A Simple Model for Estimation of Methanol Loss to Vapor Phase

As discussed in the May 2011 Tip Of The Month (TOTM), for hydrate inhibition, the most commonly used equilibrium inhibitors used in the upstream and midstream sectors of the oil and gas business are:  monoethylene or diethylene glycol (MEG or DEG) and methanol.  In general, glycols are more commonly used in systems requiring continuous inhibition. The glycol is typically recovered, regenerated and recirculated.  Methanol is more commonly used in systems that do not require continuous inhibition, i.e. systems only requiring inhibition during cold weather or upset conditions. Methanol is not commonly recovered and reused because of the difficulty of separation of the methanol from water. There are obviously exceptions to this. For example, methanol is used as a continuous inhibitor in a few offshore installations and in a handful of gas processing facilities. Another significant disadvantage of methanol relative to glycol is the high methanol losses to both the liquid hydrocarbon and vapor phase.

In the May TOTM, we reviewed experimental VLE data for methanol-hydrocarbon systems. We also revisited Figure 6.20 of reference [1] for methanol loss to the vapor phase using the experimental vapor liquid equilibrium data reported in the Gas Processors Association Research Report 117 (GPA RR 117) [2].

In this Tip of the Month, we will investigate further the methanol loss to the vapor phase and present a simple correlation to estimate methanol K-values. The K-value is defined as the mole fraction of methanol in vapor phase/mole fraction of methanol in aqueous liquid phase. Since the effect of gas composition is small, the K-values will be expressed only in terms of pressure and temperature. The estimated K-value can be used to calculate the rate of methanol loss to the vapor phase.  The objective of this TOTM is to develop a simple and generalized model for estimation of methanol losses in terms of K-values and present a generalized chart which is less dependent on the weight percent of methanol in the liquid aqueous phase.  A step-by-step calculation procedure using K-values will be presented as well.

Figure 1 (FPS). Effect of methanol concentration on methanol loss at -10 °F.

Figure 1 (SI). Effect of methanol concentration on methanol loss at -23.3 °C.

Methanol Loss in Terms of K-Value:

The polar version of Peng-Robinson [3] equation of state (PR EOS) in ProMax [4] was used to generate the required data in the following sections.

Figure 1 indicates that presenting charts for ratio of vapor to liquid composition in terms lb_m of methanol per MMSCF/(weight % methanol in aqueous phase) or kg of methanol per 10⁶ Sm³/(weight % methanol in aqueous phase) is very sensitive to the methanol concentration in liquid phase. Similar methanol concentration dependencies, as shown in Figure 1, were also observed for other isotherms. An alternative is to use the K-Values for the y-axis. However, we have found that the range of ratio of K-Values at 15 weight % to 25 weight % MeOH is from 0.95 to 1.0. Similarly, the range of ratio of K-Values at 50 weight% to 25 weight % MeOH is from 1.0 to 1.03. These ranges are much smaller than the corresponding ratios of methanol losses. Therefore, in the subsequent charts as well as for modeling we will use K-values as the dependent variables.

The K-Values over 25 weight % methanol solution are presented in Figure 2 as a function of pressure and temperature. It should be noted that Figure 2 can be used for methanol concentration up to 70 weight % in aqueous phase.

As shown in Figure 2, at lower temperatures considerable curvature is observed, which makes modeling rather difficult. However, if the same chart is replotted in terms of pressure times K-value, (P)(K) on the y-axis, as shown in Figure 3, much less curvature is observed.

In order to use Figure 2 to calculate the rate of methanol loss to vapor phase, the following steps should be followed:

1. At specified pressure (P) and temperature (T), read methanol K-Value from Figure 2.
2. Convert weight % of methanol (wt%) in aqueous phase to mole fraction (x) by: (1A)
3. Calculate methanol mole fraction in the gas phase (y) by y = (K)(x) (1B)
4. Calculate mass of methanol in vapor phase

FPS: (MeOH lb_m/MMSCF) = [(y lbmole MeOH)/(Total lbmole of gas)](32 lb_m/lbmole

MeOH) (lbmole of gas/379.5SCF) (10⁶ SCF/MMSCF) = 84 321.5 y ≈ 84 322 y    (1C)

SI: (MeOH kg/10⁶ Sm³) = [(y kmole MeOH)/(Total kmole of gas)](32 kg/kmole MeOH) (kmole of gas/23.64 Sm³) (10⁶) = 1 353 638 y ≈ 1 353 640 y     (1D)

A worked example is shown in Appendix A.

Figure 2 (FPS). Variation of methanol K-Values as a function of pressure and temperature.

Figure 2 (SI). Variation of methanol K-Values as a function of pressure and temperature.

Development of Mathematical Model

An alternative to Figure 2 is a simple and generalized correlation which can estimate the K-values easily. This will be handy when one intends to use spreadsheet calculations to estimate methanol vapor losses. A simple model presented by Wilson [5] for light hydrocarbon mixtures is shown in Equation 2.

(2)

where:

Tc_i critical temperature, °R or K

Pc_i critical pressure, psi, kPa or bar

ω_i acentric factor

P system pressure, psia, kPa or bar

T system temperature, °R or K

This correlation is applicable to low and moderate pressure, up to 500 Psia (3.5 MPa), and the K-values are assumed to be independent of composition.

We propose to use a similar equation in the form of equation 3 to estimate methanol K-value at specified pressure and temperature.

(3)

In the above equation, P^*, T^* and ω^* are the normalized pressure, temperature, and acentric factor; respectively. The same data that were used to generate Figure 2 were also used regress the above equation parameters using a non-linear program and the following expressions were developed.

P^* =  P/35  with P in Psia  (4)

T^* = T/615 with T in °R (5)

ω^* = 2.95-(0.02607)P^*+(8.92828×10^-5)(P^*)²-0.851257/ T^* (6)

We will refer to the above model as the “K-Value Express”. Spreadsheet estimation of methanol vapor losses can be developed by using equation 3 to determine methanol K values, and then applying the calculation method as discussed for the application of Figure 2.

Overall, 156 data points covering temperature range of -10 to 100 °F, and pressure range of 100 to 5000 psia for  25 weight % methanol solution were used. The overall Average Absolute Percent Error (AAPE) for the K-Values was 3.6% with a Maximum Absolute Percent Error (MAPE) for K was 19.7%. The MAPE occurred at -10 °F and 2000 psia where ProMax K was 0.001 and K-Value Express K was 0.0008.

Figure 3 presents the comparison between the methanol K-Values calculated by ProMax (solid lines in Figure 3) and those estimated by K-Value Express (identified by dashed line in Figure 3).

Results and Discussion:

The K-Value Express model with the parameters shown in Equations 4 to 6 were used without any further fitting to predict K-values over 15 and 50 weight % methanol for wide ranges of pressures and temperature. For the case of 15 weight % methanol with 149 data points, the AAPE for K was 5.2% with a MAPE of 14.7%. For the case 50 weight % methanol with 155 data points, the AAPE for K was 3.6% with a MAPE for K was 22.1%.

The maximum average absolute % error occurred at -10 °F and 2000 psia where ProMax K was 0.00098 and K-Value Express K was 0.00077 for the case of 50 weight % methanol.

Figure 4 presents the K-Value Express K-Values vs ProMax K-Values for more than 500 data points over 15, 25, and 50 weight % methanol solution. This figure indicates relatively good agreement between the two methods.

Figure 5 is a revised and extended version of Figure 6.20 in reference [1]. Notice y-axis and x-axis variables are switched.  In this way the dependent variable is on the y-axis and independent variable is on x-axis.

Conclusion:

ProMax was used to reproduce Figure 6.20 in reference 1 and presented here in this work as Figure 5.  This figure covers wider ranges of pressure, temperature, and methanol weight percent (up to 70 weight %). However, we suggest using Figure 2 as a better chart since it is less sensitive to methanol weight % in aqueous phase.  In addition, we developed a simple and generalized K-Value Express model that can be used to estimate methanol K-values for wide ranges of pressure, temperature, and methanol weight %. As shown in Figures 3 and 4, the proposed model is in good agreement with the results obtained from ProMax. The sample calculations in Appendix indicate good agreement between the methanol losses to vapor phase obtained from Figures 2, 3, 5, and the K-Values Express model.

Figure 3 (FPS). Comparison of predicted methanol K-Values by ProMax and the proposed Express K-Value model.

Figure 3 (SI). Comparison of predicted methanol K-Values by ProMax and the proposed Express K-Value model.

Figure 4. Accuracy of the proposed Express K-Value model against ProMax

Figure 5. Variation of methanol loss to vapor phase with pressure and temperature for methanol concentration of 25 weight % in the aqueous phase

Figure 5 (SI). Variation of methanol loss to vapor phase with pressure and temperature for methanol concentration of 25 weight % in the aqueous phase

To learn more about similar cases and how to minimize operational problems, we suggest attending the John M. Campbell courses; G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing-Special).

John M. Campbell Consulting (JMCC) offers consulting expertise on this subject and many others. For more information about the services JMCC provides, visit our website at www.jmcampbellconsulting.com, or email your consulting needs to consulting@jmcampbell.com.

By Dr. Mahmood Moshfeghian

Reference:

1. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
2. Ng, H. J., Chen, C. J., and D. B. Robinson, D.B.; RR-117, “The Solubility of Methanol or Glycol in Water – Hydrocarbon Systems,” Gas Processors Association (Mar. 1988).
3. Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., Vol. 15, p. 59, 1976.
4. ProMax 3.1, Bryan Research and Engineering, Inc, Bryan, Texas, 2010.
5. Wilson, G., “A modified Redlich-Kwong equation of state applicable to general physical data calculations,” Paper No15C, 65^th AIChE National meeting, May, (1968).

Appendix A – Sample Calculations

Determine mass of methanol in vapor per MMSCF (10⁶ Sm³) at 1000 psia (6 897 kPa) and 10 °F (-12.2 °C) over a rich solution containing 25 weight % methanol.

Solution: Method 1 (Figure 5)

At 1000 psia (6 897 kPa) and 10 °F (-12.2 °C) using Figure 5;

FPS:

lbm MeOH/MMSCF/Wt%=0.5  or  lb_m MeOH/MMSCF = (0.5) (25) = 12.5

SI:

kg MeOH/10⁶ Sm³/Wt% = 8.2  or  MeOH/10⁶ Sm³ = (8.2) (25) = 205

Solution: Method 2 (Figure 2 or 3)

At 1000 psia (6 897 kPa) and 10 °F (-12.2 °C) using Figure 2; K=0.00095 or

Figure 3; PK=0.95 psia which gives K=0.00095

Convert 25 wt% to mole fraction by Eq 1A:

Calculate y by Eq 1B: y = (K)(x) = (0.00095)(0.1579) = 0.00015

FPS: Using Eq 1C: (MeOH lb_m/MMSCF) = 84 322 y = 84322(0.00015)  =  12.6

SI: Using Eq 1D: (MeOH kg/10⁶ Sm³) = 1 353 640 y = 1 353 640(0.00015) = 203

Solution: Method 3 (Express K-Value Model)

At 1000 psia (6 897 kPa) and 10 °F (-12.2 °C) using Eqs 3 through 6 calculate K.

Using Eq 4: P^* =  P/35 = 1000/35 = 28.57

Using Eq 5: T^* = T/615 = (460+10)/615 = 0.762

Using Equation 6:

ω^* = 2.95-(0.02607)P^*+(8.92828×10^-5)(P^*)²-0.851257/ T^*

ω^* = 2.95-(0.02607)( 28.57)+(8.92828×10^-5)( 28.57)²-0.851257/ 0.762

ω^* = 1.161

Using Eq 3:

Calculate methanol mole fraction in gas phase ( y) by Eq 1B:

y = (K)(x) = (0.00093)(0.1579) = 0.000147

FPS: Using Eq 1C: (MeOH lb_m/MMSCF) = 84 322 y = 84322(0.000147)  =  12.4

SI: Using Eq 1D: (MeOH kg/10⁶ Sm³) = 1 353 640 y = 1 353 640(0.000147)  = 199