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3960 Energy & Fuels 2009, 23, 39603970 Oil Characterization from Simulation of Experimental Distillation Data Marco A. Satyro* and Harvey Yarranton Department of Chemical and Petroleum Engineering, the UniVersity of Calgary, Department of Chemical and Petroleum Engineering, Calgary, Alberta, Canada T2N 1N4 ReceiVed January 9, 2009. ReVised Manuscript ReceiVed June 1, 2009 The characterization of crude oil involves dividing the oil into pseudocomponents and allocating mole fractions, molar mass, specific gravity, average boiling point, and critical properties to each component. The characterization is typically based on distillation data reported in terms of true boiling points. Standard assay types such as the ASTM D86 or ASTM D1160 vacuum distillation do not provide well established saturated bubble temperatures and require empirical interconversion curves to convert the assay data into true boiling point (TBP) data. Recently developed assays such as the ASTM D5236 and Brunos new distillation assay methodology do provide well-defined saturated bubble temperatures that correspond to actual thermodynamic state points but lack an established interconversion method to a TBP, that is, a method to determine the TBP of the fluid based on the measured temperatures of the assay. In this work, a methodology is presented to determine pseudocomponent mole fractions that match the boiling point data from these new assays. The fluid is divided into pseudocomponents of different average boiling point, and the molar mass and other physical properties of each component are determined using established correlations. A simulation of the distillation is optimized to match the assay data by adjusting the mole fraction of each pseudocomponent. The characterization can also be constrained to match other data such as the bulk density and molar mass of the fluid. The proposed methodology is tested on naphtha and Alaska crude oil and then verified through three heavy oil case studies. The methodology is entirely general and can be applied to a compositional analysis from a distillation of any material. Introduction The characterization of heavy oils and bitumen is a funda- mental step in the design, simulation, and optimization of solvent extraction plants and distillation facilities. In refinery applica- tions, the oil is typically characterized based on a distillation assay. This procedure is reasonably well-defined and is based on the representation of the mixture of actual components that boil within a boiling point interval by hypothetical components that boil at the average boiling temperature of the interval. These pseudocomponents are also constrained to match the average The technique hinges on our ability to develop a true boiling point curve (TBP) for the material of interest. The TBP corresponds to a distillation performed under high reflux and large number of theoretical in order to obtain as sharp a separation as possible between the actual components that make up the oil making it expensive to run. Commonly other distillation experiments are performed under low reflux as well as at vacuum, and empirical correlations are used to convert this data into TBP curves. The most common techniques are briefly discussed below; for a more extensive description, see 2 physical properties of the original bulk fluid, such as molecular weights and densities. The set of these hypothetical components with their compositions is then used as a facsimile for the actual fluid, since its actual composition is usually too difficult to obtain using analytical techniques. Once the normal boiling point, density, and molecular weight of the pseudocomponents are determined, important physical properties such as vapor pressures, critical constants, and ideal gas heat capacities can be estimated using established correla- tions.1-3 These properties are the inputs required to use an equation of state or other thermodynamic model to calculate the thermodynamic equilibrium of the mixture. * To whom correspondence should be addressed. E-mail: msatyro ucalgary.ca. (1) Whitson, C. H.; Brule, M. R. Phase Behavior, Monograph Vol. 20, SPE, Henry L. Doherty Series, Richardson, TX, 2000. (2) Riazi, M. R. Characterization and Properties of Petroleum Fractions, 1st ed.; ASTM Manual Series, American Society of Testing and Materials: Philadelphia, PA, 2005. (3) Pedersen, K. S.; Fredenslund, A.; Thomassen, P. Properties of Oils and Natural Gases; Gulf Publishing: Houston, 1989. Riazi. Traditionally, distillation assays were designed to provide the maximum amount of fractionation while performing a batch distillation.4 The reasoning behind this is very simple: we wish to have the maximum amount of separation between the different constituents that make up the oils. In theory, if a batch distillation apparatus was operated at very high reflux rates and a very large number of equivalent equilibrium stages, a good discrimination of the original hydrocarbon mixture could be obtained. This is the motivation for true boiling point (TBP) assays. This idea has found universal use in the refinery industry, and several different distillation methods are available and described in the technical literature.5 To mitigate the costs associated with time when running TBP experiments as well (4) Kaes, G. L. Refinery Process Modeling - A Practical Guide to Steady- State Modeling of Petroleum Processes, Athens Publishing, Atlanta, GA: 2000. (5) American Petroleum Institute. Technical Data Book - Petroleum Refining, 5th ed.; Refining Department, AIP: Washington, DC, May 1992. 10.1021/ef9000242 CCC: $40.75 2009 American Chemical Society Published on Web 07/09/2009 Oil Characterization Energy & Fuels, Vol. 23, 2009 3961 as address the lack of standardized specifications for TBP apparatuses, the American Society for Testing of Materials (ASTM) has defined a series of useful experiments for the characterization of conventional hydrocarbon mixtures such as the D866 and D28877 assays. The D86 assay is one of the oldest and simplest methods for the measurement of boiling points of petroleum fractions and is used mostly for naphthas, gasolines, kerosenes, gas oils, and fuel oils. The method cannot be used for mixtures containing very heavy materials that cannot be vaporized and should be used with caution when temperatures are higher than 250 C because of possible thermal cracking of material in the still. The D2887 assay is based on gas chromatography (GC) and results in a simulated distillation curve (SD). It is now a common way to represent distillation data. Since the analysis is done via chromatographic analysis, the results are presented in %mass distilled coordinates instead of the most common %volume distilled of other assays. Results from SD are similar to TBP results, but interconversion methods are required2 and it is debated if conversion methods should be used at all and how to handle heavily aromatic fluids.4 Other assays, such as the D1160 assay,8 are designed to handle high boiling materials and the need to conduct distillation under vacuum to avoid thermal cracking that would occur if the assay was conducted at higher pressures. The American Petroleum Institute provides well-defined procedures for the conversion of distillation data collected using these standard methods to TBP data. From this point onward the data is converted into pseudocomponents that are used to model the thermodynamic properties of the mixture, which are then used for reservoir and process simulation as well as the design and simulation of separation equipment.4,9 There are two problems associated with the use of these standard methods. First, the data must be converted into an equivalent TBP curve. Although API took great care in the development of conversion procedures, inconsistencies are sometimes unavoidable because of the empirical nature of the methods such as the problems reported by Daubert10 and Satyro.11 Second, the measured values from these procedures are not easily associated with well-defined thermodynamic state points such as bubble point temperatures. The procedures are usually defined based on the performance of a related batch distillation. It is necessary to model the equipment used for the measurements very accurately if one were to associate the measurements from a normal distillation assay with true thermodynamic state points. Two recent methods, Bruno12 and D5236,13 offer a solution to these problems. Bruno12 developed a thermodynamically consistent assay procedure in which the measured distillation temperature corresponds to a true thermodynamic state point. This was (6) ASTM D86 - 07b Standard Test Method for Distillation of Petroleum Products at Atmospheric Pressure; /Standards/D86.htm (accessed Nov 30, 2008). (7) ASTM D2887 - 06a Standard Test Method for Boiling Range Distribution of Petroleum Fractions by Gas Chromatography; http:/ /Standards/D2887.htm (accessed Nov 30 2008). (8) ASTM D1160 - 06 Standard Test Method for Distillation of Petroleum Products at Reduced Pressure; /Standards/ D1160.htm (accessed Nov 30 2008). (9) VMGSim Users Manual, Version 4.0, Virtual Materials Group, Inc., Calgary, Alberta, 2009. (10) Daubert, T. E. Hydrocarbon Process. 1994, 73 (9), 7578. (11) Satyro, M. A.; Satyro, M. A. Life, Data and Everything. Pure Appl. Chem. 2007, 79 (8), 14031417. (12) Bruno, T. J. Ind. Eng. Chem. Res. 2006, 45, 43714380. (13) ASTM D5236 - 03(2007) Standard Test Method for Distillation of Heavy Hydrocarbon Mixtures (Vacuum Potstill Method); http:/www.astm. org/Standards/D5236.htm (accessed Nov 30 2008). accomplished by carefully positioning the thermometer in the boiling fluid, thus ensuring the measurement of instantaneous bubble temperatures. Brunos procedure also allows for the measurement of compositions, although this feature is not necessary for the procedure proposed in this paper. Bruno and co-workers have used this method to analyze a wide variety of different mixtures.14-16 They also propose the use of the method in association with a comprehensive equation of state package17 for the development of surrogate mixtures (mixtures of known compositions of pure components designed to represent more complex mixtures). This approach has proven successful and has been used in the development of consistent thermodynamic models for biodiesel.18 In Canada, more and heavier hydrocarbon fluid characteriza- tions are being performed using the D5236 ASTM method.13 The method was developed to assist in the characterization of high boiling point materials, and the equipment was designed in such a way as to allow distillation under high vacuum. This method is similar to Brunos method in one very important feature: the measured temperatures are also the instantaneous bubble temperature. Hence, for both the Bruno method and the D5236, the measured temperature has a precise thermodynamic meaning and can be calculated from a fluid characterization directly without a detailed knowledge of the equipment actually used for the measurements. Empirical methods of interconver- sion and detailed models of the apparatus are not required. However, neither the Bruno nor the D5236 method has a conversion procedure to TBP, thus limiting their use. The objective of this work is to develop an interconversion method for these assays. We propose a methodology based on Eckert and Vaneks19 detailed mathematical procedure for the modeling of D86 experiments. Their work was not based on raw hydrocarbon fluids but rather synthetic mixtures made of hydrocarbons ranging from 4 to 10 carbon numbers including paraffins, naphthenes, and aromatics. They used the ideal gas model for the gas phase and the NRTL model for the liquid phase, and their predictions compared reasonably well with the measured data. For most distillation assays, the complexity of the mathematical model necessary for the solution of the non- steady-state material and energy balance equations makes it difficult to use. In addition, the model must still be validated against the actual distillation campaign and idiosyncrasies related to the actual equipment. Fortunately, a simpler modeling is possible for the Bruno and D5236 assays because the temper- atures correspond to instantaneous values of the mixture boiling point and can be determined directly from the fluid characteriza- tion. The gist of the proposed method is to determine what initial composition of the pseudocomponents defining the fluid cor- responds to the same trajectory of measured temperature versus volume of material distilled. In this paper, the methodology is developed, its internal consistency is tested on two data sets (one a mixture of well-defined pure components the other a (14) Bruno, T. J.; Smith, B. L. Ind. Eng. Chem. Res. 2006, 45, 4381 4388. (15) Smith, B. L.; Bruno, T. J. Ind. Eng. Chem. Res. 2006, 46, 310 320. (16) Smith, B. L.; Bruno, T. J. Energy Fuels 2007, 21 (5), 28532862. (17) Huber, M. L.; Lemmon, E. W.; Diky, V.; Smith, B. L.; Bruno, T. J. Energy Fuels 2008, 22 (5), 32493257. (18) Ott, L. S.; Bruno, T. J. Energy Fuels 2008, 22 (4), 28612868. (19) Eckert, E.; Vanek, T. Chem. Pap. 2008, 62 (1), 2633. 3962 Energy & Fuels, Vol. 23, 2009 Satyro and Yarranton trajectory of the bubble temperature as a function of material distilled from the batch apparatus. The fundamental equation is the non-steady-state component material balance,24 eq 1: djx d = jx jy (1) Figure 1. Batch distillation without refluxing: residue curve map generation. mixture of pseudocomponents), and then it is applied to three case studies. Modeling The unifying concept for the understanding and modeling of distillation assays is the residue curve. This concept was probably put forth first by Schreinenmakers in 19012022 and since then has been used with great success as a tool for the conceptual design of distillation systems.23 The residue curve is the profile of saturation composition versus boiling temper- ature as a distillation progresses. If the original composition of a mixture is known and the pressure is specified then, for a batch apparatus, the profile can be determined based on rigorous thermodynamics and material balance equations. It is important to notice that the technique is a close representation of the measurement of a distillation assay only if the measured temperature in the assay corresponds to the actual bubble temperature of the material inside the batch apparatus and that no rectification happens during the experiment. These are the two experimental characteristics that make Brunos and D5236 distillation assays ideal for mathematical representation using residue curves. The trajectory calculation and a procedure to find the pseudocomponent compositions that fit a given trajec- tory are outlined below. Trajectory Calculation. The mathematics for modeling the temperature trajectory of a batch distillation were developed in detail by Doherty and Perkins24 and shown in Figure 1. This technique is usually referred to as residue curVe map and is the representation of the trajectory of all saturation conditions between an initial feed and a final state where the batch distillation process is stopped. Usually residue curve analysis is used to identify the topology of the bubble temperature space, such as minimum and maximum azeotropes and related distil- lation boundaries. In our case, we are concerned with another piece of information encoded in the residue curve map: the (20) Schreinenmakers, F. A. H. Z. Phys. Chem. 1901, 36, 257289. (21) Schreinenmakers, F. A. H. Z. Phys. Chem. 1901, 36, 413499. (22) Schreinenmakers, F. A. H. Z. Phys. Chem. 1903, 43, 671. (23) Doherty, M. F. Malone, M. F. Conceptual Design of Distillation Systems; McGraw-Hill: New York, 2001. (24) Doherty, M. F.; Perkins, J. D. Chem. Eng. Sci. 1978, 33 (3), 281 301. where jx represents the saturated liquid mole fraction vector, jy represents the saturated vapor mole fraction vector, and represents the warped time. The warped time is a nondimen- sional time used to describe the trajectory of the composition inside a vessel undergoing batch distillation without a reflux. At any given warped time, the temperature and vapor-phase composition can be determined from the liquid-phase composi- tion and a bubble point calculation. Doherty and Perkins also show how to convert the warped time information into hold-up information, thus allowing the distillation trajectory to be traced as a function of material distilled and the associated bubble temperature. The holdup in the batch is given by eq 2: H = H exp( ) (2) where H is the liquid holdup (remaining moles of liquid in distillation flask) at a given warped time and H is the initial holdup. The combination of eqs 1 and 2 allow for rapid determination of the temperature trajectory as a function of amount of material distilled (in mass, mole, or volume basis). If the actual distillation campaign was to be modeled, real time and real duties associated to the experiment would be required. In our case, time is immaterial; we are just interested in the bubble temperature trajectory. Given an initial state, eq 1 can be readily integrated using a variety of methods. A simple Euler first-order method was used here as follows: where m and m 1 are integration step counters, is the integration step in warped time, jx and jy are the change in liquid- and vapor-phase composition, respectively, Tsat is the saturation pressure determined from a bubble point cal