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Operational study of a monoethylene glycol (MEG) desalination pilot plant. Part I: Development of a new method for the estimation of MEG content in the presence of NaCl solid particles
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Operational study of a monoethylene glycol (MEG) desalination pilot plant. Part I: Development of a new method for the estimation of MEG content in the presence of NaCl solid particles Ruozhou Hou a , Rafael A. Lopez Rodriguez a , Simon A. Crawley-Boevey b , Brian E. Messenger b , Peter J. Martin a,∗ a b
School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK Schlumberger, Buckingham Gate, Gatwick Airport, West Sussex, RH6 0NZ, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
Conductivity measurements at different temperatureswere undertaken to investigate the
Received 22 August 2018
variation of conductivity as a function of sodium chloride solid particle concentrations in
Received in revised form 8 January
sodium chloride-saturated aqueous monoethylene glycol (MEG) solutions. A methodology
2019
has been developed that is capable of quantifying the relationship between the conductivity
Accepted 20 February 2019
measurement, sodium chloride particle concentration, temperature, and MEG concentration
Available online 2 March 2019
in the brine-saturated aqueous solution. The results indicate that the conductivity decreases
Keywords:
whereas in the absence solid particles, the conductivity of sodium chloride-saturated aque-
Monoethylene glycol (MEG)
ous MEG solutions is a polynomial function of temperature and MEG concentration. It is
exponentially as the solid sodium chloride particle concentration increases from 0 to 30 wt%,
Desalination
demonstrated that a single, universal empirical model can be developed to quantify the
Pilot plant
relationship between the conductivity and relevant process parameters across the whole
Conductivity
experimental range. The methodology can be readily adopted for in situ monitoring of solid
Sodium chloride
salt particle concentration and estimation of MEG loss in a typical industrial MEG reclama-
Sedimentation
tion process, leading to the establishment of more effective process control and operation strategies. © 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.
1.
Introduction
Monoethylene glycol (MEG) is a chemicalthat is widely used by the oil and gas industry to thermodynamically inhibit gas hydrate formation in production wellheads and pipelines (Mokhatab et al., 2007; Sloan and
to inject a large quantity of MEG into wellheads and pipelines. This can depress the hydrate formation threshold to well below the operating temperature, thus inhibiting the formation of hydrates in the gas production process. The MEG concentration required to achieve gas hydrate inhibition can be determined by the Hammerschmidt equation
Koh, 2008). Gas hydrates are solid crystalline compounds, composed of
(Hammerschmidt, 1939). Typically, MEG is added into the production
natural gas components and water that may form readily under typical deep-sea pipeline operating conditions of high pressure and low temperature. They have a strong tendency to agglomerate and plug the
pipeline in excess of the quantities required by the equation and the MEG streams in gas production flowlines typically contain 30–60 wt%
pipeline, leading to production disruptions. Gas hydrate formation has
MEG that has been in contact with the wet natural gas stream is often referred to as (water-) rich MEG, and may contain a variety of contaminants, including dissolved salts from the rock formations and
long been considered a major risk in offshore deep-water gas production operations. One economical solution to address this problem is
∗
MEG.
corrosion products from the pipelines, as well as production chemicals and dissolved and free hydrocarbons. Natural gas extracted from deep-water reservoirs, in particular, often comes with a large quantity
Corresponding author. of produced water that may have salinity close to saturation. Those E-mail address: [email protected] (P.J. Martin). https://doi.org/10.1016/j.cherd.2019.02.035 0263-8762/© 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
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Nomenclature ˛ ak , bij ˇn m c0 , c1 , c2 CMEG ,R CMEG,SaF CNaCl ,L CNaCl ,S d1 , d2 f, g i, j, k L S+L
T
Slope coefficient of log S+L vs log L (−) Coefficients of L model (mS/cm ◦ Ck, ◦ mS/cm Ci, respectively) Coefficient of L polynomial function as function of CMEG,SaF (mS/cm ◦ Cn) Coefficient of L polynomial function as function of T (mS/cm) Coefficients of S+L /L model (–,◦ C−1 , –) MEG wt% in MEG-water-NaCl solution based on all solution constituents MEG wt% in MEG-water-NaCl solution based on MEG and water only NaCl wt% in MEG-water-NaCl solution wt% based on all solution constituents Solid NaCl particle wt% suspended in solution Coefficients of simplified polynomial for CNaCl,S Generic functions Generic indices Conductivity of MEG-water-NaCl solution with no suspended solids (mS/cm) Conductivity of MEG-water-NaCl solution also containing suspended solid NaCl particles (mS/cm) Temperature (◦ C)
concentrated brines, once mixed into the MEG stream in which the mineral salts are generally much less soluble, carry a higher risk of scale formation and deposition in the production line, which may also present a serious risk to flow assurance if left untreated (Tomson et al., 2006). The large volumes of MEG required to ensure effective inhibition of gas hydrate formation throughout the entire length of the production pipeline necessitate recovery of the valuable glycol components for reinjection. The production pipeline can be several hundred kilometres in length and the MEG inventory of the systems can be in the order of several thousand metric tonnes. The contaminants in the MEG stream must be removed before the MEG can be recycled and injected back into the wellheads and pipelines. This is usually done in a MEG Recovery Unit (MRU). To date, there are more than 30 industrial-scale MRUs in operation in the world. The MEG recovery process can be divided into three operating sections (Nazzer and Keogh, 2006; Teixeira et al., 2016): 1 Pre-treatment section, where hydrocarbons and divalent salts are removed first from the rich MEG stream by heating and by chemical dosing combined with filtration, respectively. 2 Desalination section, where the liquid components (i.e., MEG and water) are recovered by contacting the rich MEG stream with a hot high-MEG-content recycle stream in a flash vaporisation separator. The vaporised MEG and water components are condensed back into the salt-free liquid form and subsequently fed into the regeneration section. The remaining monovalent salt content (mainly NaCl), on the other hand, accumulates and crystallises from the MEG recycle stream and can be discharged from the flash separator holding the high-MEG-content recycle stream. 3 Regeneration section, where the salt-free MEG and water components are separated from each other via reflux distillation to produce a (water-) lean MEG stream for reinjection at wellheads or pipelines.
Fig. 1 – A schematic illustration of the pilot plant MEG desalination system. increasingly important contributor to global gas production, demand for new and better technologies for more efficient salt removal and MEG recovery has never been stronger. In 2010, Cameron Flow Control Technology (UK) Ltd., now Cameron, a Schlumberger company, donated a 1/100th scale, 100 kg/h feed flow rate MEG desalination pilot plant system to The University of Manchester. The research presented here investigates some of the key processes involved in the desalination section operation, aiming to develop more efficient operation guidance and strategies for implementation at MEG desalination plants. The donated system focuses on the liquid components recovery and monovalent salt removal operations. It employs Schlumberger proprietary MEG reclamation technology, in which the monovalent salt crystals formed in the flash separator settle under gravity through a 6 m high, NaCl-saturated brine filled column (the downcomer) before disposal. The height of the downcomer facilitates the dis-entrainment of MEG from the settling salt crystals, resulting in a significant reduction in MEG losses during salt disposal and in a reduced demand for fresh MEG to replace these MEG losses. Fig. 1 shows a schematic illustration of the system. To minimise MEG losses during salt disposal, it is important that the MEG content in the downcomer is monitored in situ continuously. This enables the operators to better control the salt removal process. However, the downcomer contains a multicomponent dynamic inventory, in which the crystallised salt particles settle through a sodium chloride-saturated aqueous solution, with gradients of temperature, dissolved salt content, MEG concentration, and solids concentration along the whole height of the downcomer. Real-time measurements of MEG concentrations in such a complex environment are extremely difficult because of this multivariant complexity. It has been reported that electrical conductivity measurements coupled with the measurement of ultrasound velocity (Vajari, 2012; Yang et al., 2012; Yang and Tohidi, 2013) or density (Sandengen and Kaasa, 2006) could be used to determine both the MEG and salt concentrations from tertiary solutions consisting of water, MEG, and NaCl. Field trials showed that the technique required only a few simple operations and was capable of rapid, near-real-time estimation of MEG and salt contents at offshore platforms (Bonyad et al., 2011; Macpherson et al., 2012). Unfortunately, this technique cannot be applied to the in situ MEG content analysis inside the downcomer, as the presence of the salt crystal particles will interfere severely with the ultrasound velocity, density, and conductivity measurements, rendering the approach infeasible. In this study, we demonstrate that based on conductivity and temperature measurement combinations, a new and simple method can be developed to estimate both the MEG concentration and salt solid particle concentrations for NaCl-saturated MEG-water solutions. The method can be readily adapted for in situ MEG concentration analysis
One of the key targets in the MEG recovery process design and engineering is to achieve high efficiency in salt removal whilst incurring a minimum loss of MEG. As deep-water gas exploration is becoming an
in the downcomer section, thereby enabling more effective downcomer operation and minimising MEG losses. The paper is divided into two parts:
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
Table 1 – Detailed experimentalcondition matrix. MEG concentration (wt% in salt-free terms)
Temperature (◦ C)
NaCl solid particle concentration (wt%)
100 75 50 25 0
24, 45, 55, 75, 89 23, 36, 50, 69, 79 22, 42, 52, 61, 70 29, 40, 49, 59, 69 22, 41, 52, 62, 72
0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30
Part I focuses on the methodology development. Conductivity measurements at different temperatures and different NaCl solid particle concentrations in NaCl-saturated aqueous MEG solutions were conducted. The measurements enable establishing an empirical relationship describing the variation of conductivity as functions of temperature, MEG concentration, and NaCl particle concentration in NaCl-saturated aqueous solutions. The inverse solutions to the functions lead to the estimation of the MEG and salt solid concentrations from the measured conductivity data. Part II focuses on the MEG loss control strategy. In situ MEG concentration data inside the downcomer was collected using the methodology developed herein. The data were then utilised to determine how the downcomer could best be operated to control and minimise the MEG losses in the pilot plant MEG desalination system.
2.
Experimental
2.1.
Materials
The MEG was industrial grade, minimum 99% purity. It was purchased from Hydra Technologies Ltd., U.K., and used as received. NaCl salt used to make saturated solutions was a vacuum dried, off-the-shelf product, also of industrial grade. The salt used to make solid concentrations was recrystallized NaCl product from the pilot plant MEG desalination system, such that the particle size distribution was representative of that in the operating process. This was collected from the salt tank, washed by the saturated solution, filtered, dried in an oven at 70 ◦ C, and finally sieved into the 40– 125 m size range for experimental use. Fig. 2 confirms that the averaged NaCl particle size within the downcomer ranged from 38.4 (D10) to 124.9 (D90) m and that the feed flowrate had no effect on the particle size distribution. Appendix A details how the samples were taken from the downcomer and particle size distributions were measured. Ordinary tap water was used throughout the experiments.
2.2.
Procedure
The experiments were conducted in a factorial design fashion, with five levels of MEG concentration (in salt-free terms), five levels of temperature, and seven levels of NaCl solid particle concentration investigated. Table 1 lists the detailed experimental conditions. Following industry convention, in this paper the MEG contents are expressed in salt-free terms. The real MEG content CMEG,R in wt% and salt-free MEG content CMEG,SaF in wt% are connected via the following equation: CMEG,R = CMEG,SaF (
100 − CNaCl,L ) 100
(1)
where CNaCl,L denotes the salt concentration in wt% in solution.
Each experiment set started with the preparation of a MEG + water solution of different MEG concentration (e.g., 100% MEG + 0% water, or 75% MEG + 25% water). An excess of vacuum-dried NaCl was then added to the prepared solution, and the mixture was heated to the required temperature under constant stirring on an IKA C-Mag HS 7 magnetic stirrer with ceramic heating plate to make the NaCl-saturated MEG + water solution of different MEG concentration. After the solution was fully saturated, stirring was stopped. Allowing time for the NaCl particles to fully settle, approximately 200 ml of the NaCl-saturated supernatant liquid was then poured into a pre-weighed 250 ml beaker. The NaCl-saturated supernatant liquid was kept under constant stirring, and the temperature was maintained at the target value. Drops of fresh MEG + water solution of the same MEG concentration were added as necessary for fine adjustment of the saturation level. After the beaker containing the saturated solution was weighed, from which the net weight of the saturated solution could be extracted, the conductivity probe was lowered into the solution to start the conductivity and temperature measurements. The measurements continued under constant stirring, with sieved and recrystallized NaCl solid particles added in steps to make 5%, 10%, 15%, 20%, 25%, and 30% of solid concentration by weight in the NaCl-saturated MEG + water solution. Both the conductivity and temperature measurements were collected using a pre-calibrated Hamilton Conducell 4USF-PG 120 four-electrode conductivity probe. Data was logged onto a computer through dedicated software at a rate of 12 data points per minute. Typically for each experimental condition set, about 60 conductivity/temperature measurements were collected over a 5-min period. The averages of these measurements were taken as the measured conductivity and temperature values for the experimental condition set. All the raw conductivity data sets showed good consistency. The typical standard deviation for any randomly chosen data set was around 0.3% of the mean value.
3.
Results and discussion
3.1.
Conductivity measurement results
Fig. 3 shows the conductivity variation as a function of the solid NaCl concentrations in different concentrations of NaClsaturated MEG solutions and at different temperatures. Note that the measured conductivity data are presented in the logarithmic scale. In most cases, the logarithmic conductivity value decreased linearly as the solid NaCl concentration increased. The slope and intercept of each linear data set depended on the temperature and MEG concentration in the NaCl-saturated solution. Mathematically this is equivalent to the following expression: logS+L = logL (T, CMEG,SaF ) + ˛ (T, CMEG,SaF ) · CNaCl,S
(2)
in which S+L denotes the conductivities at different concentrations of NaCl solids in mS/cm and L denotes the conductivities, in mS/cm, of solid-free NaCl-saturated solutions of different MEG concentrations at different temperatures, which also represents the intercepts of the fitted lines on the vertical axis; CNaCl,S denotes the solid NaCl concentration in wt%; ˛ is the slope coefficient, to be determined through data fitting; and T is the temperature in ◦ C. L (T, CMEG,SaF ) and ˛(T, CMEG,SaF ) mean that these two parameters are a function
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
D50
D90
D10
160
Parcle Size (μm)
D10
D50
D90
140 120 100 80 60 40 20 0
0.0
1.0
2.0
3.0
4.0
5.0
0.0
1.0
Distance to Top of the Downcomer (m)
2.0
3.0
4.0
Distance to Top of the Downcomer (m)
(a)
(b) 180
D50
D90
D10
160
Parcle Size (μm)
D10
D50
D90
140 120 100 80 60 40 20 0
0.0
1.0
2.0
3.0
4.0
0.0
5.0
1.0
2.0
3.0
4.0
Fig. 2 – NaCl solid particle size distributions along the height of the downcomer at a salt influx of (a) 300, (b) 500, (c) 700, and (d) 900 kg/h m2 , respectively. D10, D50 and D90 refer to the particle sizes where 10%, 50% and 90% of the distribution lie below the respective diameters. of temperature and salt-free MEG concentration. Note that ˛(T, CMEG,SaF ) will be negative, which makes S+L converge as CNaCl,S increases. To build a valid predicative model to account for the variation of S+L as a function of CNaCl,S , a separate model describing the L as a function of T and CMEG,SaF also has to be developed. One of the approaches to achieve this is to use the thermodynamic equilibrium model that is based on an extended form of the mean-spherical approximation (MSA) theory coupled with a mixing rule (Wang et al., 2004) to calculate the conductivities of saturated MEG + water + NaCl solutions at different temperatures. Unfortunately, for our specific system, very limited number of parameter data can be found in literature (Wang et al., 2013). Thus, in this work we decided to adopt an empirical data fitting approach for the L predictions instead. Fig. 4 plots the change of L as a function of temperature at different salt-free MEG concentrations in the NaCl-saturated MEG solutions. In the absence of solid particles, the averaged conductivity of NaCl-saturated aqueous MEG solutions increases with either decreasing MEG concentration or increasing temperature. Close inspection of the graphs in Fig. 4 indicates that the conductivity data seem to fit well into a polynomial function of the temperature with MEG concentration-dependent coefficients:
L =
n
ˇn (CMEG,SaF ) · T n
(3)
where n = 1, 2, 3, . . . and ˇn (CMEG,SaF ) denote coefficients, which are a function of the salt-free MEG concentration and can be determined through data fitting. The same could also be true to fit L into a polynomial function of the MEG concentration with temperature-dependent coefficients: L =
m (T) · (CMEG,SaF )m
(4)
m
where m = 1, 2, 3, . . . and m (T) denote coefficients, which are a function of the temperature.
3.2.
Data fitting
All the data fitting work was done on the Matlab platform, using multivariate regression techniques and least squares analysis (Draper and Smith, 1981). Conductivity L can be considered to be a function of temperature and salt-free MEG concentration. This can also be expressed by applying the separation of the variables as L (T, CMEG,SaF ) = f (T) · g(CMEG,SaF )
(5)
where f(T) and g(CMEG,SaF ) are functions of T and CMEG,SaF only, respectively. It can be inferred from Fig. 4 that the L data would fit well to a polynomial function of T or CMEG,SaF when the other variable is fixed. It is thus plausible to put f(T) and
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100% MEG at 45 °C 100% MEG at 75 °C
Conducvity (mS/cm)
100% MEG at 24 °C 100% MEG at 55 °C 100% MEG at 89 °C 40
4
75% MEG at 23 °C 75% MEG at 50 °C 75% MEG at 79 °C
100
75% MEG at 36 °C 75% MEG at 69 °C
10
0
5
10
20
25
30
0
5
10
15
20
NaCl Solid Concentraon (wt%)
NaCl Solid Concentraon (wt%)
(a)
(b) 700
50% MEG at 42 °C 50% MEG at 61 °C
25% MEG at 29 °C 25% MEG at 49 °C 25% MEG at 69 °C
Conducvity (mS/cm)
50% MEG at 22 °C 50% MEG at 52 °C 50% MEG at 70 °C
300
15
30
25
30
25
30
25% MEG at 40 °C 25% MEG at 59 °C
70
0
5
10
15
20
25
30
0
5
10
15
20
NaCl Solid Concentraon (wt%)
NaCl Solid Concentraon (wt%)
(c)
(d)
0% MEG at 22 °C 0% MEG at 52 °C 0% MEG at 72 °C
0% MEG at 41 °C 0% MEG at 62 °C
100
Fig. 3 – Conductivity variations versus solid NaCl concentrations at different temperatures in NaCl-saturated solutions of (a) 100% MEG, (b) 75% MEG, (c) 50% MEG, (d) 25% MEG, and (e) 0% MEG. Discrete markers represent the measured conductivity data, whereas dotted lines are calculated conductivity values using Eq. (7). g(CMEG,SaF ) into a polynomial function of T and CMEG,SaF , respectively. After inspection of the experimental data, it was found that an optimal L model takes the following form:
L =
3 k=0
ak T k +
4 3
bij T i (100 − CMEG,SaF )
j
(6)
Table 2 – L model coefficients. a0 – a3
b11 – b14
b21 –b24
b31 –b34
2.862458061 –0.077034183 0.010410457 –6.01435E-05
0.013718637 0.00123537 –1.57337E-05 1.71693E-07
0.000558272 –7.157E-05 1.53244E-06 –1.13449E-08
–5.7528E-06 6.93116E-07 –1.52117E-08 1.06858E-10
i=1 j=1
The model coefficients ak and bij are listed in Table 2 and were determined through data fitting of the raw L data set. Fig. 4 illustrates a comparison of the measured and modelfitted L data. The data cover the MEG concentration (on a salt-free basis) ranging from 0% to 100% and temperature rang-
ing from 20 to 90 ◦ C. They are the respective compositional and temperature ranges expected within the downcomer. It can be seen from Fig. 4 that the model is able to effectively track the variation of measured data within the experimental range. The typical comparative errors between the measured and calculated conductivity values are well below 5%. The squared
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We rearranged the L model from Eq. (6) into the following form: 3 4 (100 − CMEG,SaF ) +
bi3 T i
i=1 3
(100 − CMEG,SaF )
3
bi4 T 4
i=1
3
+ Fig. 4 – Variation of L as a function of temperature at different salt-free MEG concentrations in the NaCl-saturated MEG solutions, with measured data (discrete markers) and model-fitted function (solid lines).
3
Table 3 – S+L model coefficients. c1
c2
–0.004367837
–1.44819E-05
9.84524E-06
Pearson’s correlation coefficient, which is a measure of the linear correlation between the measured and calculated L data, was calculated to be R2 = 99.89%. For the S+L data, a similar approach was applied to determine the coefficient ˛(T, CMEG,SaF ) shown in Eq. (2). The following model was found to produce the optimum results:
⁄L ) = (c0 + c1 T + c2 (100 − CMEG,SaF )) · CNaCl,S
(7)
The fitted values of the coefficients c0 , c1 , and c2 listed in Table 3 were determined through the data fitting of the log(S+L /L ) versus CNaCl,S values at different temperatures. A comparison of the measured and model calculated S+L data is illustrated in Fig. 3, which shows that the model fits well to the measured data across all the experimental ranges. The mean sum of the squares of the residuals is only 10.25 for 175 S+L data points ranging from 4.46 to 440.06 mS/cm. The squared Pearson’s correlation coefficient R2 is 99.94%.
3.3.
(100 − CMEG,SaF )
2
bi4 T 4
i=1 3
3
bi1 T i (100 − CMEG,SaF ) +
Inverse algorithm
We have so far developed empirical models to calculate L from temperature T and salt-free MEG concentration in NaClsaturated solution CMEG,SaF and S+L from L , T, CMEG,SaF and NaCl solid concentration CNaCl,S . In practical applications such as a MEG desalination system, however, it is desirable to deduce CMEG,SaF and CNaCl,S from the measured S+L data. All conductivity probes were equipped with integrated temperature measurement, thus T can be considered as a known quantity. Moreover, at any fixed T, the values of L and CMEG,SaF are both unique. This implies that it is possible to acquire CMEG,SaF and CNaCl,S through a dual measurement approach, which, in the current case, includes taking the conductivity measurements of the solid NaCl suspension (i.e., S+L ) and the supernatant liquid phase only (i.e., L ) subsequently. The second measurement leads to a solution for CMEG,SaF . This can then be used, together with the S+L measurement, to produce CNaCl,S .
ak T k − L
k=0
bi4 T 4
3
i=1
c0
log(
3 i=1
+
S+L
bi2 T i
i=1
=0
(8)
bi4 T 4
i=1
The roots of this equation are the eigenvalues of its companion matrix (Williams, 2010). Out of the four roots for (100 – CMEG,SaF ), only one root carries realistic physical meaning. With (100 – CMEG,SaF ) determined, CNaCl,S can be calculated from the logarithmic L model: CNaCl,S =
1 × log [c0 + c1 T + c2 (100 − CMEG,SaF )]
S+L
L
(9)
We also found that CNaCl,S can be equally well reproduced using the following simpler polynomial model: CNaCl,S = d1
L S+L
− 1 + d2
L S+L
2
−1
(10)
where d1 and d2 were determined through data fitting to be 117.8532 and –114.9946, respectively. Fig. 5 illustrates the comparison of the actual and inversely calculated CMEG,SaF and CNaCl,S values. Accurate MEG concentration predictions are achieved, with the differences between the calculated and real values at different levels almost negligible. The accuracy of CNaCl,S predictions is also reasonably satisfactory, considering the complex nature of particulate slurries (MacTaggart et al., 1993).
4.
Model validation
To validate the model predictions, six samples were taken from the downcomer during a randomly chosen operational run of the MEG desalination pilot plant. They were taken from each of the six conductivity probes installed on the downcomer to map the conductivity profile changes along the full height of the downcomer. The operation of the pilot plant and exact locations of the conductivity probes are discussed in detail in Part II of this paper. The collected samples were stored in 500 ml plastic sample bottles and allowed to cool to room temperature. They were then poured into 500 ml glass beakers where the conductivity measurements were conducted. A Hamilton Conducell 4USF ARC 120 conductivity probe was used to measure the suspension conductivity S+L (under constant mixing using an IKA C-Mag HS 7 magnetic stirrer) and supernatant conductivity L of each sample. The data were
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
Fig. 5 – Comparisons of the actual and inversely calculated (a) salt free MEG concentration, CMEG,SaF and (b) NaCl solid concentration, CNaCl,S . Table 4 – Model validation results. Sample location to top of the downcomer (m)
0.00 0.85 1.85 2.85 3.85 4.85
Laboratory conductivity measurements
Measured data by evaporation
T (◦ C)
S+L (mS/cm)
L (mS/cm)
CMEG,SaF (%)
CNaCl,S (%)
CMEG,SaF (%)
CNaCl,S (%)
22.8 22.8 22.8 22.8 22.8 22.8
67.82 66.97 69.46 71.26 85.03 113.23
80.16 78.95 79.15 81.34 91.26 118.64
40.4 40.9 40.8 40.0 36.3 27.5
18 17 14 14 8 5
38.1 38.2 36.8 34.5 31.0 25.5
15 16 16 15 13 9
then fed to Eqs. (8) and (10) to calculate the CMEG,SaF and CNaCl,S , respectively. A small representative portion of the particle suspension and supernatant liquid were also withdrawn from each sample. They were used to measure CMEG,SaF and CNaCl,S through an evaporation method in each sample (see Appendix A for descriptions of the method in detail). Table 4 compares the model-calculated CMEG,SaF and CNaCl,S with the measured data. The models not only correctly presented the trend of changes but also produced both CMEG,SaF and CNaCl,S predictions with reasonably good accuracies.
5.
Inverse algorithm predictions
Conclusions
In this investigation, electrical conductivity measurements at different temperatures were undertaken to investigate the variation of conductivity as a function of NaCl solid particle concentration in sodium chloride-saturated aqueous MEG solutions. Experimental results show that the conductivity decreases exponentially as the solid NaCl particle concentration increases from 0 to 30 wt%, whereas, in the absence solid particles, the conductivity of NaCl-saturated aqueous MEG solutions is a polynomial function of temperature and MEG concentration. Empirical models, based on multivariate regression analysis of the experimental conductivity measurement data, were developed to quantify the variation of conductivity as a function of the solid NaCl concentration, temperature, and MEG concentration in both the presence and absence of solid NaCl particles. Typical model prediction errors for conductivities are well below 5% across the whole experimental range covering solid NaCl concentration changes from 0 to 30%, temperature changes from 20 to 90 ◦ C, and MEG concentration changes in salt-free terms from 0 to 100%.
The models can also be utilised, through inverse algorithms, for the determination of solid NaCl particle and MEG concentrations or for determination of MEG losses in MEG reclamation processes. The calculation of solid NaCl particle concentrations, in particular, requires a dual measurement approach, which includes taking the subsequent conductivity measurements of both the particle suspension and the supernatant liquid phase only. As the measurement of conductivity is, in principle, a nonspecific technique, it is reasonable to assert that the same methodology can be readily tailored into a real-time solid particle concentration monitoring tool for any solid–liquid two-phase particulate suspension system. For such a tool to be valid, the conductivity of the supernatant liquid phase should be independent of the presence of solid particulate materials. The resulting model would be established through robust on-process training and calibrations.
Declaration of interests None.
Research data https://doi.org/10.17632/bjhc5t86vw.1.
Acknowledgements This work was financially supported by The University of Manchester EPSRC Knowledge Transfer Account (KTA002) and Cameron Flow Control Technology (UK) Limited, now Cameron, a Schlumberger company. The authors wish to
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
acknowledge Mr Andrew Downes from Cameron Flow Control Technology (UK) Limited for his assistance in running the MEG pilot plant.
Appendix A Appendix A1 Measurements of NaCl solid particle size distributions inside the downcomer
351
subsequently deduced using the linear interpolation in the NaCl in water + MEG saturation charts. Then the same procedure was followed with the solid suspension samples, from which the total NaCl content in each sample was calculated. The solid NaCl concentration, CNaCl,S , was obtained by determining the dissolved NaCl content from the total NaCl content.
References Samples were withdrawn from six sample points at 1 m intervals in the 6 m tall downcomer through the sampling lines. The sampling lines were all made of 3/8 inch OD stainless steel pipes and were inserted into the downcomer with a 45◦ downwards angle to avoid NaCl solid accumulation at the tip of each sampling point. The distances from each sampling point tip to the top of the downcomer were 0.0, 0.85, 1.85, 2.85, 3.85, and 4.85 m, respectively. The collected samples were maintained at their original temperatures and measured on a Malvern Mastersizer 3000 in saturated brines for particle size distributions within at most 3 h after the sample collections (Fig. A1). The salt influx and feed flow rate are related via the following equation: SINaCl =
QM,F CNaCl,L,F 2 4 (DDown )
(A(1)-(1)
where SINaCl denotes the salt influx in the downcomer in kg/h m2 , QM,F denotes the mass flow rate of the feed to the flash separator in kg/h, CNaCl,L,F denotes the dissolved NaCl concentration in the feed stream in wt%, and DDown denotes the inner diameter of the downcomer in m.
Appendix A2 Description of the evaporation method to measure the CMEG,SaF and CNaCl,S in a sample The method also took a dual measurement approach. A small quantity of NaCl-saturated supernatant liquid (∼0.5 ml) was taken from each sample and weighed in pre-weighed Petri dishes. The sample was heated in a vacuum oven (Thermo Scientific, Vacutherm) to 120 ◦ C at 0.1 bar until all the liquid content was evaporated. The Petri dishes were weighed again, from which the dissolved NaCl content in each NaCl-saturated supernatant liquid sample, CNaCl,L , could be calculated. The MEG content, CMEG,R , or in salt-free terms CMEG,SaF , could be
Fig. A1 – A typical size distribution profile for NaCl solid samples taken from the downcomer at different salt influxes.
Bonyad, H., Zare, M., Mosayyebi, M.R., Mazloum, S., Tohidi, B., 2011. Field evaluation of a hydrate inhibition monitoring system. Paper Presented at the 10th Offshore Mediterranean Conference and Exhibition, Also available at: https://www.onepetro.org/download/conference-paper/ OMC-2011-050?id=conference-paper%2FOMC-2011-050. (Accessed 26 July 2018. Draper, N.R., Smith, H., 1981. Applied Regression Analysis, second ed. John Wiley & Sons, New York. Hammerschmidt, E.G., 1939. Gas hydrate formation in natural gas pipelines. Oil Gas J. 37 (50), 66–71. Macpherson, C., Glenat, P., Mazloum, S., Youg, I., 2012. Successful deployment of a novel hydrate inhibition monitoring system in a North Sea gas field. Paper Presented at the Tekna 23rd International Oil Field Chemistry Symposium. MacTaggart, R.S., Nasr-El-Din, H.A., Masliyah, J.H., 1993. A conductivity probe for local solids concentration mixing tank measuring in a slurry. Sep. Technol. 3, 151–160. Mokhatab, S., Wilkens, R.J., Leontaritis, K.J., 2007. A review of strategies for solving gas-hydrate problems in subsea pipelines. Energy Sources Part A: Recovery Util. Environ. Eff. 29 (1), 39–45. Nazzer, C.A., Keogh, J., 2006. Advances in glycol reclamation technology. Offshore Technology Conference 2006 vol. 2, 820–826, Also available at: https://www.onepetro.org/ download/conference-paper/OTC-18010-MS?id=conferencepaper%2FOTC-18010-MS. (Accessed 26 July 2018). Sandengen, K., Kaasa, B., 2006. Estimation of monoethylene glycol (MEG) content in water + MEG + NaCl + NaHCO3 solutions. J. Chem. Eng. Data 51, 443–447. Sloan, E.D., Koh, C.A., 2008. Clathrate Hydrates of Natural Gases, third ed. CRC Press, Taylor & Francis Group, Boca Raton, Florida. Teixeira, A.M., Arinelli, Lde-O., de-Medeiros, J.L., Araujo, Ode-Q.F., 2016. Exergy analysis of monoethylene glycol recovery processes for hydrate inhibition in offshore natural gas fields. J. Nat. Gas Sci. Eng. 35, 798–813. Tomson, M.B., Ken, A.T., Fu, G., Al-Thubaiti, M., Shen, D., Shipley, H.J., 2006. Scale formation and prevention in the presence of hydrate inhibitors. Hesperia 11 (2), 248–258. Vajari, S.M., 2012. Development of Hydrate Inhibition Monitoring and Initial Formation Detection Techniques, PhD Thesis. Heriot-Watt University, UK. Wang, P., Anderko, A., Young, R.D., 2004. Modeling electrical conductivity in concentrated and mixed-solvent electrolyte solutions. Ind. Eng. Chem. Res. 43, 8083–8092. Wang, P., Kosinski, J.J., Anderko, A., Springer, R.D., Lencka, M.M., 2013. Ethylene glycol and its mixtures with water and electrolytes: thermodynamic and transport properties. Ind. Eng. Chem. Res. 52, 15968–15987. Williams, M.P., 2010. Solving polynomial equations using linear algebra. Johns Hopkins Appl. Tech. Dig. 28, 354–363. Yang, J., Tohidi, B., 2013. Determination of hydrate inhibitor concentrations by measuring electrical conductivity and acoustic velocity. Energy Fuels 27, 736–742. Yang, J., Chapoy, A., Mazloum, S., Tohidi, B., 2012. A novel technique for monitoring hydrate safety margin. SPE Prod. Oper. 27 (4), 376–381.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Operational study of a monoethylene glycol (MEG) desalination pilot plant. Part I: Development of a new method for the estimation of MEG content in the presence of NaCl solid particles Ruozhou Hou a , Rafael A. Lopez Rodriguez a , Simon A. Crawley-Boevey b , Brian E. Messenger b , Peter J. Martin a,∗ a b
School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK Schlumberger, Buckingham Gate, Gatwick Airport, West Sussex, RH6 0NZ, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
Conductivity measurements at different temperatureswere undertaken to investigate the
Received 22 August 2018
variation of conductivity as a function of sodium chloride solid particle concentrations in
Received in revised form 8 January
sodium chloride-saturated aqueous monoethylene glycol (MEG) solutions. A methodology
2019
has been developed that is capable of quantifying the relationship between the conductivity
Accepted 20 February 2019
measurement, sodium chloride particle concentration, temperature, and MEG concentration
Available online 2 March 2019
in the brine-saturated aqueous solution. The results indicate that the conductivity decreases
Keywords:
whereas in the absence solid particles, the conductivity of sodium chloride-saturated aque-
Monoethylene glycol (MEG)
ous MEG solutions is a polynomial function of temperature and MEG concentration. It is
exponentially as the solid sodium chloride particle concentration increases from 0 to 30 wt%,
Desalination
demonstrated that a single, universal empirical model can be developed to quantify the
Pilot plant
relationship between the conductivity and relevant process parameters across the whole
Conductivity
experimental range. The methodology can be readily adopted for in situ monitoring of solid
Sodium chloride
salt particle concentration and estimation of MEG loss in a typical industrial MEG reclama-
Sedimentation
tion process, leading to the establishment of more effective process control and operation strategies. © 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.
1.
Introduction
Monoethylene glycol (MEG) is a chemicalthat is widely used by the oil and gas industry to thermodynamically inhibit gas hydrate formation in production wellheads and pipelines (Mokhatab et al., 2007; Sloan and
to inject a large quantity of MEG into wellheads and pipelines. This can depress the hydrate formation threshold to well below the operating temperature, thus inhibiting the formation of hydrates in the gas production process. The MEG concentration required to achieve gas hydrate inhibition can be determined by the Hammerschmidt equation
Koh, 2008). Gas hydrates are solid crystalline compounds, composed of
(Hammerschmidt, 1939). Typically, MEG is added into the production
natural gas components and water that may form readily under typical deep-sea pipeline operating conditions of high pressure and low temperature. They have a strong tendency to agglomerate and plug the
pipeline in excess of the quantities required by the equation and the MEG streams in gas production flowlines typically contain 30–60 wt%
pipeline, leading to production disruptions. Gas hydrate formation has
MEG that has been in contact with the wet natural gas stream is often referred to as (water-) rich MEG, and may contain a variety of contaminants, including dissolved salts from the rock formations and
long been considered a major risk in offshore deep-water gas production operations. One economical solution to address this problem is
∗
MEG.
corrosion products from the pipelines, as well as production chemicals and dissolved and free hydrocarbons. Natural gas extracted from deep-water reservoirs, in particular, often comes with a large quantity
Corresponding author. of produced water that may have salinity close to saturation. Those E-mail address: [email protected] (P.J. Martin). https://doi.org/10.1016/j.cherd.2019.02.035 0263-8762/© 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
345
Nomenclature ˛ ak , bij ˇn m c0 , c1 , c2 CMEG ,R CMEG,SaF CNaCl ,L CNaCl ,S d1 , d2 f, g i, j, k L S+L
T
Slope coefficient of log S+L vs log L (−) Coefficients of L model (mS/cm ◦ Ck, ◦ mS/cm Ci, respectively) Coefficient of L polynomial function as function of CMEG,SaF (mS/cm ◦ Cn) Coefficient of L polynomial function as function of T (mS/cm) Coefficients of S+L /L model (–,◦ C−1 , –) MEG wt% in MEG-water-NaCl solution based on all solution constituents MEG wt% in MEG-water-NaCl solution based on MEG and water only NaCl wt% in MEG-water-NaCl solution wt% based on all solution constituents Solid NaCl particle wt% suspended in solution Coefficients of simplified polynomial for CNaCl,S Generic functions Generic indices Conductivity of MEG-water-NaCl solution with no suspended solids (mS/cm) Conductivity of MEG-water-NaCl solution also containing suspended solid NaCl particles (mS/cm) Temperature (◦ C)
concentrated brines, once mixed into the MEG stream in which the mineral salts are generally much less soluble, carry a higher risk of scale formation and deposition in the production line, which may also present a serious risk to flow assurance if left untreated (Tomson et al., 2006). The large volumes of MEG required to ensure effective inhibition of gas hydrate formation throughout the entire length of the production pipeline necessitate recovery of the valuable glycol components for reinjection. The production pipeline can be several hundred kilometres in length and the MEG inventory of the systems can be in the order of several thousand metric tonnes. The contaminants in the MEG stream must be removed before the MEG can be recycled and injected back into the wellheads and pipelines. This is usually done in a MEG Recovery Unit (MRU). To date, there are more than 30 industrial-scale MRUs in operation in the world. The MEG recovery process can be divided into three operating sections (Nazzer and Keogh, 2006; Teixeira et al., 2016): 1 Pre-treatment section, where hydrocarbons and divalent salts are removed first from the rich MEG stream by heating and by chemical dosing combined with filtration, respectively. 2 Desalination section, where the liquid components (i.e., MEG and water) are recovered by contacting the rich MEG stream with a hot high-MEG-content recycle stream in a flash vaporisation separator. The vaporised MEG and water components are condensed back into the salt-free liquid form and subsequently fed into the regeneration section. The remaining monovalent salt content (mainly NaCl), on the other hand, accumulates and crystallises from the MEG recycle stream and can be discharged from the flash separator holding the high-MEG-content recycle stream. 3 Regeneration section, where the salt-free MEG and water components are separated from each other via reflux distillation to produce a (water-) lean MEG stream for reinjection at wellheads or pipelines.
Fig. 1 – A schematic illustration of the pilot plant MEG desalination system. increasingly important contributor to global gas production, demand for new and better technologies for more efficient salt removal and MEG recovery has never been stronger. In 2010, Cameron Flow Control Technology (UK) Ltd., now Cameron, a Schlumberger company, donated a 1/100th scale, 100 kg/h feed flow rate MEG desalination pilot plant system to The University of Manchester. The research presented here investigates some of the key processes involved in the desalination section operation, aiming to develop more efficient operation guidance and strategies for implementation at MEG desalination plants. The donated system focuses on the liquid components recovery and monovalent salt removal operations. It employs Schlumberger proprietary MEG reclamation technology, in which the monovalent salt crystals formed in the flash separator settle under gravity through a 6 m high, NaCl-saturated brine filled column (the downcomer) before disposal. The height of the downcomer facilitates the dis-entrainment of MEG from the settling salt crystals, resulting in a significant reduction in MEG losses during salt disposal and in a reduced demand for fresh MEG to replace these MEG losses. Fig. 1 shows a schematic illustration of the system. To minimise MEG losses during salt disposal, it is important that the MEG content in the downcomer is monitored in situ continuously. This enables the operators to better control the salt removal process. However, the downcomer contains a multicomponent dynamic inventory, in which the crystallised salt particles settle through a sodium chloride-saturated aqueous solution, with gradients of temperature, dissolved salt content, MEG concentration, and solids concentration along the whole height of the downcomer. Real-time measurements of MEG concentrations in such a complex environment are extremely difficult because of this multivariant complexity. It has been reported that electrical conductivity measurements coupled with the measurement of ultrasound velocity (Vajari, 2012; Yang et al., 2012; Yang and Tohidi, 2013) or density (Sandengen and Kaasa, 2006) could be used to determine both the MEG and salt concentrations from tertiary solutions consisting of water, MEG, and NaCl. Field trials showed that the technique required only a few simple operations and was capable of rapid, near-real-time estimation of MEG and salt contents at offshore platforms (Bonyad et al., 2011; Macpherson et al., 2012). Unfortunately, this technique cannot be applied to the in situ MEG content analysis inside the downcomer, as the presence of the salt crystal particles will interfere severely with the ultrasound velocity, density, and conductivity measurements, rendering the approach infeasible. In this study, we demonstrate that based on conductivity and temperature measurement combinations, a new and simple method can be developed to estimate both the MEG concentration and salt solid particle concentrations for NaCl-saturated MEG-water solutions. The method can be readily adapted for in situ MEG concentration analysis
One of the key targets in the MEG recovery process design and engineering is to achieve high efficiency in salt removal whilst incurring a minimum loss of MEG. As deep-water gas exploration is becoming an
in the downcomer section, thereby enabling more effective downcomer operation and minimising MEG losses. The paper is divided into two parts:
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
Table 1 – Detailed experimentalcondition matrix. MEG concentration (wt% in salt-free terms)
Temperature (◦ C)
NaCl solid particle concentration (wt%)
100 75 50 25 0
24, 45, 55, 75, 89 23, 36, 50, 69, 79 22, 42, 52, 61, 70 29, 40, 49, 59, 69 22, 41, 52, 62, 72
0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30 0, 5, 10, 15, 20, 25, 30
Part I focuses on the methodology development. Conductivity measurements at different temperatures and different NaCl solid particle concentrations in NaCl-saturated aqueous MEG solutions were conducted. The measurements enable establishing an empirical relationship describing the variation of conductivity as functions of temperature, MEG concentration, and NaCl particle concentration in NaCl-saturated aqueous solutions. The inverse solutions to the functions lead to the estimation of the MEG and salt solid concentrations from the measured conductivity data. Part II focuses on the MEG loss control strategy. In situ MEG concentration data inside the downcomer was collected using the methodology developed herein. The data were then utilised to determine how the downcomer could best be operated to control and minimise the MEG losses in the pilot plant MEG desalination system.
2.
Experimental
2.1.
Materials
The MEG was industrial grade, minimum 99% purity. It was purchased from Hydra Technologies Ltd., U.K., and used as received. NaCl salt used to make saturated solutions was a vacuum dried, off-the-shelf product, also of industrial grade. The salt used to make solid concentrations was recrystallized NaCl product from the pilot plant MEG desalination system, such that the particle size distribution was representative of that in the operating process. This was collected from the salt tank, washed by the saturated solution, filtered, dried in an oven at 70 ◦ C, and finally sieved into the 40– 125 m size range for experimental use. Fig. 2 confirms that the averaged NaCl particle size within the downcomer ranged from 38.4 (D10) to 124.9 (D90) m and that the feed flowrate had no effect on the particle size distribution. Appendix A details how the samples were taken from the downcomer and particle size distributions were measured. Ordinary tap water was used throughout the experiments.
2.2.
Procedure
The experiments were conducted in a factorial design fashion, with five levels of MEG concentration (in salt-free terms), five levels of temperature, and seven levels of NaCl solid particle concentration investigated. Table 1 lists the detailed experimental conditions. Following industry convention, in this paper the MEG contents are expressed in salt-free terms. The real MEG content CMEG,R in wt% and salt-free MEG content CMEG,SaF in wt% are connected via the following equation: CMEG,R = CMEG,SaF (
100 − CNaCl,L ) 100
(1)
where CNaCl,L denotes the salt concentration in wt% in solution.
Each experiment set started with the preparation of a MEG + water solution of different MEG concentration (e.g., 100% MEG + 0% water, or 75% MEG + 25% water). An excess of vacuum-dried NaCl was then added to the prepared solution, and the mixture was heated to the required temperature under constant stirring on an IKA C-Mag HS 7 magnetic stirrer with ceramic heating plate to make the NaCl-saturated MEG + water solution of different MEG concentration. After the solution was fully saturated, stirring was stopped. Allowing time for the NaCl particles to fully settle, approximately 200 ml of the NaCl-saturated supernatant liquid was then poured into a pre-weighed 250 ml beaker. The NaCl-saturated supernatant liquid was kept under constant stirring, and the temperature was maintained at the target value. Drops of fresh MEG + water solution of the same MEG concentration were added as necessary for fine adjustment of the saturation level. After the beaker containing the saturated solution was weighed, from which the net weight of the saturated solution could be extracted, the conductivity probe was lowered into the solution to start the conductivity and temperature measurements. The measurements continued under constant stirring, with sieved and recrystallized NaCl solid particles added in steps to make 5%, 10%, 15%, 20%, 25%, and 30% of solid concentration by weight in the NaCl-saturated MEG + water solution. Both the conductivity and temperature measurements were collected using a pre-calibrated Hamilton Conducell 4USF-PG 120 four-electrode conductivity probe. Data was logged onto a computer through dedicated software at a rate of 12 data points per minute. Typically for each experimental condition set, about 60 conductivity/temperature measurements were collected over a 5-min period. The averages of these measurements were taken as the measured conductivity and temperature values for the experimental condition set. All the raw conductivity data sets showed good consistency. The typical standard deviation for any randomly chosen data set was around 0.3% of the mean value.
3.
Results and discussion
3.1.
Conductivity measurement results
Fig. 3 shows the conductivity variation as a function of the solid NaCl concentrations in different concentrations of NaClsaturated MEG solutions and at different temperatures. Note that the measured conductivity data are presented in the logarithmic scale. In most cases, the logarithmic conductivity value decreased linearly as the solid NaCl concentration increased. The slope and intercept of each linear data set depended on the temperature and MEG concentration in the NaCl-saturated solution. Mathematically this is equivalent to the following expression: logS+L = logL (T, CMEG,SaF ) + ˛ (T, CMEG,SaF ) · CNaCl,S
(2)
in which S+L denotes the conductivities at different concentrations of NaCl solids in mS/cm and L denotes the conductivities, in mS/cm, of solid-free NaCl-saturated solutions of different MEG concentrations at different temperatures, which also represents the intercepts of the fitted lines on the vertical axis; CNaCl,S denotes the solid NaCl concentration in wt%; ˛ is the slope coefficient, to be determined through data fitting; and T is the temperature in ◦ C. L (T, CMEG,SaF ) and ˛(T, CMEG,SaF ) mean that these two parameters are a function
347
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
D50
D90
D10
160
Parcle Size (μm)
D10
D50
D90
140 120 100 80 60 40 20 0
0.0
1.0
2.0
3.0
4.0
5.0
0.0
1.0
Distance to Top of the Downcomer (m)
2.0
3.0
4.0
Distance to Top of the Downcomer (m)
(a)
(b) 180
D50
D90
D10
160
Parcle Size (μm)
D10
D50
D90
140 120 100 80 60 40 20 0
0.0
1.0
2.0
3.0
4.0
0.0
5.0
1.0
2.0
3.0
4.0
Fig. 2 – NaCl solid particle size distributions along the height of the downcomer at a salt influx of (a) 300, (b) 500, (c) 700, and (d) 900 kg/h m2 , respectively. D10, D50 and D90 refer to the particle sizes where 10%, 50% and 90% of the distribution lie below the respective diameters. of temperature and salt-free MEG concentration. Note that ˛(T, CMEG,SaF ) will be negative, which makes S+L converge as CNaCl,S increases. To build a valid predicative model to account for the variation of S+L as a function of CNaCl,S , a separate model describing the L as a function of T and CMEG,SaF also has to be developed. One of the approaches to achieve this is to use the thermodynamic equilibrium model that is based on an extended form of the mean-spherical approximation (MSA) theory coupled with a mixing rule (Wang et al., 2004) to calculate the conductivities of saturated MEG + water + NaCl solutions at different temperatures. Unfortunately, for our specific system, very limited number of parameter data can be found in literature (Wang et al., 2013). Thus, in this work we decided to adopt an empirical data fitting approach for the L predictions instead. Fig. 4 plots the change of L as a function of temperature at different salt-free MEG concentrations in the NaCl-saturated MEG solutions. In the absence of solid particles, the averaged conductivity of NaCl-saturated aqueous MEG solutions increases with either decreasing MEG concentration or increasing temperature. Close inspection of the graphs in Fig. 4 indicates that the conductivity data seem to fit well into a polynomial function of the temperature with MEG concentration-dependent coefficients:
L =
n
ˇn (CMEG,SaF ) · T n
(3)
where n = 1, 2, 3, . . . and ˇn (CMEG,SaF ) denote coefficients, which are a function of the salt-free MEG concentration and can be determined through data fitting. The same could also be true to fit L into a polynomial function of the MEG concentration with temperature-dependent coefficients: L =
m (T) · (CMEG,SaF )m
(4)
m
where m = 1, 2, 3, . . . and m (T) denote coefficients, which are a function of the temperature.
3.2.
Data fitting
All the data fitting work was done on the Matlab platform, using multivariate regression techniques and least squares analysis (Draper and Smith, 1981). Conductivity L can be considered to be a function of temperature and salt-free MEG concentration. This can also be expressed by applying the separation of the variables as L (T, CMEG,SaF ) = f (T) · g(CMEG,SaF )
(5)
where f(T) and g(CMEG,SaF ) are functions of T and CMEG,SaF only, respectively. It can be inferred from Fig. 4 that the L data would fit well to a polynomial function of T or CMEG,SaF when the other variable is fixed. It is thus plausible to put f(T) and
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
100% MEG at 45 °C 100% MEG at 75 °C
Conducvity (mS/cm)
100% MEG at 24 °C 100% MEG at 55 °C 100% MEG at 89 °C 40
4
75% MEG at 23 °C 75% MEG at 50 °C 75% MEG at 79 °C
100
75% MEG at 36 °C 75% MEG at 69 °C
10
0
5
10
20
25
30
0
5
10
15
20
NaCl Solid Concentraon (wt%)
NaCl Solid Concentraon (wt%)
(a)
(b) 700
50% MEG at 42 °C 50% MEG at 61 °C
25% MEG at 29 °C 25% MEG at 49 °C 25% MEG at 69 °C
Conducvity (mS/cm)
50% MEG at 22 °C 50% MEG at 52 °C 50% MEG at 70 °C
300
15
30
25
30
25
30
25% MEG at 40 °C 25% MEG at 59 °C
70
0
5
10
15
20
25
30
0
5
10
15
20
NaCl Solid Concentraon (wt%)
NaCl Solid Concentraon (wt%)
(c)
(d)
0% MEG at 22 °C 0% MEG at 52 °C 0% MEG at 72 °C
0% MEG at 41 °C 0% MEG at 62 °C
100
Fig. 3 – Conductivity variations versus solid NaCl concentrations at different temperatures in NaCl-saturated solutions of (a) 100% MEG, (b) 75% MEG, (c) 50% MEG, (d) 25% MEG, and (e) 0% MEG. Discrete markers represent the measured conductivity data, whereas dotted lines are calculated conductivity values using Eq. (7). g(CMEG,SaF ) into a polynomial function of T and CMEG,SaF , respectively. After inspection of the experimental data, it was found that an optimal L model takes the following form:
L =
3 k=0
ak T k +
4 3
bij T i (100 − CMEG,SaF )
j
(6)
Table 2 – L model coefficients. a0 – a3
b11 – b14
b21 –b24
b31 –b34
2.862458061 –0.077034183 0.010410457 –6.01435E-05
0.013718637 0.00123537 –1.57337E-05 1.71693E-07
0.000558272 –7.157E-05 1.53244E-06 –1.13449E-08
–5.7528E-06 6.93116E-07 –1.52117E-08 1.06858E-10
i=1 j=1
The model coefficients ak and bij are listed in Table 2 and were determined through data fitting of the raw L data set. Fig. 4 illustrates a comparison of the measured and modelfitted L data. The data cover the MEG concentration (on a salt-free basis) ranging from 0% to 100% and temperature rang-
ing from 20 to 90 ◦ C. They are the respective compositional and temperature ranges expected within the downcomer. It can be seen from Fig. 4 that the model is able to effectively track the variation of measured data within the experimental range. The typical comparative errors between the measured and calculated conductivity values are well below 5%. The squared
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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
We rearranged the L model from Eq. (6) into the following form: 3 4 (100 − CMEG,SaF ) +
bi3 T i
i=1 3
(100 − CMEG,SaF )
3
bi4 T 4
i=1
3
+ Fig. 4 – Variation of L as a function of temperature at different salt-free MEG concentrations in the NaCl-saturated MEG solutions, with measured data (discrete markers) and model-fitted function (solid lines).
3
Table 3 – S+L model coefficients. c1
c2
–0.004367837
–1.44819E-05
9.84524E-06
Pearson’s correlation coefficient, which is a measure of the linear correlation between the measured and calculated L data, was calculated to be R2 = 99.89%. For the S+L data, a similar approach was applied to determine the coefficient ˛(T, CMEG,SaF ) shown in Eq. (2). The following model was found to produce the optimum results:
⁄L ) = (c0 + c1 T + c2 (100 − CMEG,SaF )) · CNaCl,S
(7)
The fitted values of the coefficients c0 , c1 , and c2 listed in Table 3 were determined through the data fitting of the log(S+L /L ) versus CNaCl,S values at different temperatures. A comparison of the measured and model calculated S+L data is illustrated in Fig. 3, which shows that the model fits well to the measured data across all the experimental ranges. The mean sum of the squares of the residuals is only 10.25 for 175 S+L data points ranging from 4.46 to 440.06 mS/cm. The squared Pearson’s correlation coefficient R2 is 99.94%.
3.3.
(100 − CMEG,SaF )
2
bi4 T 4
i=1 3
3
bi1 T i (100 − CMEG,SaF ) +
Inverse algorithm
We have so far developed empirical models to calculate L from temperature T and salt-free MEG concentration in NaClsaturated solution CMEG,SaF and S+L from L , T, CMEG,SaF and NaCl solid concentration CNaCl,S . In practical applications such as a MEG desalination system, however, it is desirable to deduce CMEG,SaF and CNaCl,S from the measured S+L data. All conductivity probes were equipped with integrated temperature measurement, thus T can be considered as a known quantity. Moreover, at any fixed T, the values of L and CMEG,SaF are both unique. This implies that it is possible to acquire CMEG,SaF and CNaCl,S through a dual measurement approach, which, in the current case, includes taking the conductivity measurements of the solid NaCl suspension (i.e., S+L ) and the supernatant liquid phase only (i.e., L ) subsequently. The second measurement leads to a solution for CMEG,SaF . This can then be used, together with the S+L measurement, to produce CNaCl,S .
ak T k − L
k=0
bi4 T 4
3
i=1
c0
log(
3 i=1
+
S+L
bi2 T i
i=1
=0
(8)
bi4 T 4
i=1
The roots of this equation are the eigenvalues of its companion matrix (Williams, 2010). Out of the four roots for (100 – CMEG,SaF ), only one root carries realistic physical meaning. With (100 – CMEG,SaF ) determined, CNaCl,S can be calculated from the logarithmic L model: CNaCl,S =
1 × log [c0 + c1 T + c2 (100 − CMEG,SaF )]
S+L
L
(9)
We also found that CNaCl,S can be equally well reproduced using the following simpler polynomial model: CNaCl,S = d1
L S+L
− 1 + d2
L S+L
2
−1
(10)
where d1 and d2 were determined through data fitting to be 117.8532 and –114.9946, respectively. Fig. 5 illustrates the comparison of the actual and inversely calculated CMEG,SaF and CNaCl,S values. Accurate MEG concentration predictions are achieved, with the differences between the calculated and real values at different levels almost negligible. The accuracy of CNaCl,S predictions is also reasonably satisfactory, considering the complex nature of particulate slurries (MacTaggart et al., 1993).
4.
Model validation
To validate the model predictions, six samples were taken from the downcomer during a randomly chosen operational run of the MEG desalination pilot plant. They were taken from each of the six conductivity probes installed on the downcomer to map the conductivity profile changes along the full height of the downcomer. The operation of the pilot plant and exact locations of the conductivity probes are discussed in detail in Part II of this paper. The collected samples were stored in 500 ml plastic sample bottles and allowed to cool to room temperature. They were then poured into 500 ml glass beakers where the conductivity measurements were conducted. A Hamilton Conducell 4USF ARC 120 conductivity probe was used to measure the suspension conductivity S+L (under constant mixing using an IKA C-Mag HS 7 magnetic stirrer) and supernatant conductivity L of each sample. The data were
350
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
Fig. 5 – Comparisons of the actual and inversely calculated (a) salt free MEG concentration, CMEG,SaF and (b) NaCl solid concentration, CNaCl,S . Table 4 – Model validation results. Sample location to top of the downcomer (m)
0.00 0.85 1.85 2.85 3.85 4.85
Laboratory conductivity measurements
Measured data by evaporation
T (◦ C)
S+L (mS/cm)
L (mS/cm)
CMEG,SaF (%)
CNaCl,S (%)
CMEG,SaF (%)
CNaCl,S (%)
22.8 22.8 22.8 22.8 22.8 22.8
67.82 66.97 69.46 71.26 85.03 113.23
80.16 78.95 79.15 81.34 91.26 118.64
40.4 40.9 40.8 40.0 36.3 27.5
18 17 14 14 8 5
38.1 38.2 36.8 34.5 31.0 25.5
15 16 16 15 13 9
then fed to Eqs. (8) and (10) to calculate the CMEG,SaF and CNaCl,S , respectively. A small representative portion of the particle suspension and supernatant liquid were also withdrawn from each sample. They were used to measure CMEG,SaF and CNaCl,S through an evaporation method in each sample (see Appendix A for descriptions of the method in detail). Table 4 compares the model-calculated CMEG,SaF and CNaCl,S with the measured data. The models not only correctly presented the trend of changes but also produced both CMEG,SaF and CNaCl,S predictions with reasonably good accuracies.
5.
Inverse algorithm predictions
Conclusions
In this investigation, electrical conductivity measurements at different temperatures were undertaken to investigate the variation of conductivity as a function of NaCl solid particle concentration in sodium chloride-saturated aqueous MEG solutions. Experimental results show that the conductivity decreases exponentially as the solid NaCl particle concentration increases from 0 to 30 wt%, whereas, in the absence solid particles, the conductivity of NaCl-saturated aqueous MEG solutions is a polynomial function of temperature and MEG concentration. Empirical models, based on multivariate regression analysis of the experimental conductivity measurement data, were developed to quantify the variation of conductivity as a function of the solid NaCl concentration, temperature, and MEG concentration in both the presence and absence of solid NaCl particles. Typical model prediction errors for conductivities are well below 5% across the whole experimental range covering solid NaCl concentration changes from 0 to 30%, temperature changes from 20 to 90 ◦ C, and MEG concentration changes in salt-free terms from 0 to 100%.
The models can also be utilised, through inverse algorithms, for the determination of solid NaCl particle and MEG concentrations or for determination of MEG losses in MEG reclamation processes. The calculation of solid NaCl particle concentrations, in particular, requires a dual measurement approach, which includes taking the subsequent conductivity measurements of both the particle suspension and the supernatant liquid phase only. As the measurement of conductivity is, in principle, a nonspecific technique, it is reasonable to assert that the same methodology can be readily tailored into a real-time solid particle concentration monitoring tool for any solid–liquid two-phase particulate suspension system. For such a tool to be valid, the conductivity of the supernatant liquid phase should be independent of the presence of solid particulate materials. The resulting model would be established through robust on-process training and calibrations.
Declaration of interests None.
Research data https://doi.org/10.17632/bjhc5t86vw.1.
Acknowledgements This work was financially supported by The University of Manchester EPSRC Knowledge Transfer Account (KTA002) and Cameron Flow Control Technology (UK) Limited, now Cameron, a Schlumberger company. The authors wish to
Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 344–351
acknowledge Mr Andrew Downes from Cameron Flow Control Technology (UK) Limited for his assistance in running the MEG pilot plant.
Appendix A Appendix A1 Measurements of NaCl solid particle size distributions inside the downcomer
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subsequently deduced using the linear interpolation in the NaCl in water + MEG saturation charts. Then the same procedure was followed with the solid suspension samples, from which the total NaCl content in each sample was calculated. The solid NaCl concentration, CNaCl,S , was obtained by determining the dissolved NaCl content from the total NaCl content.
References Samples were withdrawn from six sample points at 1 m intervals in the 6 m tall downcomer through the sampling lines. The sampling lines were all made of 3/8 inch OD stainless steel pipes and were inserted into the downcomer with a 45◦ downwards angle to avoid NaCl solid accumulation at the tip of each sampling point. The distances from each sampling point tip to the top of the downcomer were 0.0, 0.85, 1.85, 2.85, 3.85, and 4.85 m, respectively. The collected samples were maintained at their original temperatures and measured on a Malvern Mastersizer 3000 in saturated brines for particle size distributions within at most 3 h after the sample collections (Fig. A1). The salt influx and feed flow rate are related via the following equation: SINaCl =
QM,F CNaCl,L,F 2 4 (DDown )
(A(1)-(1)
where SINaCl denotes the salt influx in the downcomer in kg/h m2 , QM,F denotes the mass flow rate of the feed to the flash separator in kg/h, CNaCl,L,F denotes the dissolved NaCl concentration in the feed stream in wt%, and DDown denotes the inner diameter of the downcomer in m.
Appendix A2 Description of the evaporation method to measure the CMEG,SaF and CNaCl,S in a sample The method also took a dual measurement approach. A small quantity of NaCl-saturated supernatant liquid (∼0.5 ml) was taken from each sample and weighed in pre-weighed Petri dishes. The sample was heated in a vacuum oven (Thermo Scientific, Vacutherm) to 120 ◦ C at 0.1 bar until all the liquid content was evaporated. The Petri dishes were weighed again, from which the dissolved NaCl content in each NaCl-saturated supernatant liquid sample, CNaCl,L , could be calculated. The MEG content, CMEG,R , or in salt-free terms CMEG,SaF , could be
Fig. A1 – A typical size distribution profile for NaCl solid samples taken from the downcomer at different salt influxes.
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