is essential that the engineer doing the evaluation has a solid understanding of the process and the process control design within the facility. If the lead engineer is conducting an existing plant review or working on the design of a new facility, it is critical that they evaluate all potential relieving scenarios that may be required. If a scenario is missed, then there is a possibility that the system will not be protected if that missed scenario was the limiting case. ANSI / API Standard 521 ISO 23251, 5th Edition [5] specifies requirements and provides guidelines for examining the principal causes of overpressure; determining individual relieving rates; and selecting and designing disposal systems, including the details on specific components of the disposal system. Only with experience and training do engineers develop the competency level to complete these evaluations effectively. Participation in Process Safety Hazards Reviews and Analyses promote the development of an engineer’s skills in identifying and resolving potential process hazards, and can help develop a junior engineer’s skills and understanding of the evaluation of these systems.
API Recommended Practice 520, 7th Edition, Part 1 [4], and the International Organization for Standardization (ISO) Standards in the 4126 series (will not all be referenced here, and it should be noted that these only apply to systems designed and installed in the European Union Member States), addresses the methods to determine the pressure safety valve sizing requirements for the different relieving scenarios and provides guidance on how to select the proper relief valve type. Both over-sizing and under-sizing a relief valve can result in mechanical failures, thus it is critical that the valve sizing and selection are correct.
If a facility is being debottlenecked and modified all pressure safety valves that will be affected by the modification must be checked for adequate capacity. Many facilities are not applicable to the U.S. Occupational Safety and Health Administration (OSHA) Process Safety Management (PSM) Standard 29 CFR 1910.119 [6].It is strongly recommended that a Management of Change (MOC) procedure be used to ensure that no facility modification will pose a safety risk or undermine the existing safety equipment provided within the facility. Pressure safety valves for all modified systems must be verified to safely handle the new required rates and compositions that result from debottlenecking the facility.
In addition, it is essential that operation’s personnel are trained in the proper handling and testing of relief valves. There have been cases when operations and maintenance personnel have increased the set pressure on a pressure relief valve that was frequently relieving. The increase in set pressure results in the vessel operating above the stamped maximum allowable working pressure and may result in mechanical failure. Trained staff will understand that the solution to the problem is to correct the process condition that is resulting in the high pressure, not increase the set point on the pressure safety valve.
PSV Inlet and Discharge Piping
Another area that requires close attention is the proper design of the inlet and discharge piping of the pressure safety valves. API Recommended Practice 520, 5th Edition, Part 2 [7], and ANSI / API Standard 521 [5] provide guidance on the installation and design of the inlet and discharge piping for pressure safety valves.
For inlet piping to pressure safety valves, the recommended practice is to maintain the inlet hydraulic losses at no more than 3% of the set pressure of the pressure safety valve. This is because the relief valve is designed to normally close at 97% of the set pressure. A PSV with no inlet flow will sense the same pressure as exists in the protected equipment. Once open however, the pressure at the inlet to the relief will be the pressure at the protected equipment minus the friction loss in the inlet line. If this friction loss exceeds 3%, the valve will close and then reopen once the flow stops. This chattering can destroy the valve. Over sizing of a pressure safety valve can also result in “chatter” from essentially the same phenomenon. There is a potential for pressure relief valve or piping failure from prolonged “chattering” due to mechanical fatigue and potentially thermal fatigue.
If the inlet piping design cannot be configured to meet this requirement, then the use of a remote sensing pilot pressure safety valve can be used. This is not preferred due to the potential for the sensing line to plug or freeze.
Typically, relief valves are mounted almost directly on the equipment they protect. You will often find, however, that in existing plants this is not always the case. Some pressure safety valves may be located remotely with long inlet lines and the 3% criteria must be carefully checked. Even with new plant designs, there are times when the piping designer must locate the pressure safety valve remotely. It is important to always check the inlet line losses by utilizing the piping isometric drawings.
A study conducted by Berwanger, et al [1], found that 16% of all pressure safety valve installations reviewed were out of compliance with accepted engineering practices and standards as a result of improper installations. 35.5 % of these valves were out of compliance due to excessive inlet pressure drop. Experience indicates that in many older plants, the pressure safety valve inlet and discharge piping is set at the inlet size and outlet size of the pressure safety valve and the pressure drop calculations were not performed – or were performed on incorrect assumptions for inlet pipe routing. A crude oil fire occurred in a Shell facility as a result of improper inlet piping design. This caused severe vibration and caused a 6” flange to fail, losing containment of the process stream [8].
For systems with 600# ratings and above, the valve manufacturer may supply a relief valve with an inlet flange rating of 600# and an outlet flange rating of 300#. Be aware that a “typical” 150# flange rating on the PSV discharge piping is not always acceptable for the higher pressure systems. The velocity at the outlet of the pressure safety valve can not exceed sonic. Thus, for high pressure systems the flow through the relief valve may require a pressure greater than the max pressure rating of a 150# system to maintain sonic flow. It is important to check the pressure required to maintain sonic based on the size of the pressure safety valve outlet. If a 300# flange is required then a 300# pipe fitting is installed to expand the pipe to a diameter where the pressure corresponding to a 150# system is not exceeded. For large systems, it is recommended to use a flare network software program to predict the backpressure at the outlet of each pressure safety valve for various relief scenarios. During a fire, several reliefs may open simultaneously and the backpressure must be known at the outlet of each relieving pressure safety valve under these circumstances.
The piping design for the inlet and discharge of pressure safety valves should be reviewed to determine that the piping can meet the mechanical and thermal stresses that will develop when the pressure safety valves relieve. Threaded connections for high set pressure safety valves or on pressure safety valves that are installed near vibrating equipment are not recommended. The threaded connections have a tendency to fail or become “unscrewed” from the vibrations, and / or forces during relieving
Proper valve and discharge piping support design is essential. Piping and valve support becomes more critical on larger pressure safety valves and pressure safety valves that have high set pressures discharging to atmosphere. The reaction forces that can develop from the valves relieving to atmosphere can be significant. Even though the outlet piping may not be excessively long, the internal thrust created at the 90 degree elbow as the discharge piping turns up can be excessive. The flow will most likely be sonic velocity at the elbow and the discharge vent must be adequately supported to prevent failure. One incident occurred when the inlet piping on a 4X6 pressure safety valve set at 1350 psig failed. The valve became a projectile as a result. Fortunately, no one was hurt by flying debris and the gas line was isolated before the vapor cloud was ignited. This “near miss” was likely the direct result of poor welding and poor support on the valve installation.
The reaction forces in closed systems tend to be less, but in some cases the reaction forces in a closed system can become significant if there are sudden large pipe expansions or during unsteady flow conditions within the piping. Inadequate design and supports for pressure safety valves and the associated piping can result in mechanical failure during a relieving event.
Flare Header Design
If the pressure safety valve discharges into a flare header the superimposed and built up back pressure is critical and can impact the valves relieving capacity if the actual back pressure is higher than the originally calculated or assumed back pressure. The maximum allowable back pressure at which a pressure safety valve can function properly depends upon the type of the pressure safety valve. A study conducted by Berwanger, et al [1], found that almost 24% of all PSV installations reviewed were out of compliance with accepted engineering practices and standards because of improper installations. 12 % of these valves were out of compliance due to the outlet pressure drop being too high. If the built up back pressure is greater than the maximum value the valve can function with, then the upstream pressure of the valve will increase above the set pressure of the valve as a result. This condition increases the likelihood of a failure.
A flare network software program should be used to calculate backpressure in large relief systems. For most pressure safety valves the maximum flow that can pass through the orifice size is larger than the required relieving flow. The maximum flow must be used to calculate the inlet line loss and the resulting backpressure. Modulating pilot valves can be used, if required, to control the maximum flow that is required to be relieved. In the design of the flare system, several types of valves are available, as explained in API 520 Part 1 [4]. Conventional, bellows, and pilot valves are typically used. The valve manufacturer must be consulted to define the maximum flow and backpressure requirements for each type of valve. The final flare design can not be completed until the actual pressure safety valves have been selected.
Depending upon the fluids which are being relieved and the pressures involved, it is possible to have relieving events that require stainless steel discharge piping, Flare Header, Flare KO Drum and Flare Stack because of cryogenic relieving temperatures from the Joule-Thompson Effect through the pressure safety valve. There have been multiple cases where carbon steel flare headers have failed due to the cryogenic relieving temperatures that developed during relieving events. The failure of a flare header completely undermines the purpose of the Pressure Relief System, and can result in a catastrophic event.
In today’s’ market, the recovery of NGL’s from natural gas is quite common. Particular attention is required in designing the relief systems for the cryogenic vessels. The pressure safety valves most likely will be relieving cold (at -20 F or below) two phase fluids. The pressure safety valve downstream piping will be exposed to very cold temperatures when the valves relieve. The recommended method for sizing two phase flow valves is by utilizing the DIERS equations. API 520 Part 1, Appendix D [4] summarizes these equations and provides an example calculation. The calculation procedure is long and tedious but it is recommended to perform a hand calculation before utilizing in house spreadsheets. The couple of hours spent performing the calculation will provide valuable insight to the key parameters used in the equations and will serve as a verification check of a spreadsheet.
There should be no dead legs in any piping from the discharge of the relief valve to the Flare KO Drum. Any pockets or dead legs can fill with liquids which may result in excess back pressure during relieving events There may also be large reaction forces in the flare header as a result of the slug of liquids forced down the header. In 1999, the flare header of a Tosco refinery in California was overpressured due liquid accumulation at a low point in the flare header. This resulted in a facility shutdown.There were no injuries reported [9].
Flare KO Drum and Flare Stack / Tip
Flare KO Drum and Flare Stack sizing is also critical to the safety of the plant. Oil and Gas Industry Flares are designed to destroy vapor streams only and require an adequately sized Flare KO Drum to prevent flammable liquids from raining out of the flare tip. In determining the sizing, it is important that a Flare Study be conducted to determine the worst case scenario for Flare KO Drum and Stack capacity and to select the proper droplet size separation criteria that the selected flare tip can adequately destroy. ANSI / API Standard 521[5] provides guidance on sizing, design and selection of this equipment.
A good example of the consequences of liquids flowing out of a Vent Stack was the Texas City Refinery explosion of 2005. This catastrophic incident resulted in a process upset where the amount of liquids that flowed to the KO Drum overwhelmed the drum size, and flowed up the vent stack and to the surrounding atmosphere which resulted in the tragic explosion [10]. If a Flare would have been installed in the Texas City Refinery rather than a Vent Stack, the consequences of the event would have been reduced. The vapor phase hydrocarbons that were originally flowing to the vent stack would have been destroyed in the Flare Tip, and the vapor cloud that exploded would have been prevented. Flowing liquid hydrocarbons to a Flare Tip is still a dangerous situation. If a Flare KO Drum were overwhelmed with hydrocarbon liquids the Flare Stack would likely be raining fire, and not liquid hydrocarbons.
Based on the stack sizing, ANSI / API Standard 521 [5] outlines procedures to estimate the radiation effect from the flare. With today’s’ specialized design of flare stacks, consultation with the flare manufacturer is recommended for the radiation confirmation.
Depressurization Valves
In the gas processing industry, it has become a standard practice to block in the treating facility with Emergency Shut Down (ESD) Valves rather than depressure the entire facility to the flare. One primary reason for this philosophy is that natural gas fires are not equivalent to liquid hydrocarbon pool fires. Natural gas fire protection and mitigation requires different protection methods than for those used for fighting liquid hydrocarbon pool fires, which can be extinguished using a fire water system or a foam system. . It is standard natural gas industry practice to isolate the hydrocarbon gas sources to the facility and evacuate all personnel from the facility. Once the source of the gas is isolated, the feed to the fire is terminated and the fire is quickly extinguished from lack of fuel.
In the case where a facility must be depressurized in an upset condition, careful attention must be given to the design of the depressurization valves, their timing and flare capacity. There exists the potential to overwhelm the Flare Tip if the Tip was not designed for the high depressurization rates. In addition, consideration for required depressurization time, resulting Flare Header temperatures, and depressurization control schemes must be given close attention. These systems can be highly complex due to the transient nature of the process and require careful design procedures to ensure a safe Depressurization System.
By: Kindra Snow-McGregor
Senior Process Consultant and Instructor
References:
Non-Conformance of Existing Pressure Relief Systems with Recommended Practices, A Statistical Analysis, Patrick C. Berwanger, PE, Robert A Kreder, and Wai-Shan Lee. Berwanger, Inc., 2002.
AIChE. Emergency Relief System (ERS) Design Using DIERS Technology. American Institute of Chemical Engineers, New York, NY, 1995.
U.S. Chemical Safety and Hazard Investigation Board, Investigation Report, Catastrophic Vessel Overpressurization, Report No. 1998-002-I-LA.
Sizing, Selection, and Installation of Pressure-Relief Devices in Refineries, Part 1 – Sizing and Selection, API Recommended Practice 520, 7th Edition, January 2000.
ANSI / API Standard 521, / ISO 23251, Pressure Relieving and Depressuring Systems, 5th Edition, January 2007.
Occupational Safety and Health Standards, Process Safety Management of Highly Hazardous Chemicals, 29-CFR-OSHA-1910.119, 57 FR 23060, June 1, 1992; 61 FR 9227, March 7, 1996.
Sizing, Selection, and Installation of Pressure-Relief Devices in Refineries, Part 2 – Installation, API Recommended Practice 520, 5th Edition, August 2003.
Poor Relief Valve Piping Design Results in Crude Unit Fire, Politz, FC., API Mid-year Refining Meeting, 14 May 1985, Vol / Issue 64.
In this tip of the month (TOTM) we will present the results of several case studies showing the effect of gas molecular weight on the performance and efficiencies of centrifugal compressors. We have considered several “what if” scenarios such as variation of compressor speed as a function of molecular weight, while maintaining the same suction and discharge pressures and mass flow rate. Variation of polytropic head and efficiencies as a function of gas molecular weight for a given compression ratio, and compressor speed has also been studied. In addition, the impact of thermodynamic properties package has been studied.
Compressors can be generally classified in two categories:
Positive displacement; this type of compressor includes reciprocating, rotary screw, sliding vane, liquid ring and rotary lobe. The compression principle is volumetric displacement – reducing the gas volume increases pressure.
Kinetic or Dynamic: this type of compressor includes centrifugal and axial compressors. The compression principle is acceleration and deceleration of the gas – kinetic energy is converted to pressure rise.
Reciprocating and centrifugal compressors are the most popular compressors used in E & P applications. Rotary screw compressors are gaining in popularity in low to moderate pressure gas boosting service, refrigeration systems and fuel gas compression for gas turbines. Further detail may be found in reference [1].
From a calculation viewpoint alone, the power calculation is particularly sensitive to the specification of flow rate, inlet temperature and pressure, and outlet pressure. Gas composition is important but a small error here is less important providing it does not involve the erroneous exclusion of corrosive components. A compressor is going to operate under varying values of the variables affecting its performance. Thus the most difficult part of a compressor calculation is specification of a reasonable range for each variable and not the calculation itself. Maddox and Lilly [2] emphasize that using a single value for each variable is not the correct way to evaluate a compression system.
Normally, the thermodynamic calculations are performed for an ideal (reversible process). The results of a reversible process are then adapted to the real world through the use of an efficiency. In the compression process there are three ideal processes that can be visualized: 1) an isothermal process, 2) an isentropic process and 3) a polytropic process. Any one of these processes can be suitably used as a basis for evaluating compression power requirement by either hand or computer calculation. The isothermal process, however, is seldom used as a basis because the normal industrial compression process is not even approximately carried out at constant temperature.
Due to practical limitation the compression ratio per stage is often in the range between 2 and 6. For large overall compression ratio applications multistage compressors are used. The choice of the interstage pressure is an economic decision and can be estimated by equal compression ratios for each section but may be adjusted to minimize total power requirement.
In order to study the effect of feed gas molecular weight on the performance of centrifugal compressors, several computer simulations using HYSYS [3] were performed.The gas mixtures with the composition shown in Table 1 with molecular weights ranging from 18.2 to 23.17, corresponding to relative density of 0.63 to 0.80, respectively, were used in this study. The characteristics curves for the centrifugal compressors used in this study are shown in Figures 1 and 2. These performance curves were supplied to the simulation software and used in the course of simulations.
Case 1: Effect of Molecular Weight on Flow Rate for Fixed ?P (Constant Speed)
For a fixed inlet pressure of 700 kPa, 35 °C, and 15000 RPM, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In order to maintain the outlet pressure, the feed flow rate has to vary. We are essentially fixing P1 and P2 and wanting to see the effect on the compressor of varying molecular weight feed. The set up shown in Figure 3 was used to generate the simulation results. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figure 4. The PR EOS [4] is used for thermodynamic properties calculations.
Figure 4 indicates that as the relative density decreased, the flow rate must decrease. Note, for the case of compression ratio of 2.5, no convergence could be achieved for relative density of 0.63 and 0.65 due to the fact the surge limit had been reached. For the same case, the required power as a function of relative density is shown in Figure 5. Since, the flow rate decreased with decreasing relative density, the required power decreased.
Finally, the variation of polytropic head as a function of inlet actual volumetric flow rate is shown in Figure 6. Note that the relative densities are identified on this diagram to show their influence on the performance of the compressor.
Case 2: Variable Speed
As in the case 1, for a fixed inlet pressure of 700 kPa, 35 °C, and mass flow rate of 1000 kmol/hr, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In this case, the compressor is varying speed to maintain flow rate at the P speed imposed on it. The schematic setup to generate simulation results is shown in Figure 7. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figures 8 and 9. In addition to the results by the PR EOS, the results obtained by BWRS are shown on these diagrams. The difference between the results of these two EOS for these cases is negligible.
As shown in Figure 8, as the relative density increases, the compressor speed dropped. However, as relative density or molecular weight increased, the required power increased, see Figure 9.
As shown in Figures 10 and 11, the polytropic efficiency and head decrease with relative density. More detail of simulation results can be found in Reference [5].
Conclusions
The impact of relative density (molecular weight) on the performance of a centrifugal compressor was studied by performing a series of computer simulations. Based on the simulation results, it is found that:
For the same feed condition, compression ratio, compressor speed, the flow rates must decrease as the relative density decreases, and will eventually approach a surge condition.
For the same feed condition, compression ratio, compressor speed, as the relative density increases, the flow rate increases which results in more power consumption.
For the same feed condition and rate, and compression ratio, the compressor speed decreases with molecular weight but as expected, the power requirement increases.
The PR EOS and BWRS EOS produced the same simulation results
Campbell, J. M., “Gas Conditioning and Processing, Vol. 2, the Equipment Modules, 8th Ed., Campbell Petroleum Series, Norman, Oklahoma, 2001
Maddox, R. N. and L. L. Lilly, “Gas conditioning and processing, Volume 3: Advanced Techniques and Applications,” John M. Campbell and Company, 2nd Ed., Norman, Oklahoma, USA, 1990.
Peng, Y. D., Robinson, D. B., “A New Two-Constant Equation of State,” Ind. Eng. Chem. Fund., 15, 59, 1976
Moshfeghian, M., Bothamley, M., and Lilly, L.L., “Feed gas molecular weight affects performance of centrifugal efficiency,” Oil and Gas J., May 10, 2008
Gas density estimates are of fundamental importance for process simulation, equipment design, and process safety engineering. In the previous Tip of the Month (TOTM), two shortcut methods for predicting sour and acid gas density were evaluated. We showed that Katz correlation gives accurate results for lean sweet gases and it is the most accurate in comparison to Wichert-Aziz method or the SRK EOS. For binary mixtures of CH4 and CO2, Wichert-Aziz method gives the most accurate result for CO2 content of between 10 and 90 mole percent. As H2S and CO2 content increased, the accuracy of the Katz correlation decreased, but its accuracy increased as the mixture approached a single component. The percentage difference between the Katz and Wichert-Aziz [1] methods for gas mixtures containing acid gases was greater for H2S than CO2.
Process simulation software often use the Benedict-Webb-Rubin-Starling (BWRS), Soave-Redlich-Kwong (SRK) and/or Peng-Robinson (PR) equations of state for gas density calculations. Other sources of gas density calculation are NIST REFPROP (Reference Fluid Thermodynamic and Transport Properties) program and GERG-2004 [2, 3], a reference equation of state for natural gases.
Due to the importance of CO2 injection for enhanced oil recovery and the increasing interest in CO2 capture and sequestration, this study was undertaken to evaluate the accuracy of density calculations for gases containing nil to 100% CO2. An experimental data base was used for the basis of comparison. The study reviews all of the above mentioned methods and will report their accuracies. Table 1 presents the summary of the temperature, pressure, and CO2 mole percent ranges for the data used in this study. The sources of experimental data were reference [4, 5]. This table also presents the average absolute average percent error and the overall average percent error.
Table1 – Summary of error analysis and comparison of accuracy of sour gas and acid gas density prediction by several methods:
Table 1 provides the overall accuracy of the various methods. It should be noted that the relative accuracy of each method varies depending on the CO2-CH4 proportion, the temperature and pressure. The AGA 8 did not return values for many of the low temperature cases where two phases were present. These points were ignored in the analysis.
Next, we plotted the experimental data reported in the GPA RR-138 [3] and GPA RR 68 [4] to evaluate the accuracy of Katz, Wichert-Aziz and the best four of the detailed methods. The results of this evaluation for the T=350°K and 320°K cases are shown in Figures 1 through 5, for CO2 content of 9.83 to 100 mole percent. In Figure 1, Katz method is the most accurate and the accuracy of the other methods are almost the same.
In Figure 2, Katz method has the least accuracy and even though the accuracy of the other methods look the same, GERG 2004 is slightly better than the others.
In Figure 3, Katz method again has the least accuracy and even though the accuracy of the other methods look the same, AGA8 provided slightly better estimates than the others.
In Figure 4, Wichert-Aziz method has the least accuracy and even though the accuracies of the other methods look the same, AGA8, GERG-2004 and REFPROP are slightly more accurate than the PR EOS.
In Figure 5, Wichert-Aziz method has the least accuracy and REFPROP, GERG 2004 and AGA 8 equally have the best accuracy.
Based on the work done in this study and in the previous TOTM, the following can be concluded:
Katz correlation gives accurate results for pipeline quality gases (lean sweet gases)
For pure CO2, AGA 8, REFPROP, and GERG 2004 methods equally are the most accurate method
For binary mixtures of CH4 and CO2, REFPROP and GERG 2004 methods equally give the most accurate result for CO2 content of between 10 and 90 mole percent.
As CO2 content increases, the accuracy of the Katz correlation decreases, but its accuracy increases as the mixture approaches a single (pure) component.
The Peng-Robinson EOS provides a better density estimate than the SRK EOS.
Results from either the PR or the SRK EOS in ProMax are slightly more accurate than the comparable results from HYSYS.
Binary interaction parameters which have been optimized to predict VLE behavior may not provide the best density prediction.
At several low temperatures, AGA8 did not provide density estimates. The average errors reported here ignored these missing data. Note that AGA8 is not valid for liquid nor for the extended region near the critical point.
Table 1 indicates that REFPROP and GERG 2004 give equally the best results.
Wichert, E. and Aziz, K., Hydr. Proc., p. 119 (May 1972).
Lemmon, E.W., Huber, M.L., McLinden, M.O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 8.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2007.
Kunz, O., Klimeck, R., Wagner, W., and Jaeschke, M. “The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures,” GERG Technical Monograph 15 (2007)
Hwang, C-A., Duarte-Garza, H., Eubank, P. T., Holste, J. C. Hall, K. R., Gammon, B. E., March, K. N., “Thermodynamic Properties of CO2 + CH4 Mixtures,” GPA RR-138, Gas Processors Association, Tulsa, OK, June 1995
Hall, K. R., Eubank, P. T., Holste, J., Marsh, K.N., “Properties of C02-Rich Mixtures Literature Search and Pure C02 Data, Phase I,” GPA RR-68, A Joint Research Report by Gas Processor Association and the Gas Research Institute, Gas Processors Association, Tulsa, OK, June 1985
Gas density is needed for process simulation and equipment design. For example, accurate predictions of gas density are needed for calculation of pressure drop in piping/pipeline and for vessel sizing. Accurate gas density is also essential for custody transfer metering. Gas density, , is calculated by:
(1)
Where:
&Gas density, kg/m3 (lbm/ft3)
Absolute temperature, K (ºR)
Pressure, kPa (psia)
MW Molecular weight kg/kmole (lbm/lbmole)
Gas compressibility factor
Universal gas constant, 8.314 (kPa)(m3)/(kmole)(K) or 10.73 (psia)(ft3)/(lbmole)(ºR)
In equation 1, “z” represents gas compressibility factor. For ideal gases, “z” is equal to 1. Gas densities are sometime expressed in terms of relative density (specific gravity), , and is defined as:
(2)
Substituting Equation 1 for gas and air into Equation 2 and assuming ideal gas behavior at standard conditions, Equation 2 will be transformed to:
At the standard condition and for simplicity, Equation 3 can be written as
In Equation 1, the key parameter is the compressibility factor “z”, which is a function of pressure, temperature and gas composition. Compressibility factor is a dimensionless surrogate of non-ideal gas density. In general, equations of state are probably the most widely used for calculation of z. They are not necessarily the most accurate. Empirical correlations developed for a specific mixture or a narrow range of mixtures provide better accuracy, but may be less general. An example would be the Katz chart which is quite good when applied to “sweet” pipeline quality gases, but less reliable for gases containing H2S, CO2 and/or N2. Figure 3.2 in Chapter 3 of Gas Conditioning and Processing [1] shows the Katz chart for sweet natural gases as prepared by Standing and Katz [2]. The chart was developed by using experimental data on methane binary mixtures with ethane, propane, butane and other natural gases over a wide range of composition with a maximum molecular weight of 40.
For fiscal metering of natural gas, an accurate experimental database has been developed and compressibility factor correlations, with uncertainties generally within ±0.2%, have been published in the industry standards, AGA Report No. 8 and ISO 12213. A summary of some common “z” correlations and their effect on gas measurement accuracy can be found in reference [3]. Since many people use the Katz compressibility factor chart, the question is often asked how it may be extended to gases containing H2S and CO2. There are two methods available for this application.
The approach proposed by Robinson et al. [4]
The approach proposed by Wichert and Aziz [5]
In this Tip of the Month (TOTM) we will demonstrate the accuracy of the second approach. The details of this method are presented in Chapter 3 of Gas Conditioning and Processing [1].
Let’s consider the gas mixture shown in Table 1 with total acid gas (H2S and CO2) of 14.68 mole percent. At 13.94 MPa (2021 psia) and 58 ºC (136 ºF), the compressibility factors are 0.797 (120.1 kg/m3) and 0.832 (114.8 kg/m3), using Katz chart and Wichert-Aziz method respectively. The percent deviation between two answers from each other is 4.4%.
In order to show the effect of acid gas on compressibility factor determined from Katz chart and Wichert-Aziz methods, we varied the acid gas content of the gas in Table 1 from 0 to 37 mole percent. This was accomplished by diluting the non-acid gas components with a 50:50 mixture of CO2 and H2S. Figure 1 presents the percentage difference between the two methods as a function of acid gas content. The graph shows that as the H2S and CO2 content increases, the deviation of Katz chart from Wichert-Aziz method increases almost linearly. This graph also indicates that the percentage difference between the two methods is greater for the case of diluting gas with only H2S than only CO2.
Next, we used the experimental data reported in the GPA RR-138 [6] and GPA RR 68 [7] to evaluate the accuracy of Katz, Wichert-Aziz and SRK equation of state (EOS) for binary mixtures of CO2 and CH4. The results of this evaluation are shown in Figures 2 through 6, for CO2 content of 9.83 to 100 mole percent. The figures indicate that the Katz correlation accuracy decreases as the mole percent of CO2 increases. However; Figure 5 indicates that as the gas becomes very rich in CO2, the accuracy of the Katz correlation and the Wichert-Aziz method are practically identical. Figure 6 shows that the Katz correlation best predicts the density of pure CO2, and also when the gas approaches pure CH4. The experimental data for pure CO2 in Figure 6 is from GPA RR 68 [7]. Figure 2 through 6 also indicate that the SRK EOS has low accuracy. In this study, a binary interaction parameter of 0.12 between CH4 and CO2 which had been determined from experimental vapor-liquid-equilibrium (VLE) data was used.
Based on the work done in this study, the following can be concluded:
Katz correlation gives accurate results for pipeline quality gases (lean sweet gases)
For pure CO2, Katz correlation is the most accurate in comparison to Wichert-Aziz method or the SRK EOS.
For binary mixture of CH4 and CO2, Wichert-Aziz method gives the most accurate result for CO2 content of between 10 and 90 mole percent.
As H2S and CO2 content increases, the accuracy of the Katz correlation decreases, but its accuracy increases as the mixture approaches a single (pure) component.
The percentage difference between the Katz and Wichert-Aziz methods for gas mixtures containing acid gases is greater for H2S than CO2.
Binary interaction parameters which have been optimized to predict VLE behavior, may not provide the best density prediction.
Campbell, J. M., and Hubbard, R. A., Gas Conditioning and Processing, Vol. 1 (8th Edition, 2nd Printing), Campbell Petroleum Series, Norman, Oklahoma, (2001).
Standing, M.B. and Katz, D.L.; “Density of Natural gas gases,” AIME Trans., 146, 140-49 (1942)
Hannisdal, N.E., “Gas Compression Equations Evaluated,” Oil and Gas J., p. 38-41 (May 4, 1987)
Robinson, D. F. et al. Trans. AIME, Vol 219, P. 54, (1960).
Wichert, E. and Aziz, K., Hydr. Proc., p. 119 (May 1972).
Hwang, C-A., Duarte-Garza, H., Eubank, P. T., Holste, J. C. Hall, K. R., Gammon, B. E., March, K. N., “Thermodynamic Properties of CO2 + CH4 Mixtures,” GPA RR-138, Gas Processors Association, Tulsa, OK, June 1995
Hall, K. R., Eubank, P. T., Holste, J., Marsh, K.N., “Properties of C02-Rich Mixtures Literature Search and Pure C02 Data, Phase I,” GPA RR-68, A Joint Research Report by Gas Processor Association and the Gas Research Institute, Gas Processors Association, Tulsa, OK, June 1985
There are a few computer tools designed specifically for modeling and analysis of complex multiphase systems such as PipePhase, PipeSim, OLGA, and etc [1]. Modeling and simulation of multiphase system, even under steady-state condition, is complex. In the June Tip of the Month (TOTM), we illustrated how the process simulation programs can be used to simulate a natural gas transmission pipeline. These programs are based on mechanistic models and laboratory developed correlations and rely on complex iterative algorithms to perform the tedious calculations.
However, for hand calculation, the Flanigan correlation (which is based on field data for gas dominated transmission pipelines) has been developed and can be used in relatively straight manual calculations. This correlation has proven useful even though it is relatively simple. The relationship between gas flow rate, diameter and pressure drop is represented by Panhandle A gas flow equation (which is based on the Basic Gas Flow Equation modified with field data). The basic equation is single phase flow for gas as is the Panhandle A Equation. The basic equation is derived from basic principles, while the Panhandle A and Flanagan Equation are best fits to a range of field data. Two corrections are made in the Flanagan Equation for two-phase flow:
The value of outlet pressure is adjusted for the pressure loss due to uphill and downhill flow of two phases, including the effect of liquid holdup.
The efficiency term is correlated to reflect measured system performance based on gas velocity and liquid-gas ratio.
For the detail of the Panhandle A equation and the Flanigan correlation, refer to chapter 10 of Gas Conditioning & Processing, Vol 1 [2]. The algorithms for computer simulation are discussed in the Gas Conditioning & Processing, Vol 3, [3].
In this TOTM (which is a continuation of the June TOTM), we will demonstrate the accuracy and application of the Flanigan correlation.
Let’s consider the same case study as was used in the June TOTM. The composition and conditions of the natural gas are shown in Table 1. The gas enters a 20 inch diameter pipeline with an inside diameter of 18.81 inches (47.8 cm) at rate of 180 MMSCFD, equivalent to 19800 lbmole/hr (8989 kgmole/h). The pipeline length and elevation profile are shown in Figure 1. The ambient temperature was assumed to be 60 °F (15.6 °C). The gas enters the line at 1165 psia (8032 kPa) and 95 °F (35 °C). The pipeline is buried under ground with an overall heat transfer coefficient of 1 Btu/hr-ft2-°F (5.68 W/m2-°C). Due to the high content of H2S and CO2 (25.6 and 9.9 mole %, respectively) and to prevent corrosion and hydrate formation, the gas has been dehydrated before entering the pipeline.
Three methods used in this analysis include the basic gas flow equation [2], the Flanigan correlation, and the computer models using the Beggs-Brill correlation with the original liquid hold-up correlation. The SRK equation of state (EOS) was used to perform the phase behavior calculations in the computer based analyses.
The pipeline is divided into 14 segments to match with the number of up-hill and down-hill sections in the line. In addition, each segment is divided into 10 equal increments to achieve higher calculation accuracy. This division is not required for the Flanigan correlation and is done for the sake of comparison with other methods.
Figures 2 through 5 present the pressure, temperature, and liquid formation profiles along the pipeline. Figure 2 indicates that the pressure profiles predicted by the Flanigan matches very well with the results obtained by the more rigorous computer analyses using Beggs-Brill method. However, as expected, due to presence of liquid formation in the line, the basic gas equation results deviate from the two phase flow correlations.
Figure 3 indicates that the temperature profiles predicted by the three correlations fall on top of each other. The small amount of liquid condensation in the line has smaller effect on the temperature profile than on the pressure profile. The liquid formation profiles predicted by the three correlations are shown in Figure 4. As shown in this figure, the amounts of liquid formation predicted by the Flanigan and Beggs-Brill correlations match very well, but the liquid formation predicted by the basic gas equation is different from the two-phase correlations. This can be explained by the fact the pressure drop and consequently the temperature change predicted by the basic equation are different from those predicted by the other two methods.
In this study, the same normal boiling point, relative density, and molecular weight for C6+, as shown in Table 1, are used for all three correlations. Therefore, the same predicted critical properties and acentric factor are used. These properties and the binary interaction parameters are needed to perform the phase behavior calculations by a cubic EOS such as SRK. In addition, the same binary interaction parameters between different components and C6+ are used.
The work reported here clearly shows the value of simple Flanigan correlation and how it can used to model and analyze the behavior of a gas transmission pipeline. However, care must be taken to utilize this correlation properly. Even though the Flanigan correlation is simple, its results match very well with the more rigorous method of Beggs-Brill. However, we expect the agreement between these two correlations deteriorate as the amount of liquid formation in the line increases. As expected the basic gas equation predicted smaller pressure drop in the line due to the fact the liquid formation in the line is ignored. Although the Flanagan Equation results are not sensitive to the elevation correction term, it is important to include the elevation term with a reasonable estimate of the total upward and downward elevation changes. The results are also relatively insensitive to the efficiency factor, therefore average values for liquid and gas ratios can be used for each segment.
Ellul, I. R., Saether, G. and Shippen, M. E., “The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial,” The Proceeding of Pipeline Simulation Interest Group, Paper PSIG 0403, Palm Spring, California, 2004.
Campbell, J. M., and Hubbard, R. A., Gas Conditioning and Processing, Vol. 1 (8th Edition, 2nd Printing), Campbell Petroleum Series, Norman, Oklahoma, 2001.
Maddox, R. N. and L. L. Lilly, Gas Conditioning and Processing, Vol. 3 (2nd Edition), Campbell Petroleum Series, Norman, Oklahoma, 1990.
is the ratio of inertia force to viscous force); therefore, the friction factor decreases (refer to the Moody friction factor diagram in the March 2009 TOTM).
