The existing forms of multiphase flow measurement typically require a pressure vessel that occupies a large volume, has a high wet weight, has a large footprint and costs a relatively large amount of money. Furthermore, vessels require periodic maintenance of cleaning, painting, device calibration, divert valve leakage testing and control valve maintenance. The newer MPFM technologies may weigh in the range of 2000 to 4000 pounds (907 1814 kg), have a footprint of less than 30 ft² (2.8 m^{2}) and a height of generally no more than 9 feet (2.7 m). If the newer MPFM technology is shown to be equivalent to separation measurement then a weight and space improvement can be realized. Depending on the pricing and trending capability of the new technology it would be feasible to have a MPFM on each well. The pricing of these MPFM’s is highly dependent on the size and range of the meter, the uncertainty, whether it uses a gamma radiation source and other items. The one common item among all MPFM’s is they have to be “calibrated (verified in place)”.

For allocation measurement using a vessel the test duration may be anywhere from 8 to 24 hours. Some of that time is to allow operations to perform other tasks while the tests are proceeding. Multiphase meters require no retention time during operation, typically measuring instantaneously every second which provides a flowing profile over time that is not available using a vessel-type flow measurement system. Slugging and other well performance patterns are readily seen in the output of a MPFM.

These MPFMs determine the instantaneous, incremental gas volume fraction, the water cut and mass or volume rates many times per second. Water cut measurement requires knowledge of oil volume, water volume and salinity plus oil and water density. All MPFM vendors have their own special purpose instrumentation along with off-the-shelf process instrumentation like temperature, pressure and differential pressure instruments. All vendors also have their own empirically derived equations that are solved using fast computers. Some vendors use gamma radiation devices for density and water cut, some vendors use a specialized 0 to 100% water cut meter, some vendors use a venturi for rate, some vendors use mathematical cross-correlation for rate. Some vendors partially separate some of the gas from the flow stream. This would be called a partial separation multiphase flow meter.

What are the issues with multiphase measurement besides an infinite number of instantaneous flow regime scenarios and the fact that most systems must be site calibrated?

The main issues with multi-phase measurement are the multiple and varied fluid properties and flow regime present at the point of measurement. The flow regime is a function of how much oil, water and gas is flowing either vertically, horizontally or slanted, the water salinity, water cut (WC), the oil, water and gas densities, the fluid viscosities, particle sizes, surface tensions and others with flow regimes changing in fractions of seconds. Existing, externally mounted instrumentation such as pressure, temperature, differential pressure, permittivity, and conductivity did not provide all the low uncertainty, instantaneous data required to measure the three phases at low average uncertainties over all conditions of velocity, water cut and gas volume fraction.. Instrumentation and software development is ongoing and improving and provides lowered MPFM uncertainties in larger ranges.

One of the ways to represent the multiphase measurement task is to plot the multiphase measurement requirements on a chart of actual superficial gas rate versus actual superficial liquid rate overlaid with lines of constant GVF (Gas Volume Fraction). These graphs may be on either Cartesian or log-log coordinates. Actual testing of multiphase meters in multiple, precise flow loops in the world has shown that for a given type of multiphase meter uncertainty profiles depend on the meter’s technology and the fluid types and rates. Water cut is represented as the third dimension or z-axis to the gas and liquid coordinates.

Actual testing of multiphase meters has shown that fluid rate uncertainties are a function of water cut, salinity, density and GVF. WC uncertainty tends to increase as the water cut falls below 3 to 6% or is greater than 95%. WC uncertainty may also tend to increase in the range where liquid changes from oil continuous to water continuous phase. Both issues are affected by GVF at the point of measurement.

One common, good characteristic of multiphase meters is repeatability per well but each well might be different. Even though rate uncertainties may be high for a given flow stream, repeatability may be 1% or less. In fact, some meter vendors specify repeatability over uncertainty allowing MPFM data to be very trendable.

Older, more mature production tends to have lower gas volume fractions (in the range of 20 – 50%) which is generally easier to measure with an MPFM. However, MPFM’s are relatively expensive (but costs are coming down); consequently, less complex equipment and technology is often used. Examples are Accu-flo and the GLCC (Gas-Liquid Cylindrical Cyclone compact separator) based systems. These systems separate gas and liquid then use single phase technologies to measure oil, water and gas.

Some secondary production methods such as gas lift causes the produced gas volume fraction to be in the range of 85 to 95% which falls more or less in the general area of “slugging” flow, which in the past has been problematic for full range MPFM’s. “Wet gas” production is normally defined as having a gas volume fraction greater than 95% which with today’s MPFM technology has spawned either meters designed for this range or options for a more traditional full range MPFM with high end options.

**Establishing MPFM Requirements:**

Let’s cover the ranges of flow measurement requirements that may be found in oil and gas production which may be illustrated by a GVF map. The map has actual gas rates along the horizontal and actual liquid rates along the vertical. If plotted as a rectangular plot, Figures 1 and 2, the lines of constant GVF run upper right to lower left with the lowest GVF on the bottom and the highest on the top. If plotted on log-log coordinates, Figure 3, the constant GVF lines run in parallel increasing left to right. Also, notice for the log-log plot that as GVF increases the constant GVF lines move further apart.

The variation of fluid properties such as viscosity, salinity, particle size and others from well to well helps to explain why an MPFM may work well on one well and not on another even though the rates are very similar.

**Figure 1**. Variation of actual liquid rate with actual gas rate and gas volume fraction (full GVF range)

**Figure 2**. Variation of actual liquid rate with actual gas rate and gas volume fraction (high GVF range)

**Figure 3**. Variation of actual liquid rate with actual gas rate and gas volume fraction (log scale)

**General MPFM Measurement Process:**

Resolving a multiphase flow stream into oil, water and gas depends on gas density, oil and water density,watercut, conductivity, salinity, capacitance and particle size which may be measurable and effects of flowing viscosity, electrostatic attraction, acid gasses and flow orientation which typically are not measurable.

For most MPFMs it is required to determine the GVF followed by the liquid density or watercut followed by the mass or volumetric rate of each fluid. These iterative, proprietary, calculations are completed at about 30-40 per second on fluid moving anywhere from about 1 m/s to > 30 m/s (3.3 ft/sec to > 98 ft/sec). It is very difficult to describe turndown or rangeability of MPFM systems due to the multiple interactions but may be expressed in terms of each phase.

1. Flowing total fluid density:

Single energy gamma densitometer or a dual acting venturi provides instantaneous flowing fluid density as a function of undetermined gas volume fraction and water cut.

The instantaneous liquid density is highly dependent on instantaneous oil mass or volume rate and density plus the instantaneous mass or volume rate of water and water’s salinity at the instant of measurement.

2. Water-cut is a function of electrical properties as well as water-oil volumes and oil water continuous phase condition:

The measurement of WC uses the electrical property of oil and water called permittivity. There is about a 30:1 to 40:1 permittivity ratio of water to oil but when the fluid is in the water continuous phase conductivity (resistance) is added which almost always affects the measurement. Watercut becomes an iterative solution. If water cut is missed all other calculations are thrown off. When gas is added to oil-water it decreases the average permittivity making the MPFM report more oil.

Water cut or water liquid ratio (WLR) is the volumetric ratio of water volume to total liquid volume:

3. GVF is gas volume to total fluid volume fraction at process conditions:

It is equal to gas void fraction if there is no “Hold-up” or “Slip” between phases.

4. Gas liquid ratio (GLR) is the ratio of actual gas volume (rate) to total liquid volume (rate):

5. The homogeneous (no slip) relation between GVF and GLR:

One of the ongoing issues with multiphase measurement is whether the assumption that “Slip” is 0 (all phases are flowing at the same velocity) is valid for all flow regimes. Some vendors are now evaluating the flow stream cross section thousands of times per second using technology such as scanning sonar that infers fluid properties. PVT analysis is also applied or sampled properties are hand loaded. Some blind testing has shown that at least for one MPFM the measured properties did better than the PVT calculated properties. Direct measurement of salinity is showing promise both as an instrument and in helping to reduce the measurement uncertainty.

The multiphase measurement system has to solve for gas volume fraction, watercut and fluid volumetric or mass velocity depending on different methods (Table 1).

**Table 1**: General methods for measuring multiphase flow variables

New instrumentation in MPFM technology better discern instantaneous oil/water/gas fractions: Here is a summary extracted from thesis by Da Silva [1].

1. Complex permittivity needle probe: This technology can detect the phases of a multiphase flow at its probe tip by simultaneous measurement of the electrical conductivity and permittivity at up to 20 kHz repetition rate.

2. Capacitance wire-mesh sensor: This newly developed technology can obtain two-dimensional images of the phase distribution in pipe cross-section. The sensor can discriminate fluids with*different relative permittivity (dielectric constant) values* in a multiphase flow and achieve frame frequencies of up to 10,000 frames per second.

3. Planar array sensor: The third sensor can be employed to visualize fluid distributions along the surface of objects and near-wall flows. The planar sensor can be mounted onto the wall of pipes or vessels and thus has a minimal influence on the flow. It can be operated by a conductivity-based as well as permittivity-based electronics at imaging speeds of up to 10,000 frames/s.

All three sensor modalities have been employed in different flow applications which are discussed in Da Silva thesis [1].

**Electrical Impedance Methods (Capacitance and Conductance):**

Impedance methods have attracted a great deal of interest due to their non-invasive instrumentation and almost instantaneous dynamic response. Electrical impedance methods operate by characterizing the multiphase fluid flowing through a pipe section as an electrical conductor. Either contacting or non-contacting electrodes are employed to quantify the electrical impedance across the pipe diameter of the multiphase flow line thus enabling determination of the capacitance or conductance of the fluid mixture. The frequency of the input signal determines whether the measurement is in the impedance or the capacitance mode. By measuring the electrical impedance across two electrodes, the measured resistance and capacitance can be calculated, Blaney [2].

The technical and economical advantages of MPFMs are behind the increasing number of MPFM field installations worldwide in recent years. In addition, some of the major operators have made multiple orders of up to 40 MFMSs for full-field application. Figure 4a shows the actual trend up to and including 1999 plus a 2000 forecast published in 1997 [3]. Figure 4b presents the regional distribution of MPFM installed during 1994-2004 worldwide [4]. Figure 4c presents the total number of MPFM installed up to 2010 and estimated forecast beyond 2010. Based on Figure 4c, an extrapolation for the next 5-10 years of MPFM installations suggests that the number of MPFM installation may double from 2010 estimate [4].

**Figure 4a**. Growth rate of MPFM installations [3].

**Figure 4b**. Approximate distribution of MPFM installations worldwide.

**Figure 4c. **MPFM installation and estimated growth forecast [4]

**Summary:**

In summary, multiphase measurement flowmeters became possible with fast computer processors. Virtually all MPFM devices utilize proprietary software solutions combined with a combination of proprietary and off the shelf instrumentation. Recent blind tests suggests that measuring fluid properties instead of PVT calculated properties provided improved certainty. The final observation is that proving an MPFM after installation may only require calibrating instruments or quite like proving gas orifice meters.

To learn more about similar cases and how to minimize operational problems, we suggest attending our**IC3** (Instrumentation and Controls Fundamentals for Facilities Engineers), **G4 (**Gas Conditioning and Processing**)****,** **G5** (Practical Computer Simulation Applications in Gas Processing)** **and **G6** (Gas Treating and Sulfur Recovery) courses.

Fractionation or distillation columns are named based upon the products that they produce overhead, for example, a deethanizer will produce a distillate stream that primarily contains ethane and lighter components such as methane and nitrogen, with a bottoms product of propane and heavier components (C_{3+}). Similarly, a depropanizer will produce a distillate stream that is primarily propane, and the bottoms stream is butane and heavier components (C_{4+}). Chapter 16 of the Gas Conditioning and Processing presents an excellent overview of fractionation and absorption fundamentals [1].

Predicting the optimum feed tray location in the design phase is not easy, particularly if a short-cut calculation is used. Virtually all short-cut calculation methods of estimating feed tray location are based on the assumption of total reflux [1].

This tip of the month (TOTM) will demonstrate how to determine the optimum location of a feed tray in an NGL fractionation or distillation column by a short-cut method and the rigorous method using a process simulator. As an example, we will consider sizing a deethanizer by performing material and energy balances, distillation column short-cut calculations, and rigorous tray-by-tray calculations. Finally, the TOTM will determine the optimum feed tray location by the short-cut and rigorous methods.

**Deethanizer Case Study: **

Let’s consider a deethanizer column with the feed compositions, flow rate, temperature and pressure presented in Table 1. It is desired to size the deethanizer column:

A. To recover 90 mole percent of propane of the feed in the bottoms product and

B. Ethane to propane mole ratio equal to 2 % in the bottoms product

For understanding the concept, the TOTM will do the sizing in three steps:

1. Material and energy balances

2. Distillation column short-cut method

3. Distillation column rigorous tray-by-tray calculations

All of the above steps can be done by the available tools/operations in a process simulator. In this TOTM all calculations are performed using UniSim Design [2] with the Peng-Robinson [3] equation of state option. Figure 1 presents the process flow diagram (operations/tools) for the above steps [2].

**Table 1**. Feed composition and condition

**Figure 1**. Process flow diagram [2]

**Material and Energy Balances:**

Let’s choose ethane as the light key (LK) component and propane as the heavy key (HK) component because their separation requirements are specified. Assume that all of the components lighter than the LK component go to top and all of the components heavier than the HK component go to bottom.

Column condenser pressure is normally set based on the cooling media temperature. Typical operating pressure range for a deethanizer is 375–450 psia (2586–3103 kPa) [1]. Since the feed pressure is 435 psia (3000 kPa), assume the column top pressure is 403 psia (2779 kPa) and bottom pressure is 410 psia (2828 kPa).

We can use the “component splitter” tool in the process simulator to perform initial material and energy balances. The “component splitter is shown in the lower part of Figure 1. The split for propane (HK) is specified (90 mole % goes to bottom and remaining 10 mole % to top). The ethane split is unknown but can be determined by trial and error manually or by using the “adjust” or “solver” tool of the process simulator which essentially varies the ethane spilt so the mole ratio of ethane to propane in the bottoms product becomes 2 %. The estimated ethane split of 97 mole % goes to top.

The estimated mole fractions of the LK and HK components in the top and bottoms and the specified values in the feed stream are presented in in Table 2. The “component splitter” also determines the estimates of top and bottoms flow rates, compositions, temperature and the energy requirement.

**Table 2**. Specified (feed) and estimates of key components compositions

**Distillation column short-cut calculation method:**

Using the top and bottom column pressures and the key components mole fractions (from Table 2), the short-cut distillation column operation in the process simulator can be used to determine the minimum number of equilibrium (theoretical) trays and the minimum reflux ratio (Reflux rate /Distillate rate), (L/D)_{min}. The process flow diagram for the distillation column short-cut method is presented in the middle of Figure 1.

The estimated minimum number of trays using Fenske’s correlation[1,4] is 6.1 and the minimum reflux ratio using Underwood’s correlation [1,5] is (L/D)_{min} = 0.618. The operating reflux ratio is typically in the range of 1.05–1.25 times (L/D)_{min} [1]. Assuming operating reflux ratio is 1.15 times (L/D)_{min} then the operating reflux ratio is 0.711. For this operating reflux ratio, the program determines the number of equilibrium trays using Gilliland’s Correlation [1,6], the optimum feed tray using Kirkbride’s correlation [1,7], components compositions in the overhead and bottoms products, top and bottoms flow rates, temperatures, and condenser and reboiler duties. Table 3 presents the summary of the short-cut results.

**Table 3**. Summary of the specified and calculated values from column short-cut method

Predicting the optimum feed tray location in the design phase is not easy, particularly if a shortcut calculation is used. Virtually all the short-cut calculation methods of estimating feed tray location assume total reflux. A convenient empirical correlation by Kirkbride [1,7] is in Equation 1.

(1)

N + M = S (2)

Where: N = number of equilibrium trays above feed tray

M = number of equilibrium trays below feed tray

B = bottoms rate, moles

D = distillate rate, moles

x_{HKF} = composition of heavy key in the feed

x_{LKF} = composition of light key in the feed

x_{LKB} = composition of light key in the bottoms

x_{HKD} = composition of heavy key in the distillate

S = Number of equilibrium trays in column

Substituting the corresponding parameter values from Tables 2 and 3 in Equations 1 and 2 results in the values of N and M.

Since N + M = 16.9, N = 5.42 and M = 11.48, the estimated optimum feed tray location matches well with the value reported in Table 3. Approximately 5.42 equilibrium trays will be required above the feed tray and 11.48 equilibrium trays (including reboiler) below.

The actual number of trays in the column can be estimated by dividing equilibrium number of trays by the overall tray efficiency. Typical deethanizer overall tray efficiency is 50–70 % [1]. Assuming an overall tray efficiency of 60%, the actual number of trays will be 16.9/0.6 = 28, which is in the range of typical deethanizer actual number of trays of 25–35 [1].

**Distillation column rigorous tray-by-tray calculations:**

By performing the short-cut calculations, we have good estimates of different variables for this deethanizer column. For the specified ethane and propane specifications, 17 equilibrium trays (including reboiler) plus a condenser, top and bottom pressure, estimated feed tray location, and an estimate of operating reflux ratio, rigorous computer simulation can be performed. Note that the number of equilibrium trays, the estimate of feed tray location, and the operating reflux rate were determined in the preceding sections.

Because the short-cut method estimated of feed tray location and other variables, we will use tray-by-tray calculations by computer simulation to improve deethanizer sizing and locate a better optimum feed tray location. The deethanizer column tray-by-tray process flow diagram is shown on the top of Figure 1.

The tray-by-tray rigorous simulation results for the conditions provided in this case study are presented in Table 4 and Figure 2. Several feed tray locations are simulated and the one yielding the lowest condenser duty (reboiler duty) is the optimum location. The optimum feed tray location is tray 3 from top (N=3 and M=14 including reboiler).

**Table 4**. Condenser and reboiler duty vs feed tray location

**Figure 2**. Condenser and reboiler duties as a function of feed tray location

The column temperature profiles as a function of feed tray location are shown in Figure 3. The optimum feed tray location should result in a smooth temperature profile. Improper feed tray location is usually manifested by a sharp discontinuity in the slope of the temperature profile. Multiple feed nozzles and or a feed preheater are typically used to provide flexibility to adjust to changing feed conditions.

**Figure 3**. column temperature profile vs feed tray location

Several key design parameters for feed tray location of 3 are presented in Table 5.

**Table 5**. Summary of key design parameters for feed tray location of 3

Alternatively, a column profile of molar ratio of LK/HK composition with tray number can be plotted. The optimum feed location is determined by matching the molar ratio of LK/HK in the feed to the column profile of LK/HK. This method results in minimizing the reboiler and condenser duties for the distillation column.

**Summary:**

This TOTM demonstrated how a process simulator can be used to size a deethanizer and determine the optimum feed tray location by minimizing the reboiler and condenser duties. This procedure is equally applicable to other NGL fractionators.

Selection of the proper feed tray location is important in order to optimize the operation of the fractionator. Placing the feed tray too high in the tower can result in excessive condenser duty (reflux ratio) to meet distillate product specification. Too low a feed location may result in excessive reboiler heat to meet bottom product specification.

Because short-cut methods provide a rough estimate of feed tray location, a rigorous tray-by-tray simulation program should be used to determine the optimum location of the feed tray by minimizing the condenser/reboiler duties.

Multiple feed nozzles and or a feed preheater are typically used to provide flexibility to adjust to changing feed conditions.

To learn more about similar cases and how to minimize operational problems, we suggest attending our **G4 (**Gas Conditioning and Processing**)****,** **G5** (Practical Computer Simulation Applications in Gas Processing)**, **and **G6** (Gas Treating and Sulfur Recovery) courses.

*PetroSkills *offers consulting expertise on this subject and many others. For more information about these services, visit our website at http://petroskills.com/consulting, or email us at consulting@PetroSkills.com.

*By: Dr. Mahmood Moshfeghian*

*Sign up to receive Tip of the Month emails!*

**References**

- Kirkbride, C. G., Petroleum Refiner 23(9), 321, 1944.
- Gilliland, E. R., Multicomponent Rectification: estimation of number of theoretical plates as a function of reflux ratio, Ind. Eng. Chem., 32, 1220-1223. 1940.
- Underwood, A. J. V, The theory and practice of testing stills. Trans. Inst. Chem. Eng., 10, 112-158, 1932.
- Fenske, M. R. Fractionation of straight-run Pennsylvania gasoline, Ind. Eng. Chem.; 24 482-485.1932.
- Peng, D.Y. and D. B. Robinson, Ind. Eng. Chem. Fundam. 15, 59-64, 1976.
- UniSim Design R443, Build 19153, Honeywell International Inc., 2017.
- Campbell, J.M., Gas Conditioning and Processing, Volume 2: The Equipment Modules, 9
^{th}Edition, 2^{nd}Printing, Editors Hubbard, R. and Snow–McGregor, K., Campbell Petroleum Series, Norman, Oklahoma, 2014

In this TOTM, we will evaluate pressure and temperature applicability ranges and accuracy of the ideal water content correlation for sweet natural gases. In addition, the performance of the ideal water content correlations will be compared with the equation of state based rigorous calculation methods.

**Equilibrium Water Content at Low Pressures **

Assuming vapor phase is an ideal gas and liquid phase is an ideal solution, the equality of water fugacities at equilibrium simplifies to the Raoult’s law.

(1)

Where:

*y _{w}* = mole fraction water in the vapor phase

*P ^{V}* = vapor pressure of water at system temperature

*P* = system pressure

*x _{w}* = mol fraction water in the liquid water phase

The liquid mole fraction can be taken as *x _{w}* = 1.0 because of the low solubility of the hydrocarbon phase in the aqueous phase and to cover cases where no liquid hydrocarbon is present – just vapor + liquid water. Thus, for a known pressure and water vapor pressure the mole fraction water in the vapor phase is found from Equation 1.

Under ideal conditions, the mole fraction of water in the gas phase can be estimated by dividing water vapor pressure, *P ^{V}*, at the specified temperature, T, by the system pressure, P. The vapor pressure of pure water, from 0 to 360 °C, (32 to 680 °F) can be calculated by the following correlation [3].

(2)

Where:

τ = 1 – (T/T_{C})

The critical temperature,* T _{C}* = 647.096 K (1164.77 °R) and critical pressure,

a_{1} = −7.85951783

a_{2} = 1.84408259

a_{3} = −11.7866497

a_{4} = 22.6807411

a_{5} = −15.9618719

a_{6} = 1.80122502

Knowing one kmole of water = 18 kg (lbmole=18 lb_{m}) and one kmole of gases occupy 23.64 Sm^{3} at standard condition of 15 °C and 101.3 kPa (one lbmole of gases occupy 379.5 SCF at standard condition of 60 °F and 14.7 psia), the ideal water content is calculated by:

(3)

**Bukacek Correlation**

Bukacek [4] suggested a relatively simple correlation for the water content of lean sweet gases as follows:

(4)

(5)

where *T* is in °F and *P ^{V}* and

This correlation is reported to be accurate for temperatures between 60 and 460°F (15.5 and 238°C) and for pressure from 15 to 10,000 psia (0.105 to 69.97 MPa). The pair of equations in this correlation is simple in appearance. The added complexity that is missing is that it requires an accurate estimate of the vapor pressure of pure water. In this study, we have used equation 2 for water vapor pressure.

**Evaluation of the Raoult’s Law (Ideal) Water Content**

The performance of the Raoult’s law for estimating water content of sweet natural gases was evaluated against Bukacek correlation [4], GCAP software [5] and two simulation programs. The water content of GCAP is based on Figure 6.1 of Campbell book [1]. The SRK EOS (Soave-Redlich-Kwong equation of state) with its default binary interaction parameters was used in both simulation programs. The composition of gases needed for simulation study are shown in Table 1. The Raoult’s law, GCAP program and Bukacek correlation are independent of gas composition.

In simulators, there are several options to predict the equilibrium water content of a gas stream which may give different answers. In this study, the mole fraction of water in the desired stream is multiplied 47430 to get lb_{m}/MMscf (or 761420 to get kg/10^{6} Sm^{3}).

Figure 1 through 5 present the percent deviations of water content estimated by Raoult’s law from GCAP program, and two simulation programs (Sim B and Sim C). In each figure, the percent deviations of Raoult’s law water content from those predicted by GCAP, Sim B and Sim C are presented on the vertical axis. The Raoult’s law and GCAP methods are independent of composition while Sim B and Sim C are composition dependent.

The pressure values are 25, 50, 100, 200, and 300 psia (172, 344, 690 1379, and 2069 kPa); respectively. For each pressure, the results for four isotherms of 40, 80, 120, and 160 °F (4.4, 26.7, 48.9, 71.1 °C) are presented.

Figure 1 indicates that at low pressure of 25 psia (172 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -4 to +1%, span of 5%.

Figure 2 indicates that at low pressure of 50 psia (345 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -3 to +2%, span of 5%.

Figure 3 indicates that at low pressure of 100 psia (690 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -1 to +4%, span of 5%.

**Fig 1.** Water content by Raoult’s law vs GCAP and two simulators at 25 psia (172 kPa)

**Fig 2. **Water content by Raoult’s law vs GCAP and two simulators at 50 psia (345 kPa)

**Fig 3.** Water content by Raoult’s law vs GCAP and two simulators at 100 psia (690 kPa)

The analysis of Figures 1 through 3 indicates that the for pressures up to 100 psia (690 kPa) the Raoult’s law water content deviations from real state water content are within about +4% and -4%.

Figure 4 indicates that at the higher pressure of 200 psia (1379 kPa), the deviations of Raoult’s law water content from the other three methods are higher and within 0 to +9%, span of 9%. This figure also indicates that the Raoult’s law percent deviation from GCAP is the largest while simulator B gives lower values of deviations.

Figure 5 indicates that at the higher pressure of 300 psia (2069 kPa), the deviations of Raoult’s law water content from the other three methods are within +5 to +14%, span of 9%. This figure also indicates that the Raoult’s law percent deviations from GCAP is the largest while simulator B gives lower values of deviations.

In general, for a combination of pressure and temperature which results in less dense gas (low pressure and high temperature), there are fewer deviations of Raoult’s law from simulator results that are based on an EOS (equation of state).

Table 2 presents the absolute percent deviations and the overall average absolute percent deviations of Raoult’s law from GCAP, Sim B, Sim C, and Bukacek methods for 140 evaluated points. Note for each temperature, four gases with compositions shown in Table 1 were evaluated. Table 2 indicates that Raoult’s law results have the least deviation from Bukacek and the most deviation is from GCAP and the overall average absolute percent deviations is less than 4 % for pressures up to 300 psia (2069 kPa) and temperatures up to 160°F (71°C).

**Fig 4.** Water content by Raoult’s law vs GCAP and two simulators at 200 psia (1379 kPa)

**Fig 5. **Water content by Raoult’s law vs GCAP and two simulators at 300 psia (2069 kPa)

**Table 2.** Raoult’s law water content average absolute percent deviations from 4 methods

In addition to the sweet natural gas system, we have determined the equilibrium water mole fraction of propane vapor by simulators B and C, Bukacek method, and Raoul’s law (ideal). Table 3 presents the percent deviation of these 4 methods from the smoothed experimental water mole fraction reported in the GPA RR 132 [6]. The accuracy of these four methods are within experimental data. It should be noted that for temperatures of 53.8°F and 47.9°F, the corresponding experimental pressures were 98 psia and 90 psia, respectively. Since at these pressures and temperatures the state of propane was liquid, these two pressures were reduced slightly to 97.35 psia and 88.6 psia to produce 100% propane vapor.

**Table 3.** Propane vapor water content predictions vs RR 132 experimental data [6]

**Conclusions:**

The performance of Raoult’s law for predicting the water content of sweet natural gases against 4 methods is presented. The four methods are GCAP, Simulators A and B and Bukacek correlation. The following conclusions can be made:

- The Raoult’s law (Eq. 1) combined with an expression to estimate water vapor pressure (Eq. 2) is a simple tool for predicting the water content of sweet natural gases.
- In general, for a combination of pressure and temperature which results in less dense gas (low pressure and high temperature), there are fewer deviations of Raoult’s law from simulator results that are based on an EOS (equation of state).
- Table 2 indicates that Raoult’s water content predictions have the least deviation from Bukacek correlation and the most deviations from GCAP.
- The overall average absolute percent deviations for the systems considered in this tip are less than 4% and the maximum deviation is less than 13.6% (Table 2) for pressures up to 300 psia (2069 kPa) and temperatures up to 160°F (71°C).

To learn more about similar cases and how to minimize operational problems, we suggest attending our **G4 (**Gas Conditioning and Processing**),** **G5** (Practical Computer Simulation Applications in Gas Processing)**, **and **G6** (Gas Treating and Sulfur Recovery) courses.

*PetroSkills *offers consulting expertise on this subject and many others. For more information about these services, visit our website at http://petroskills.com/consulting, or email us at consulting@PetroSkills.com.

*By: Dr. Mahmood Moshfeghian*

*Interested in receiving Tip of the Month email updates? Sign up today!*

References

- R. Kobayashi, “Water content of ethane, propane, and their mixtures in equilibrium with water and hydrates,” Gas Processor Association Research Report (GPA RR 132), Tulsa, Oklahoma, 1991.andSong, K
- GCAP 9.2.1, Gas Conditioning and Processing, PetroSkills/Campbell, Norman, Oklahoma, 2015.
- Bukacek, R.F., “Equilibrium Moisture Content of Natural Gases” Research Bulletin IGT, Chicago, vol 8, 198-200, 1959.
- Wagner, W. and Pruss, A., J. Phys. Chem. Reference Data, 22, 783–787, 1993.
- GPSA Engineering Data Book, Section 20, Volume 2, 13
^{th}Edition, Gas Processors and Suppliers Association, Tulsa, Oklahoma, 2012. - Campbell, J.M., Gas Conditioning and Processing, Volume 1: The Basic Principles, 9
^{th}Edition, 2^{nd}Printing, Editors Hubbard, R. and Snow–McGregor, K., Campbell Petroleum Series, Norman, Oklahoma, 2014.

The details of a simple single-stage refrigeration system and a refrigeration system employing one flash tank economizer and two stages of compression are given in Chapter 15 of Gas Conditioning and Processing, Volume 2 [2]. The process flow diagram for a flash tank economizer refrigeration system with two stages of compression is shown in Figure 1. Note that provisions have been made to consider pressure drop in the suction line of the first stage compressor.

**Figure 1**. Process flow diagram for a refrigeration system with a flash tank economizer and two stages of compression

Let’s consider removing 10.391×10^{6} kJ/h (2886 kW) from a process gas at -35°C and rejecting it to the environment by the condenser at 35°C. Pure propane is used as the working fluid. In this study, all the simulations were performed by UniSim Design software [3]. Assuming 5 kPa pressure drop in the chiller, the pressure of saturated vapor leaving the chiller at -35°C is 137.4 kPa. Also, assuming 30 kPa pressure drop in the suction line, the first stage compressor suction pressure is 107.4 kPa. The condensing propane pressure at 35°C is 1220 kPa. The condenser pressure drop plus the pressure drop in the line from the compressor discharge to the condenser was assumed to be 50 kPa; therefore, compressor discharge pressure is 1270 kPa. In addition, an adiabatic efficiency of 75% was assumed for both stages of compression.

Assuming no pressure drop between the two stages, Figure 2 presents the variation of the compressor stages 1, 2, and the total power as a function of the interstage pressure.

**Method 1:**

The “Databook” option from “Tools” menu of the UniSim was used to generate powers (dependent variables) as a function of interstage pressure (Independent variable). The interstage pressure was varied from 200 kPa to 1000 kPa with an increment of 10 kPa.

As can be seen in this figure, the optimum interstage pressure is about 470 kPa. This pressure corresponds to the minimum total power and also the equality of stages 1 and 2 power.

**Figure 2**. Impact of interstage pressure on compressor power.

Similarly, Figure 3 presents the compressor total power, stages 1 and 2 compression ratios. Figure 3 clearly shows that the minimum total compressor power does not occur at equal stage compression ratios of 3.44. Yet Chapter 14 (Compressors) of Gas Conditioning and Processing, Volume 2 [2] states “The total power is typically minimized when the ratio in each stage is the same.” Why is that not the case here?

The ideal optimum interstage pressure based on equal compression ratios can be found by the following equation:

The equal compression ratio for each stage is R_{1 }= 369.3/107.4 = 3.44 and R_{2 }= 1270/369.3 = 3.44. The above equation is valid if the mass flow rates through both stages were the same and the suction temperatures for both stages were equal. In a refrigeration system with flash tank economizers and multiple stages of compression, usually neither of these conditions are met. In this case, the mass flow rates through stages 1 and 2 are 3.106 x 10^{4} and 4.171 x 10 ^{4} kg/h, respectively. The suction temperatures are -35.8°C and 21.1°C, respectively.

**Figure 3**. Impact of interstage pressure on the total compressor power and stages compression ratio.

**Method 2: **

An alternative and easier method to determine the optimum interstage pressure is the “Adjust” tool in the simulation software. As shown in Figure 1, ADJ-2 was used to vary interstage pressure (stream R-12) so that first stage “R-Comp-LP Power” power becomes equal the second stage “R-Comp-HP Power” power. The setup for ADJ-2 is shown in Figure 4 and the detail of iterations and final results are shown in Figure 5. As shown in Figure 5, the optimum interstage pressure is 471.3 kPa and each stage compression power is 793 kW which adds up to a minimum total power of 1586 kW.

**Summary:**

Because the mass flow rates and suction temperatures were different in each stage of compression, the minimum total compressor power does not occur at equal compression ratios in each stage.

Two methods of “Databook” and “Adjust” were used to minimize the total compression power and condenser duty by selecting the optimum interstage pressure.

In the first method “Databook”, the optimum interstage was determined by minimizing the total compressor power. In the second method “Adjust”, the interstate pressure was determined by equalizing stages 1 and 2 powers. Both methods gave the same interstage pressure and total compressor power.

**Figure 4**. Detail of “Adjust” set up

**Figure 5**. Iteration and final results of “Adjust”

For the same chiller duty, chiller and condenser temperatures, and pressure drops, the results of the flash tank economizer system are compared with the results of a simple refrigeration system in Table 1. This table indicates that the compressor power and condenser duty saving are 17.4 % and 6.97 %, respectively. The interstage pressure drop is unique to flash tank economizer and its effect is the reduction of the power saving when compared to the simple refrigeration system and increases the condenser duty.

**Table 1**. Refrigeration specifications and calculated results

To learn more about similar cases and how to minimize operational problems, we suggest attending our **G4 (**Gas Conditioning and Processing**)****,** **G5** (Practical Computer Simulation Applications in Gas Processing)**, **and **G6** (Gas Treating and Sulfur Recovery) courses.

*PetroSkills *offers consulting expertise on this subject and many others. For more information about these services, visit our website at http://petroskills.com/consulting, or email us at consulting@PetroSkills.com.

*Sign up to receive Tip of the Month emails!*

**References:**

- Moshfeghian, M., http://www.jmcampbell.com/tip-of-the-month/2008/01/refrigeration-with-flash-economizer-vs-simple-refrigeration-system/, Tip of the Month, January 2008.
- Printing, Editors Hubbard,
^{nd}Edition, 2^{th}Campbell, J.M., “Gas Conditioning and Processing, Volume 2: The Equipment Modules,” 9R. and Snow–McGregor, K., Campbell Petroleum Series, Norman, Oklahoma, 2014. - UniSim Design R443, Build 19153, Honeywell International Inc., 2017.

Based on ASTM D323, there are figures and monographs for conversion of RVP to TVP for NGLs (Natural Gas Liquids) and crude oil at a specified temperature [1, 2]. Continuing the February 2016 [3] Tip of The Month (TOTM), this tip will present simple correlations for determination TVP and RVPE (Reid Vapor Pressure Equivalent) as described by ASTM Standard D6377-14 [4] at a specified temperature. The correlations are easy to use for hand or spreadsheet calculations.

Standard D6377 describes the use of automated vapor pressure instruments to determine the vapor pressure exerted in the vacuum of crude oils. This test method is suitable for testing samples that exert a vapor pressure between 25 kPa and 180 kPa at 37.8 °C (3.63 psia and 26.1 psia at 100 °F) at vapor-liquid ratios from 4:1 to 0.02:1 (V/L = X = 4 to 0.02). A TVP reading can be determined by taking vapor pressure measurements at different expansion (V/L = X) ratios and extrapolating to V/L= X = 0. Refer to reference [4] for detail description of this standard procedure.

To demonstrate the ASTM Standard D6377 procedure we generated vapor pressures of a sample condensate shown in Table 1 at four expansion ratios of X = 1, 2, 3, 4 using ProMax simulation program [5] based on the Soave Redlich Kwong equation of state [6]. In this table, the heavy ends are presented by F-fractions and their properties are shown in Table 2.

Table 3 presents the generated vapor pressure at 37.8 °C (100 °F) for four expansion ratios by ProMax mimicking the experimental measurements.

**Quadratic Equation:**

The vapor pressures (VP) as a function of expansion ratio (X) in Table 3 were curve fitted to a quadratic equation as follows.

VP = a + bX +cX^{2}

The fitted parameters a, b, and c are presented in Table 4 for pressures of Table 3 in kPa and psia.

^{1}AAPD = Average Absolute Percent Deviation

^{2}MAPD = Maximum Absolute Percent Deviation

^{3}NP = Number of data Points (NP)

Figure 1 presents the generated vapor pressure (filled circles) and the quadratic fit (solid line) of the condensate of Table 1. The extrapolated vapor pressure at X=0 (expansion ratio) is 8.56 psia (59.0 kPa). This extrapolated vapor pressure matches very closely with the predicted bubble point of condensate of Table 1 by ProMax.

**Exponential Equation:**

The vapor pressures (VP) as a function of expansion ratio (V/L = X) in Table 3 can also be fitted to an exponential equation as follows.

VP = αe^{(βX)}

The fitted parameters α and β are presented in Table 5 for pressures in Table 3 in kPa and psia.

^{1}AAPD = Average Absolute Percent Deviation

^{2}MAPD = Maximum Absolute Percent Deviation

^{3}NP = Number of data Points (NP)

Figure 2 presents the generated vapor pressure (filled circles) and the exponential fit (solid line) of the condensate of Table 1. The extrapolated vapor pressure at X=0 (expansion ratio) is 8.56 psia (59.0 kPa). Similar to the quadratic fit, this extrapolated vapor pressure matches very closely with the predicted bubble point of condensate of Table 1 by ProMax.

**ASTM D6377 RVPE:**

The RVPE (Reid Vapor Pressure Equivalent) can be estimated by the following correlations:

a. Average bias of different crude oils [7]

RVPE = A x VPCR^{X=4} (at 100 °F or 37.8°C) + B

where A = 0.752 and B=0.88 psi (6.07 kPa).

For the condensate of Table 1 and from Table 3, VPCR^{X=4} = 7.63 psi (52.63 kPa)

RVPE = 0.752 x 7.63 + 0.88 = 6.62 psi

RVPE = 0.752 x 52.62 + 6.07 = 45.64 kPa

b. New correlation for ‘live’ crude oils (for samples in pressurized ﬂoating piston cylinders) [4]

RVPE = 0.834 x VPCR^{X=4} = 7.63 psi (52.63 kPa)

RVPE = 0.834 x 7.63 = 6.36 psi

RVPE = 0.834 x 52.62 = 43.89 psi

c. New correlation for ‘dead’ crude oils (for samples in non-pressurized 1-liter sample containers) [4]

RVPE = 0.915 x VPCR^{X=4} (at 100 °F or 37.8°C)

**Summary:**

For accurate measurements, standard procedures outlined in ASTM D6377–14 and other guidelines should be consulted. Several organizations are currently working to improve the accuracy of TVP estimation from RVP and/or VPCRx (ASTM D6377) measurement techniques. In all cases, Federal and State Laws and Regulations should be followed for safety and environmental protection.

A quadratic and an exponential correlation were presented to curve fit the measured vapor pressures at different expansion (V/L = X) ratios (e.g. 1, 2, 3, and 4). To demonstrate ASTM D6377 true vapor pressure measurements, a sample condensate vapor pressures at expansion ratios of V/L = X = 1, 2, 3, and 4 were estimated by ProMax, mimicking vapor pressure measurements. The estimated vapor pressures were curve fitted and extrapolated to zero expansion ratio (V/L = X) to estimate TVP. Then correlations of D6377 were used to estimate RVPE using the vapor pressure measurement at the expansion ratio of V/L = X = 4.

Figures 1 and 2 present almost a linear relationship between vapor pressure vs expansion ratio due to the narrow range of expansion ratio (1 through 4). As shown in the Appendix, for a wider range of expansion ratios (5 through 50), vapor pressure vs expansion ratio is non-linear. In addition, the quadratic fit with three coefficients gives a better fit compared to exponential fit with only two coefficients.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Advanced Applications in Gas Processing), and PF4 (Oil Production and Processing Facilities), courses.

PetroSkills offers consulting expertise on this subject and many others. For more information about these services, visit our website at http://petroskills.com/consulting, or email us at consulting@PetroSkills.com.

By: Dr. Mahmood Moshfeghian

References:

- Campbell, J.M., Gas Conditioning and Processing, Volume 1: The Basic Principles, 9th Edition, 2nd Printing, Editors Hubbard, R. and Snow–McGregor, K., Campbell Petroleum Series, Norman, Oklahoma, 2014.
- ASTM D323: Standard Test Method for Vapor Pressure of Petroleum Products (Reid Method), 1999.
- Moshfeghian, M., http://www.jmcampbell.com/tip-of-the-month/2016/02/correlations-for-conversion-between-true-and-reid-vapor-pressures-tvp-and-rvp/, 2016
- ASTM D6377: Standard Test Method for Determination of Vapor Pressure of Crude Oil: VPCRX (Expansion Method), 2014
- ProMax 4.0, Bryan Research and Engineering, Inc., Bryan, Texas, 2017.
- Soave, G., Chem. Eng. Sci. Vol. 27, No. 6, p. 1197, 1972.

ASTM D6377: Standard Test Method for Determination of Vapor Pressure of Crude Oil: VPCRx (Expansion Method), 2003.

**Appendix:**

^{1}AAPD = Average Absolute Percent Deviation

^{2}MAPD = Maximum Absolute Percent Deviation

^{3}NP = Number of data Points (NP)

]]>