Article pubs.acs.org/EF
Deep-Vacuum Fractionation of Heavy Oil and Bitumen, Part II: Interconversion Method M. C. Sánchez-Lemus,† F. Schoeggl,† S. D. Taylor,‡ K. Růzǐ čka,§ M. Fulem,§ and H. W. Yarranton*,† †
Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 ‡ DBR Technology Center, Schlumberger Canada Limited, 9450 17th Avenue NW, Edmonton, Alberta, Canada T6N 1M9 § Department of Physical Chemistry, Institute of Chemical Technology, Prague, Technická 5, CZ-166 28 Prague 6, Czech Republic ABSTRACT: In Part I of this two-part series, a recently developed deep-vacuum fractionation apparatus (DVFA-II) was standardized and used to fractionate heavy oil samples by boiling point at a pressure below 1 Pa. Up to 50 wt % of a Western Canadian bitumen was distilled, compared with 26 wt % distilled with conventional spinning band distillation (SBD), and eight cuts were recovered. Here, an interconversion technique is developed to determine the normal boiling point (NBP) curve from the low-pressure boiling point data collected using DVFA-II. A simultaneous correlation of vapor pressure and heat capacity data based on the Clapeyron equation was used to determine the NBP of each cut. Of the vapor pressure correlations considered, the three-parameter Cox equation best fit the data, with average absolute relative deviations within 7% and 1% for the vapor pressure and heat capacity data (ΔC′exp), respectively. The estimated maximum and minimum errors in the calculated NBPs were 2.2% and −2.5% (8 and 9 K), respectively, and the calculated NBPs were within 2% of the SBD data. It was demonstrated that the distillation data for a heavy oil sample follow a Gaussian distribution and therefore that the NBP curve of heavy oil maltenes can be represented well using a Gaussian extrapolation.
1. INTRODUCTION Minable and in situ heavy oil and bitumen make up approximately 80% of Canada’s oil reserves. There are also significant heavy oil reserves in Venezuela, the Middle East, Mexico, Brazil, and Russia. Thermal production methods are typically employed for relatively shallow and cool deposits, but these methods are energy-intensive and use significant amounts of water. Therefore, the use of solvents (alone or to assist thermal methods) is attractive because it can reduce energy usage, water consumption, and environmental impact. However, mixtures of solvent and heavy oil are challenging from a fluid modeling perspective because they can form more than one liquid phase and may experience asphaltene precipitation. In order to design and optimize these methods, an accurate phase behavior model is required that is based on a more rigorous characterization of the heavy oil than is usually required for thermal processes. Distillation assays are the most common basis for fluid characterization in refinery operations. These assays provide a boiling point distribution, that is, the normal boiling point (NBP) as a function of the cumulative weight or volume percent distilled. The NBP distribution is also the basis for determining other property distributions (molecular weight, density, critical properties) from measurements or correlations. There are several standardized physical and simulated distillation methods to characterize hydrocarbons. For conventional oils, atmospheric and vacuum distillation (ASTM D-86, D-1160, D-2892, and D-5236) provide data to characterize 80− 95 wt % of a conventional oil.1 Heavy oils are commonly distilled at low pressures so that more fluid will boil below the thermal decomposition (or cracking) temperature (approximately 573 K). Advanced vacuum distillations, such as ASTM © 2014 American Chemical Society
1160 (1330 Pa) and spinning band distillation (SBD) (400 Pa), can fractionate up to approximately 20−35 wt % of a heavy oil. The nondistillable residue must be characterized on the basis of extrapolations of the distillation curve. Hence, there is considerable uncertainty in the property distributions for approximately 80−65 wt % of a heavy oil. In Part 1 of this series (DOI 10.1021/ef500489y), a procedure was developed to distill up to 50 wt % of a bitumen using a deep-vacuum fractionation apparatus, denoted as DVFA-II. This apparatus reaches pressures as low as 1 × 10−6 Pa under clean conditions and therefore is suitable for fractionating samples of extremely low volatility. However, to use a distillation assay measured at reduced pressure as a characterization technique, the boiling temperatures read at the operational pressure must be interconverted to normal boiling points, since most pseudocomponent physical property estimation methods are based on NBP data. The choice of interconversion method depends on the availability of vapor pressure data for the cuts. When no vapor pressure data are available, interconversions are performed using a vapor pressure correlation. The vapor pressure correlation developed for petroleum fractions by Maxwell and Bonnell2 is the accepted industry standard. Other vapor pressure correlations proposed by Myers and Fenske3 and Van Nes and Van Westen4 are less commonly used for this purpose. The reliability of this approach is unknown, particularly for heavy oils.1 Received: February 28, 2014 Revised: April 22, 2014 Published: April 22, 2014 2866
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When vapor pressure data are available, there are two options for interconversion: equation-of-state modeling or extrapolation of the experimental vapor pressure toward the normal boiling point. Using an equation of state and mixing rules can be an accurate method for estimating boiling points from vapor pressure; however, critical properties and interaction parameters are also required, and their availability for heavy fractions is limited at best. On the other hand, the second approach requires an accurate extrapolation of low-vapor-pressure data to atmospheric pressure. Růzǐ čka and Majer5,6 developed an extrapolation procedure for n-alkanes constrained using both vapor pressure and heat capacity data between the triple point and normal boiling temperatures of the n-alkane series. The purpose of including thermal data is to constrain the extrapolation of the low-range vapor pressure measurements with heat capacity data measured over a broader range of temperature. Low-temperature heat capacity data are arguably more accurate than low-temperature vapor pressures and therefore provide a convenient experimental constraint. A number of vapor pressure equations were tested by Růzǐ čka and Majer, 6 and the best performance in the fitting and extrapolation of vapor pressure and heat capacity data was obtained with the Cox equation. Advantages of the DVFA-II apparatus are that (1) sufficient volume of each fraction is obtained for property measurements and (2) the same apparatus, with a slight modification in its configuration (DVFA-I), can be used to measure the vapor pressures of the cuts. Castellanos et al.7 designed a vapor pressure measurement procedure for the apparatus and measured the vapor pressures of heavy hydrocarbons within 6% of literature values and heavy oils and bitumen samples with a repeatability of ±3%. Hence, the data required to develop a vapor-pressure-based interconversion method are attainable. The objectives of this work were (1) to measure the vapor pressures and heat capacities of bitumen fractions obtained with DVFA-II, (2) to develop an interconversion method for heavy oil and bitumen DVFA-II cuts based on the constrained extrapolation of vapor pressure and heat capacity data toward the NBP for each of the fractions, and (3) to construct the NBP curve for a Western Canadian bitumen. The interconverted NBPs were validated against SBD data where possible. It should be noted that the interconversion technique developed here can be applicable to any crude oil sample fractionated using DVFAII or any other reduced-pressure distillation method as long as vapor pressure data for the cuts are available.
Table 1. Selected Physical Properties of WC_Bit_B1 Bitumen property
value
average molecular weight [g/mol] average specific gravity initial boiling point [K] asphaltene/solids content [wt %] wt % distilled using SBD
510 1.007 486 17 26
Table 2. Spinning Band Distillation (SBD) Assay of WC_Bit_B1 normal boiling temperature [K]
wt % distilled
511 526 541 552 563 575 587 597 613 623 631 640 648 653
3.2 4.9 6.5 8.1 9.7 11.4 13 14.6 17.9 19.5 21.1 22.7 24.3 26
Table 3. DVFA-II Distillation Data for WC_Bit_B1 cut
cut temperature [K]
0 1 2 3 4 5 6 7 residue
403 430 450 468 493 513 533 563 >563
cumulative wt % of bitumen distilled 5.8 16.3 21.4 28.8 35.0 40.5 45.9 51.7
molecular weight [g/mol]
density [kg/m3]
213 247 272 327 352 362 480 490 1010
893.3 920.6 961.9 973.2 982.2 992.0 999.6 1016.8 1035.0
The vapor pressure, liquid heat capacity, and elemental analysis data were measured for each cut. However, cut 0, cut 7, and the residue were not included in the interconversion method. Cut 0 (the lightest cut) had a vapor pressure higher than the upper limit of the diaphragm (pressure) gauge. Cut 7 and the residue had vapor pressures below the lower limit of the same diaphragm gauge. 2.2. Vapor Pressure. The vapor pressures of the fractions were measured using the static method developed by Castellanos et al.7 The principle is simple: a liquid sample is allowed to equilibrate with its vapor at a fixed volume and temperature. The DVFA-I apparatus was designed to achieve pressures below 0.1 Pa. It should be noted that since the heavy oils are multicomponent mixtures, the saturation pressure measured is not technically a vapor pressure. However, the term vapor pressure is often used in the literature in this situation, and we have continued with this convention. DVFA-I Apparatus. The apparatus consists of a sample vessel, two valves used to control the operating cycles, a diaphragm gauge, a liquid trap, and a turbomolecular pump (Figure 1). The pressures are measured with an Inficon diaphragm gauge capable of measuring pressures in the 0.1−133 Pa range. Readouts of the pressure gauge are recorded in a digital file using LabView 8.6. The desired temperature is attained using electric heating tapes that are uniformly wrapped on the apparatus. J-type thermocouples are attached to the pipe system to
2. EXPERIMENTAL METHODS Explanations of the fractionation apparatus and procedure were provided in Part 1 of this series and are not repeated here. The properties of the bitumen and its cuts are provided again for convenience. The vapor pressure, liquid heat capacity, and elemental analysis measurement procedures are also described. Elemental composition is required for the interconversion method, as it is an input variable for the ideal gas heat capacity equations developed by Laštovka and Shaw.8 2.1. Materials. A Western Canadian bitumen sample (WC_Bit_B1) was utilized in this work; selected physical properties are provided in Table 1. The SBD assay for the whole bitumen is reported in Table 2. The bitumen was deasphalted, and the maltenes were then fractionated into eight cuts plus a residue using the DVFA-II apparatus, as described in the Part 1 of this series. The DVFA-II distillation data and the molecular weight and density of each fraction are summarized in Table 3. 2867
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Table 4. Elemental Analyses (wt %) for Boiling Fractions Obtained Using DVFA-II cut
N
C
H
S
O
1 2 3 4 5 6 residue
0.13 0.00 0.24 0.29 0.45 0.34 0.54
83.19 83.60 83.49 84.21 83.80 83.62 81.92
11.45 10.66 10.44 10.70 10.55 10.45 10.03
3.23 4.36 4.56 4.70 4.90 5.47 6.91
1.72 2.06 2.11 1.93 2.14 1.97 2.04
3. INTERCONVERSION METHODOLOGY 3.1. General Concept. The proposed interconversion approach is illustrated in Figure 2. The left plot demonstrates how the measured vapor pressure in the low-pressure region of a single cut is extrapolated to the normal boiling point. The extrapolation is made with a correlation constrained to fit both thermal and vapor pressure data as a function of temperature. The NBPs from the extrapolations of all of the cuts are then assembled to create the desired boiling point curve, as demonstrated in the right plot of Figure 2. The key to the method is the relationship between vapor pressure, enthalpy of vaporization, and heat capacity. This relationship has been extensively studied not only as an extrapolation technique but also as a methodology to assess the quality of the available experimental data for pure compounds.12−14 The thermodynamic relationship between vapor pressure and caloric properties is given by the Clapeyron equation:
Figure 1. Simplified schematic of the deep-vacuum apparatus DVFA-I. read the temperature, and PID temperature controllers maintain the temperature within ±0.1 K. Measurement. Baking out of the empty apparatus and degassing of the samples are required to eliminate contaminants that would invalidate the vapor pressure readings. The degassing process was carried out at 313 K to minimize possible fractionation of the cuts. The fractions were stored in sealed vials with nitrogen caps at 273 K in order to minimize any potential contamination prior to the vapor pressure measurement. After degassing, the vapor pressure was measured using the following procedure.9 The liquid sample was placed in the sample vessel, and the apparatus was heated to the desired temperature. The pump was switched on, and once the apparatus reached the minimum pressure (or baseline) given by the turbomolecular pump, the vapor pressure was measured in the test section between valves 1 and 2 in cycles. First, the test section was opened to the pump (by opening valve 2 while keeping valve 1 closed) for 2 min. Then the test section was isolated from the pump and opened to the sample (by closing valve 2 and opening valve 1) until the pressure reached a constant value. Finally, valve 1 was closed to isolate the sample, and valve 2 was opened to begin a new cycle. The process was repeated until the peak pressures of at least three consecutive cycles were constant. To account for the leak rate, the pressure reading for each cycle was corrected by extrapolating the pressure back to the time when the cycle started. The repeatability of the measurements is within 3%. The measured vapor pressures for naphthalene and n-hexadecane were within 13% and 4%, respectively, of the literature values.9 The error in the vapor pressure measurements for the boiling fractions is expected to have a maximum error of 13%. 2.3. Liquid Heat Capacity Measurements. The liquid heat capacities of the boiling fractions were measured at the Institute of Chemical Technology, Prague with a Tian−Calvet calorimeter (Setaram μDSC IIIa) in the range from 258 to 355 K using an incremental temperature scanning mode with 5 K steps and a heating rate of 0.3 K/min followed by isothermal delays of 2600 s. A synthetic sapphire (NIST standard reference material no. 720) was used as the reference material. The typical mass of samples was 0.4−1 g. The combined expended uncertainty (0.95 level of confidence) of the heat capacity measurements was estimated to be 1%. Details of the calorimeter, measurement procedure, and its calibration can be found elsewhere.10,11 2.4. Elemental Analysis. The elemental compositions of the boiling fractions were determined by the Chemistry Department at the University of Alberta using a Carlo Erba EA 1108 elemental analyzer. Standards fell within 0.3% of the theoretical values. The experimental values are reported in Table 4
ΔH vap ⎛ d ln P ⎞ ⎟ = ΔH′ RT 2⎜ = ⎝ dT ⎠sat Δz vap
(1)
where R is the gas constant, T is the absolute temperature, P is the vapor pressure, ΔHvap is the enthalpy of vaporization, and Δzvap stands for the difference between the compressibility factors of the saturated vapor and the saturated liquid. ΔH′ represents the ratio of the enthalpy of vaporization to the difference in compressibility factors. Given an expression for vapor pressure as a function of temperature, eq 1 allows the simultaneous correlation of enthalpy of vaporization and vapor pressure as a function of temperature using only one set of constraints. In this case, the available thermal data are heat capacities, and a relationship between vapor pressure and heat capacity is required. First, we define the change in heat capacity, ΔC′, as follows: ΔC′ =
⎛ dΔH′ ⎞ d ⎡ 2⎛⎜ d ln P ⎞⎟⎤ ⎜ ⎟ = ⎢RT ⎝ ⎥ ⎝ dT ⎠sat dT ⎣ dT ⎠⎦sat
(2)
where the second equality comes from eq 1. When the compressibility factor is expressed in terms of a volume-explicit virial expansion truncated after the second virial coefficient and the relation between the heat capacities of the saturated gas and an ideal gas are incorporated into eq 2, the following expression is obtained:5 2868
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Figure 2. Proposed interconversion methodology for deep-vacuum distillation using DVFA-II.
d(B − v l) ⎛ dP ⎞ d2B ⎜ ⎟ − 2T 2 ⎝ dT ⎠sat dT dT ⎛ d2P ⎞ − T (B − v l )⎜ 2 ⎟ ⎝ dT ⎠sat
fractions. They developed two correlations. The first of these, for aromatic hydrocarbons (C0p1), is given by
0 ΔC′ = ΔCvap − TPsat
0 C p1 = A2 +
(3)
×
ΔC0vap
where is the difference in the heat capacities of the saturated phases, B is the second virial coefficient, and vl is the molar volume of the liquid phase. However, the last three terms in eq 3 are significant only at higher values of vapor pressure (P > 5000 Pa). At low pressures, the enthalpy of vaporization and the change in heat capacity expressions reduce to
ΔH′ = ΔH vap
⎛ C11 + C12α ⎞2 exp[−(C11 + C12α)/T ] ⎜ ⎟ ⎝ ⎠ 1 − exp[−(C11 + C12α)/T ] T
⎛ C + C22α ⎞2 ⎟ + (B21 + B22 α)⎜ 21 ⎝ ⎠ T ×
(4)
exp[−(C21 + C22α)/T ] 1 − exp[−(C21 + C22α)/T ]
Their second correlation, for aliphatic hydrocarbons given by
and 0 ΔC′ = ΔCvap = C p0 − Cpl
A1 − A 2 + (B11 + B12 α) 1 + exp[(α − A3)/A4 ]
(6)
(C0p2),
is
⎛ C + C12α ⎞2 0 ⎟ C p2 = A1 + A 2 α + (B11 + B12 α)⎜ 11 ⎝ ⎠ T
(5)
where C0p is the heat capacity of the ideal gas and Clp is the heat capacity of the saturated liquid. This approach has mainly been used to extrapolate vapor pressures in the middle pressure range (between 1000 and 200 000 Pa) toward the triple point; hence, the accuracy of the extrapolation toward the boiling point is unknown. Thus, the required elements for this method are a correlation of vapor pressure to temperature, vapor pressure data, enthalpy of vaporization and/or liquid heat capacity data, and the ideal gas heat capacity. The following steps are required to complete the interconversion method: (1) Collect the following experimental data for each cut: vapor pressure, liquid heat capacity, elemental analysis, and molecular weight. (2) Calculate the ideal gas heat capacity for each cut using the Laštovka−Shaw equations and the elemental analysis of the cut. (3) Select a vapor pressure correlation. (4) Regress the vapor pressure and heat capacity data with an appropriate optimization function and initial guesses. (5) Validate the calculated NBPs versus the data obtained from a spinning band distillation. The data collection procedures were described in Experimental Methods. The remaining steps are described below. 3.2. Ideal Gas Heat Capacity. The correlations for specific ideal gas heat capacity as a function of temperature reported by Laštovka and Shaw8 were shown to give accurate estimates for various hydrocarbon families and ill-defined petroleum
×
exp[−(C11 + C12α)/T ] + (B21 + B22 α) 1 − exp[−(C11 + C12α)/T ]
×
⎛ C21 + C22α ⎞2 exp[−(C21 + C22α)/T ] ⎜ ⎟ ⎝ ⎠ 1 − exp[−(C21 + C22α)/T ] T (7)
In eqs 6 and 7, the A, B, and C parameters are constants and α is the similarity variable, which is given by 5
α=
∑i = 1 (wi /Mi) 5
∑i = 1 wi
(8)
where wi and Mi are the mass fractions and molecular masses of hydrogen, oxygen, nitrogen, sulfur, and carbon (i = 1−5, respectively). The values of the constants are provided in Table 5. The reported relative deviations were 2.9% for aromatic and acyclic aliphatic hydrocarbons and 2.5% cyclic aliphatic hydrocarbons. The ideal gas heat capacity of each cut j was determined as a weighted average of the C0p values obtained from eqs 6 and 7 as follows: C pj0 = w1C p01j + w2C p02j
(9)
where w1 = (H/C)j − 1 and w2 = 1 − w1 for (H/C)j < 1.5 and w2 = 2 − (H/C)j and w1 = 1 − w2 for (H/C)j > 1.5. This weighting is based on a maximum H/C atomic ratio of 2 for 100% paraffinic compounds and a minimum H/C atomic ratio of 1 for highly aromatic compounds. The accuracy of the 2869
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corresponding variables, and Kc is a weighting factor. The experimental vapor pressures were measured directly, and the experimental values of ΔC′ were determined using eq 5. A Kc value of unity was found to provide the best match to the SBD data and was used for all cuts while minimizing the OF. The optimization was sensitive to the initial guess, and a single-step procedure was found to be slow and not always stable. Therefore, the following multistep procedure was adopted: (1) Initialize the optimization with constants fitted to the vapor pressure of eicosane (Table 6) and the heat capacity data of Růzǐ čka and Majer.5 The vapor pressure of eicosane is similar to the vapor pressures of the lightest cuts.
Table 5. Parameters for the Predictive Ideal Gas Heat Capacity Correlations parameter
eq 6
eq 7
A1 A2 A3 A4 B11 B12 C11 C12 B21 B22 C21 C22
0.58 1.25 0.17338 0.014 0.739174 8.883089 1188.281 1813.046 0.048 302 4.356567 2897.019 5987.804
−0.17935 3.869444 − − −0.08053 9.699713 686.4342 1820.466 −0.99964 17.262 43 1532.256 5974.871
Table 6. Vapor Pressure of Eicosane Measured Using DVFAI
predicted ideal heat capacities for the cuts is unknown, but it is expected to be within the accuracy reported by Laštovka and Shaw (within 3%). The liquid and ideal gas specific heat capacities were then converted to molar heat capacities using the molecular weights from Table 3. 3.3. Vapor Pressure Equation. Five different vapor pressure equations were tested for the extrapolation of the vapor pressure data: the Antoine equation, the quasipolynomial equations 6 with two and three adjustable parameters, the Cox equation, and the Korsten equation. The criteria for selecting an appropriate equation were a low number of fitting parameters and an accurate fit of the trends in experimental vapor pressure and heat capacity with temperature. The best result was obtained for the three-parameter Cox equation, given by
(10)
where Pcalc is the calculated saturation pressure, T is the absolute temperature at the saturation pressure, Pb is the atmospheric pressure, Tb is the absolute boiling temperature under atmospheric conditions (i.e., the NBP), and A0, A1, and A2 are the adjustable parameters in the Cox equation. The corresponding equation obtained from the relationship of heat capacity to vapor pressure (eq 2) has the following form: ΔC′
= RT exp(A 0 + A1T + A 0T )
⎛ ln P exp − ln P calc ⎞2 i i ⎟⎟ exp P ln ⎝ ⎠ i
∑ ⎜⎜ i=1
2 m ⎛ ΔC′ exp − ΔCi′ calc ⎞ ⎟ + Kc ∑ ⎜⎜ i ⎟ ΔCi′ exp ⎠ i=1 ⎝
0.3 0.8 2.2 5.6 13.9 33.1 84.8
⎡1 d=⎢ ⎢⎣ n
⎤1/2
∑
⎡ 1 dr = ⎢ ⎢n ⎣
⎛ X calc − X exp ⎞2 ⎤ ∑ ⎜⎜ i exp i ⎟⎟ ⎥⎥ Xi ⎠⎦ i=1 ⎝
n i=1
n
(Xicalc
−
Xiexp)2 ⎥ ⎥⎦
(13) 1/2
(14)
4. RESULTS AND DISCUSSION 4.1. Vapor Pressure and Liquid Heat Capacity Data. The vapor pressures of the WC_Bit_B1 fractions measured with the deep-vacuum apparatus are provided in Table 7. Each fraction has a different temperature range for vapor pressure measurements. The lower limit was selected on the basis of the minimum gauge resolution (low volatility range), and the upper limit was selected to avoid significant losses of the lower-boiling components, which would alter the cut composition. For instance, if the boiling range of a cut was between 453 and 473 K, the maximum temperature at which vapor pressure was measured was 373 K, 80 K below the initial cut temperature. The precision of the vapor pressure measurements for the set of six cuts was within 2.2% based on the pressure differences obtained from the last five cycles for a given temperature. While the accuracy of the cut vapor pressures could not be confirmed,
where the superscript “calc” indicates a calculated value. The Cox equation has four fitting parameters: A0, A1, A2, and Tb. 3.4. Regression Method. The regression is a least-squares minimization of the following objective function (OF) through adjustment of the constants in the Cox equation: n
323 338 353 368 383 398 413
where n is the number of data points, X indicates either ΔC′ or ln P, and the superscripts “exp” and “calc” indicate the measured and calculated values, respectively.
2
× {2A1 + 4A 2 T + (T − T0)[2A 2 + (A1 + 2A 2 T )2 ]} (11)
OF =
p [Pa]
(2) Optimize the Cox constants for vapor pressure only (first term in eq 12). The optimized constants are the initial condition for the next step. (3) Simultaneously optimize vapor pressure and heat capacity (all terms in eq 12). The deviations of the fits to the data are reported as standard deviations (d) and relative standard deviations (dr):
⎛ T ⎞ ln P calc = ln Pb + ⎜1 − b ⎟ exp(A 0 + A1T + A 2 T 2) ⎝ T⎠
calc
T [K]
(12)
where n and m are the numbers of experimental vapor pressure and ΔC′ values, respectively, the subscripts “calc” and “exp” denote calculated and experimental values, respectively, of the 2870
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Table 9. ΔC′exp Values for WC_Bit_B1 Boiling Fractions
Table 7. Measured Vapor Pressures of WC_Bit_B1 Boiling Fractions
ΔC′exp [J mol−1 K−1]
cut
T [K]
p [Pa]
cut
T [K]
p [Pa]
cut
T [K]
p [Pa]
T [K]
cut 1
cut 2
cut 3
cut 4
cut 5
cut 6
1 1 1 1 1 4 4 4 4 4
313.2 333.2 343.2 353.2 363.2 403.2 413.2 423.2 433.2 443.2
0.5 2.5 5.3 11.7 25.5 0.7 1.3 2.2 3.8 6.4
2 2 2 2 2 5 5 5 5
333.2 353.2 373.2 393.2 413.2 423.2 433.2 443.2 458.2
0.06 0.6 2.3 8.6 33.8 2.2 3.6 6.0 12.1
3 3 3 3 3 6 6 6
323.2 353.2 393.2 413.2 433.2 433.2 443.2 453.2
0.002 0.05 2.2 7.2 23.0 1.3 2.1 3.5
258.1 263.2 268.3 273.4 278.5 283.6 288.7 293.8 298.9 304.0 309.1 314.3 319.4 324.5 329.6 334.7 339.8 344.9 350.0 355.1
−139.3 −138.0 −136.9 −135.7 −134.5 −133.4 −132.3 −131.1 −130.0 −128.9 −127.8 −126.8 −125.8 −124.7 −123.7 −122.8 −121.8 −120.9 −120.0 −119.1
−157.2 −155.9 −154.6 −153.4 −152.1 −150.9 −149.7 −148.4 −147.2 −146.0 −144.9 −143.7 −142.6 −141.5 −140.4 −139.3 −138.2 −137.2 −136.2 −135.3
−187.3 −185.8 −184.5 −183.1 −181.7 −180.4 −179.0 −177.7 −176.3 −175.0 −173.7 −172.5 −171.2 −170.0 −168.8 −167.6 −166.4 −165.3 −164.2 −163.1
−213.9 −212.3 −210.8 −209.2 −207.7 −206.2 −204.6 −203.1 −201.6 −200.1 −198.7 −197.2 −195.8 −194.4 −193.0 −191.7 −190.4 −189.1 −187.9 −186.7
−248.8 −245.9 −243.8 −241.1 −239.0 −236.9 −234.8 −233.2 −230.6 −228.3 −226.3 −224.5 −222.8 −221.3 −219.7 −218.2 −216.9 −215.6 −214.3 −212.7
−281.9 −278.7 −276.4 −273.4 −271.1 −268.8 −266.4 −264.7 −261.8 −259.3 −257.2 −255.1 −253.3 −251.7 −249.9 −248.2 −246.9 −245.4 −244.0 −242.3
the measured eicosane vapor pressures were within 8% of the literature data.15 The temperature range over which vapor pressure can be measured is more limited for less volatile cuts; for example, only three data points were collected for cut 6. The range is limited by (1) the lower limit of the gauge readouts, (2) the maximum operating temperature of the gauge, and (3) the maximum temperature that can be used to measure vapor pressure before the loss of the lower-boiling components. The liquid heat capacities of the cuts are provided in Table 8, and Table 9 shows the ΔC′exp values obtained from
4.2. Optimized Fit of the Cox Equation to Vapor Pressure and Heat Capacity Data. The three-parameter Cox equation was used to fit both vapor pressure (Figure 3a) and heat capacity (Figure 3b). The average relative standard deviations for vapor pressure and ΔC′exp were 7% and 1%, respectively, within the experimental error in both cases. It should be noted that the vapor pressures of cuts 4 and 5 overlap even though their heat capacities do not. Possible explanations are (1) experimental errors associated with the high leak rates when the vapor pressures of these fractions were measured; (2) errors in the fractionation temperatures; and (3) significant compositional overlap of these cuts, which would make the vapor pressure differences too small to be determined using the deep-vacuum apparatus. As will be shown later, the extrapolated NBP for cut 5 is off trend from the other cuts, indicating that the measured vapor pressure was lower than expected. It is likely that there was an experimental error in the vapor pressure measurement for this cut. As mentioned in the description of the regression scheme, the average relative deviation dr and average standard deviation d were calculated to evaluate the quality of the temperature fits for the individual properties. Table 10 summarizes the results of the fitting of the Cox equation after the OF was minimized. The vapor pressure and ΔC′exp deviations are within the experimental error. It should be noted that the sensitivity of the interconversion method increases in going from cut 1 to cut 6, as the vapor pressure data become scarce and the low vapor pressure values are less reliable since they are more affected by the leak rate of the deep-vacuum apparatus. 4.3. Interconverted Boiling Points Using Vapor Pressure and Heat Capacity Data. Figure 4 presents the measured boiling points at the apparatus pressure and the interconverted NBPs for WC_Bit_B1. A statistical summary of the final OF values is presented in Table 11. To approximately estimate the effect of the error in the vapor pressure and heat capacity data on the final NBPs, the simultaneous correlation was rerun, changing the experimental values between their maximum and minimum uncertainties described in the first part
Table 8. Measured Liquid Heat Capacities of WC_Bit_B1 Boiling Fractions Clp [J mol−1 K−1] T [K]
cut 1
cut 2
cut 3
cut 4
cut 5
cut 6
258.1 263.2 268.3 273.4 278.5 283.6 288.7 293.8 298.9 304.0 309.1 314.3 319.4 324.5 329.6 334.7 339.8 344.9 350.0 355.1
420.9 425.5 430.0 434.6 439.1 443.7 448.2 452.8 457.3 461.8 466.4 470.9 475.5 480.0 484.6 489.1 493.7 498.2 502.8 507.3
459.8 464.7 469.6 474.5 479.4 484.3 489.2 494.1 499.0 503.9 508.8 513.6 518.5 523.4 528.3 533.2 538.1 543.0 547.9 552.8
536.7 542.4 548.1 553.8 559.5 565.3 571.0 576.7 582.4 588.1 593.8 599.6 605.3 611.0 616.7 622.4 628.1 633.9 639.6 645.3
612.4 619.0 625.5 632.0 638.5 645.1 651.6 658.1 664.6 671.2 677.7 684.2 690.8 697.3 703.8 710.3 716.9 723.4 729.9 736.5
692.3 698.6 705.4 711.7 718.6 725.5 732.4 739.8 746.0 752.7 759.7 766.7 773.9 781.3 788.4 795.7 803.2 810.5 817.9 825.0
775.7 782.7 790.4 797.4 805.1 812.9 820.6 828.9 835.9 843.4 851.2 859.1 867.1 875.4 883.4 891.5 899.9 908.1 916.5 924.4
experimental liquid heat capacities and the calculated ideal gas heat capacities (eq 5). The values of ΔC′exp have four main sources of error: (1) the error in the measured liquid heat capacity, estimated to be 1%; (2) the error in the elemental analysis, estimated to be 0.3 wt %; (3) the error in the measured molecular weight, estimated to be 3.2%; and (4) the error in the ideal gas heat capacity calculated using Laštovka and Shaw correlations, reported to have a maximum deviation of 2.8%. 2871
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Figure 3. Simultaneous fitting of experimental (a) vapor pressure and (b) heat capacity data using the three-parameter Cox equation.
Table 10. Error Analysis of the Optimized Correlation Using the Cox Equation ΔC′exp
vapor pressure cut
d [Pa]
dr [%]
1 2 3 4 5 6
1.1 0.5 0.2 0.1 0.3 0.1
5.2 8.7 3.0 7.8 9.0 10.5
Table 11. Average Absolute Relative Deviations Obtained after Simultaneous Correlation of Vapor Pressure and Heat Capacity Data
d [J mol
−1
0.92 1.17 1.27 1.26 3.05 2.41
K−1]
dr [%] 1.0 1.0 0.8 0.6 1.3 1.0
cut
calculated NBP [K]
OF
maximum deviation [%]
minimum deviation [%]
1 2 3 4 5 6
606 651 690 698 707 743
0.003 0.004 0.044 0.009 0.013 0.004
3.7 4.4 3.6 0.09 0.06 1.1
4.7 3.6 3.2 0.01 0.00 3.3
The calculated NBPs of the first two cuts are within 2% of the SBD data, validating the proposed interconversion method and the DVFA-II fractionation results. For all of the remaining cuts except cut 5, the interconverted normal boiling points follow a Gaussian extrapolation of the SBD data. Hence, for WC_Bit_B1, the Gaussian model is validated as an accurate method for extrapolating distillation data for maltenes as mentioned in Part 1 of this work. Caution is advised with asphaltenes, which self-associate and may not follow the same trend.16 The recommended vapor pressure parameters of the Cox equation are presented in Table 12. It should be noted that the Table 12. Parameters for the Cox Equation Used to Fit Vapor Pressure and ΔC′exp Data with p0 Set to 101 325 Pa Figure 4. Interconverted normal boiling points extrapolated from the simultaneous correlation of vapor pressure and heat capacity. The vertical error bars correspond to the maximum and minimum deviations obtained during the error analysis, and the horizontal error bars correspond to the experimental errors estimated on the basis of the repeatability of the distillation procedure.
of this section. On the basis of a statistical estimate from the expected errors in vapor pressure and ΔC′exp, a propagation of error analysis was computed, and the error bars presented in Figure 4 were determined for each NBP. The error bars in the interconverted boiling point data in Figure 4 represent the maximum and minimum deviations found during the sensitivity analysis; the corresponding deviations obtained for each data point are reported in Table 11. The maximum and minimum relative deviations in the NBPs were 2.2% and −2.5% (corresponding to +8 and −9 K), respectively.
cut
A0
A1 [10−4 K]
A2 [10−6 K−2]
Tb [K]
1 2 3 4 5 6
3.11221 3.21997 3.30326 3.44185 3.51200 3.54805
−22.21270 −21.65373 −23.05355 −22.25477 −23.61439 −26.63337
1.69391 1.79536 1.82732 1.70515 1.68252 2.03107
605.031 651.160 690.603 698.031 706.730 743.266
number of significant digits for Tb does not correspond to the accuracy of the calculated NBP but is required for the accuracy of the correlation from a numerical point of view. In general, the magnitudes of the parameters increased monotonically from the first cut to the last. Hence, the parameters could be correlated to any other property that changes monotonically over a distillation curve, and there is potential to develop a general correlation for heavy oil vapor pressures, heat capacities, and normal boiling points. However, more data 2872
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(7) Castellanos-Diaz, O.; Schoeggl, F. F.; Yarranton, H. W.; Satyro, M. A. Measurement of Heavy Oil and Bitumen Vapor Pressure for Fluid Characterization. Ind. Eng. Chem. Res. 2013, 52, 3027−3035. (8) Laštovka, V.; Shaw, J. M. Predictive correlations for ideal gas heat capacities of pure hydrocarbons and petroleum fractions. Fluid Phase Equilib. 2013, 356, 338−370. (9) Castellanos Díaz, O.; Schoeggl, F.; Yarranton, H. W.; Satyro, M. A.; Lovestead, T. M.; Bruno, T. J. Modeling the Vapor Pressure of Biodiesel Fuels. World Acad. Sci., Eng. Technol. 2012, 6, 839−849. (10) Straka, M.; Růzǐ čka, K.; Růzǐ čka, V. Heat Capacities of Chloroanilines and Chloronitrobenzenes. J. Chem. Eng. Data 2007, 52, 1375−1380. (11) Fulem, M.; Laštovka, V.; Straka, M.; Růzǐ čka, K.; Shaw, J. M. Heat Capacities of Tetracene and Pentacene. J. Chem. Eng. Data 2008, 53, 2175−2181. (12) King, M. B.; Al-Najar, H. A Method for Correlating and Extending Vapour Pressure Data to Lower Temperatures Using Thermal Data: Vapour Pressure Equations for some n-Alkanes at Temperatures below the Normal Boiling Point. Chem. Eng. Sci. 1974, 29, 1003−1011. (13) Ambrose, D.; Counsell, J. F.; Davenport, A. J. The Use of Chebyshev Polynomials for the Representation of Vapour Pressures between the Triple Point and the Critical Point. J. Chem. Eng. Thermodyn. 1970, 2, 283−294. (14) Růzǐ čka, K.; Majer, V. Simultaneous Correlation of Vapour Pressures and Thermal Data: Application to 1-Alkanols. Fluid Phase Equilib. 1986, 28, 253−264. (15) Chirico, R. D.; Nguyen, A.; Steele, W. V.; Strube, M. Vapor Pressure of n-Alkanes Revisited. New High-Precision Vapor Pressure Data on n-Decane, n-Eicosane, and n-Octacosane. J. Chem. Eng. Data 1989, 34, 149−156. (16) Catellanos Díaz, O.; Modaresghazani, M.; Satyro, M. A.; Yarranton, H. W. Modeling the Phase Behavior of Heavy Oil and Solvent Mixtures. Fluid Phase Equilib. 2011, 304, 74−85.
from a variety of source oils are required to determine whether a generalized correlation is possible and what are the best correlation parameters.
5. CONCLUSIONS An interconversion method based on a simultaneous correlation of vapor pressure and heat capacity data was developed for the deep-vacuum fractionation apparatus DVFAII. Measurements of vapor pressure and heat capacity were fitted using a three-parameter Cox equation. The average relative deviations for experimental vapor pressure and heat capacity were within 7% and 1%, respectively. Errors introduced in the interconversion method due to uncertainties in the measured values were analyzed by shifting the original values by their respective error limits and repeating the simultaneous correlation. Average maximum and minimum deviations of 2.2% and −2.5% in the NBP were found for the interconversion technique applied for cuts 1−6. The interconverted boiling points of the first two cuts are within 2% of the NBP curve obtained from spinning band distillation. A Gaussian extrapolation of the spinning band distillation data is equally consistent with the interconverted NBP values, proving that a Gaussian extrapolation is an appropriate model to extrapolate the distillation data of a crude oil, at least for maltenes. DVFA-II extends the range of distillation data to as much as 50 wt % of a bitumen, decreasing the extent of the extrapolation and therefore increasing the certainty in the characterization of bitumen and heavy oil samples.
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AUTHOR INFORMATION
Corresponding Author
*Telephone: (403) 220-6529. Fax: (403) 282-3945. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The authors are grateful to the sponsors of the NSERC Industrial Research Chair in Heavy Oil Properties and Processing: Petrobras, Shell, Schlumberger, and Virtual Materials Group. We thank Drs. O. Castellanos Diaz and V. Laštovka from Shell and M. A. Satyro from Virtual Materials Group for helpful discussions.
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