Article pubs.acs.org/EF
Kinetic Modeling of a Heat Generator for the Fluidization of Paraffin Deposits Using In-line Infrared Spectroscopy with the Development of a Graphical User Interface Vinicius Kartnaller, Marcos V. Romualdo, Victor T. V. Lobo, and Joaõ Cajaiba* Pólo de Xistoquímica, Instituto de Química, Universidade Federal do Rio de Janeiro (UFRJ), Rua Hélio de Almeida 40, Cidade Universitária, Rio de Janeiro, Rio de Janeiro 21941-614, Brazil S Supporting Information *
ABSTRACT: Nitrogen-generating systems (NGS) have been used by the oil industry for treatments in flow assurance, because the system consists of a highly exothermic nitrosation reaction that can act as an in situ generator of heat for the fluidization of low-melting-point organic deposit or gas hydrate buildup. In this work, attenuated total reflection/Fourier transform infrared spectroscopy (ATR/FTIR) was used to monitor and quantify the components in the NGS reactions and a 24 central composite design of experiment was used to model the total amount of heat released by the system at different times, working as an empirical kinetic modeling. The modeling showed great results for the prediction of the kinetic profile in new conditions, showing an average percentage error of 7.5% when compared to the experimental measurement using ATR/FTIR. With the achieved models, a graphical user interface was constructed in MATLAB for the prediction of the kinetic profile of the NGS, with possible applications for the fluidization of paraffin/wax in tanks by the industry.
1. INTRODUCTION Nitrogen-generating systems (NGS) have been suggested and used by the oil industry for treatments in flow assurance since the idea was suggested by the Shell Oil Company in 1978.1 The system consists of a nitrosation reaction of a nitrogencontaining molecule in the presence of an acid catalyst, which can lead to highly exothermic reactions.2,3 The most applied system comprises the reaction of ammonium chloride and sodium nitrite, which produces nitrogen, water, and sodium chloride and is an environmentally green reaction, as shown by eq 1.
Attempts have been made to delay the reaction, such as the encapsulation of the reagent solutions11−14 and the use of a catalyst that needs to undergo a reaction before deprotonating.15 Deposition may also occur after oil production, such as that of paraffin in tanks for storage and transportation.16,17 In these cases, NGS may be used directly over the deposits, so that the heat is transferred to the material until it melts and can be removed.6 To understand how the NGS can be used to dissolve these solids, it is necessary to know the rate in which the reaction occurs over different conditions. Studies have been performed to evaluate the kinetic model that rules the reaction; however, different mechanisms have been suggested.18−20 Even though the reaction looks simple, it involves multiple steps and has possible side reactions, which can make it difficult for an exact evaluation of the kinetics. The aim of this work is hence to model the kinetics of the NGS reaction using an empirical model to respond to the heat released by the system. This model can be used for applications in the dissolution of paraffin deposits in tanks, facilitating the treatment and cleaning of these facilities. Attenuated total reflection/Fourier transform infrared spectroscopy (ATR/ FTIR) was used to monitor the NGS reactions. This technique works in real time, where information is gathered in a time series, generating the kinetic profile over the course of the reaction. The empirical modeling was performed using a central composite design, and additional experiments were performed
H+
⎯ N2(g) + 2H 2O(l) + NaCl(aq) NH4Cl(aq) + NaNO2(aq) ⎯→ ΔH = −309.6 kJ/mol N2
(1)
With the combination of thermal, chemical, and physical effects, the NGS can be used as an in situ generator of nitrogen and heat by the oil industry for the irreversible fluidization of lowmelting-point organic deposit4−8 or gas hydrate buildup,9,10 increasing the efficiency of this kind of treatment. Khalil et al. reported a quantitative financial benefit of this treatment in which it brought a substantial recovery of production, increasing it by about 30%, which represented an economy of approximately USD 200 000/day.4 Alternative treatments may have elevated costs, reaching millions of dollars, while nontreatment may lead to great loss, as happened with the Lasmo field (U.K.), leading to a financial loss of USD 100 000 000.11 The idea for this treatment is to increase the local temperature around the deposits formed in the production line or storage tank to change its phase equilibrium. For deposition in production lines, usually in off-shore production, it is necessary to delay the NGS reaction as much as possible to avoid heat loss before reaching the point of incrustation. © XXXX American Chemical Society
Special Issue: 16th International Conference on Petroleum Phase Behavior and Fouling Received: September 17, 2015 Revised: December 3, 2015
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DOI: 10.1021/acs.energyfuels.5b02101 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
parameters calculated for the models in the environment GUIDE within MATLAB 2013a.
to test the achieved model. Finally, a graphical user interface (GUI) was made in MATLAB for the direct and practical prediction of the heat released by the NGS for batch applications.
3. RESULTS AND DISCUSSION For this work, the response was measured by ATR/FTIR, which can be an automated technique with time resolution, and the ATR probe was immersed at the reaction medium set to measure the spectra every 15 s. Each spectrum taken is dependent upon the concentration of the components in the medium. Hence, if their concentration varies as a result of the reaction, the signal also varies, enabling the monitoring of the reaction. The spectrum of the NGS mixture contains absorption bands related only to the reagents (nitrite and ammonium) and the solvent (water). Figure 1 shows the spectra variation of one NGS reaction at different times as a result of reagent consumption. Figure 1 shows three different bands, where only two of them show variation in the signal. The first band (1650 cm−1) corresponds to the water absorption; the second band (1450 cm−1) corresponds to the ammonium absorption; and the third band (1240 cm−1) corresponds to the nitrite absorption. As the reaction progresses, ammonium and nitrite react with each other and their concentration decreases. According to the Beer−Lambert law, the signal related to their absorptions is proportional to their concentrations; hence, a decrease is seen with time in Figure 1. A quantification was made correlating the area of the nitrite band to its concentration using a univariate calibration model; a more detailed view can be seen in a previously published work.21 The response of interest in the NGS is the heat released by the reaction. Hence, a conversion must be made to transform the concentration measured by the ATR/FTIR to the heat released. This was performed using the molar enthalpy of reaction (ΔH°r = −309.6 kJ mol−1) as in eq 2.
2. MATERIALS AND METHODS 2.1. Materials. Sodium nitrite and ammonium chloride stock solutions were prepared using type I water from a Milli-Q system (Millipore). The nitrite solution was kept in an amber glass, and both solutions were kept refrigerated. Acetic acid was used as a buffering agent as well as a catalyst for the reactions. All reagents were from Vetec (Brazil) and of analytical grade and were used without further purification. 2.2. Equipment and Reaction Data Collection. A ReactIR 45m (Mettler Toledo) spectrometer was used for monitoring the NGS in the aqueous medium reactions; it was equipped with an AgX 9.5 mm × 2 m fiber (silver halide), with a 6.35 mm diamond crystal with six internal reflections as an ATR element, ZnSe as a support/focusing element, and a mercury cadmium telluride (MCT) detector using Happ-Genzel apodization. The spectra were acquired in the range of 2000−650 cm−1 with a wavenumber resolution of 8 cm−1 in a 15 s interval between each spectrum (average of 25 scans). All reactions were carried out in a 0.1 L reactor controlled by the EasyMax workstation (Mettler Toledo). The temperature of the reaction was regulated by the equipment with a Pt100 temperature sensor and through a Peltier system jacket. To monitor the reactions, nitrite and ammonium solutions were added to the reactor and the temperature was set according to the temperature defined by the design of experiment with a stirring rate of 200 rpm by a mechanical propeller stirrer. After stabilization, acetic acid was added to the solution and the reaction started. The ATR/ FTIR probe was immersed in the reaction medium over the course of the whole experiment, and the reaction conversion was evaluated for a stipulated time of 3 h. Quantification was made for nitrite using a univariate model, described in our previous work.21 2.3. Design of Experiment and Modeling. A 24 central composite design was employed to model the kinetics of the heat released with a quintuplicate in the central point to evaluate the experimental variance, totaling 29 experiments. The design table is presented in the Supporting Information, and the factor levels are presented at Table 1.
ΔH(t ) = ΔHr°Δc(t )V
In this equation, ΔH(t) is the total heat that was released until time t, ΔHor is the molar enthalpy of reaction, Δc(t) is the variation of the concentration at time t, and V is the volume of the reaction solution. Figure 2 illustrates the transformation of the response from the concentration to heat made for the experiment shown in Figure 1. This type of automated in-line method, such as that of the ATR/FTIR, is advantageous for analyzing reaction systems, because it can generate a large amount of measurements without the need for sampling. For instance, for the defined 3 h study of the NGS reaction, which was defined because the majority of the heat that is released by the reaction happens until this time, 720 infrared spectra were taken. To develop a GUI that enables the calculation of the heat released by the NGS, a modeling methodology must first be chosen. Works have been published previously in which the kinetics were studied by attempts to define the mechanism of the reaction; however, they are usually limited to pH intervals or do not take into consideration possible side reactions, leading to different suggestions of the kinetic equation. For industrial application, specifically here for the oil industry, userfriendly programs that can calculate the kinetics can be useful. Hence, empirical models that can account for unexpected variables are the best choice. In this work, a design of experiment was chosen to model the response. Because the response is time-dependent (that is, the total heat that is released by the reaction increases with time), a choice needs to
Table 1. Experimental Factors and Levels Investigated in the Experiment for the Coded Variables in the Aqueous NGS parameter values factors X1, temperature (°C) X2, [NO2−] (M) X3, [NH4+] (M) X4, % (v/v) catalyst
axial low (−2)
low level (−1)
central point (0)
high level (+1)
axial high (+2)
2.5
10.0
17.5
25.0
32.5
1.20
1.70
2.20
2.70
3.20
1.20
1.70
2.20
2.70
3.20
0.85
1.70
2.55
3.40
4.25
(2)
The response used for the design of experiment was the heat released by the reaction at different times and was measured in real time by infrared spectroscopy. The response was converted from absorbance to heat using a calibration curve to quantify the variation of the nitrite concentration and using the known molar enthalpy of reaction.21 After the modeling, four additional experiments were conducted to compare to the response estimated by the achieved models of the design of experiments. All calculations were made using the program MATLAB 2013a from Mathworks. Finally, a GUI was made using the B
DOI: 10.1021/acs.energyfuels.5b02101 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 1. (a) Three-dimensional (3D) and (b) two-dimensional (2D) views illustrating the NGS reaction progress monitored by ATR/FTIR.
Figure 2. Transformation of the ATR/FTIR information to the heat released by the NGS reaction.
can be used to model the heat released until 60 min or until 120 min or at any time of the reaction, producing different models for different times. This is because the response, y in this case, is a function dependent upon not only the variables chosen for the design of experiment but also time.
Table 2. Additional Experiment Table for the Evaluation of the Power of Prediction by the Achieved Models experiment
X1
X2
X3
X4
1 2 3 4
1 1 1 1
0 0 −0.7 0.7
−0.7 0.7 0 0
1 1 1 1
y = f (X1 , X 2 , ..., X n , t )
(3)
The infrared technique used gives 720 different possible design of the experiment models. In this case, if only one choice is made, then 99.9% of the data measured is thrown away. Now, if instead of modeling the response for a particular point in the progress of the reaction or using “time” as an independent
be made regarding the modeling: At which time of the reaction will the response be represented by the heat released? For an example, a design of experiment can be used to model the heat released until 10 min. However, another design of experiment
Figure 3. Comparison of the total heat released by the NGS reaction measured by ATR/FTIR and calculated using the achieved models of the design of experiment. C
DOI: 10.1021/acs.energyfuels.5b02101 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 4. (a) RMSEP calculated for the additional experiments and (b) percentage of the RMSEP in relation to the average response.
Figure 5. Main window of the NGS_KOS program.
These coefficients can be estimated simultaneously for all of the designs of experiments using multivariate linear regression, where eq 4 can be rewritten as follows:
variable of the design of experiment, all points of the progress of the reaction are modeled individually using the design of experiment and the time-dependent response measured, enabling the modeling of the entire kinetics of the reaction. A central composite design was chosen as the design of experiment, because it allows for the estimation of the curvatures in the response measured. For the independent variables of the model, the following were chosen: temperature and nitrite, ammonium, and catalyst concentrations, because these are the four main variables of the NGS. The equation model that correlates the response and variables for this design of the experiment is as follows: 4
y = bo +
4
4
where Y is the response matrix (size 2 × t, where t is the number of points in time in which the response is being analyzed and 2k is the number of experiments in the design), B is the coefficient matrix (size b × t, where b is the number of coefficients in the equation model), and X is the design matrix (size 2k × b). Multivariate least-squares regression can then be used to solve eq 5 and estimate the coefficient matrix, as show in eq 6. k
4
∑ bixi + ∑ ∑ bijxixj + ∑ biixi 2 i
i
j
