The Modeling and Simulation of the Convection Section of the Atmospheric Distillation Plant Heaters

The Modeling and Simulation of the Convection Section of the Atmospheric Distillation Plant Heaters CRISTIAN PATRASCIOIU* Petroleum-Gas University of Ploiesti,39 Bucuresti Blvd., 100520, Ploiesti, Romania The paper presents the research results of the design and adaptation of the mathematical model destined to convection heater zone simulation of the crude unit plant. The paper is structured in four parts: the convection heater zone structure, the heat transfer model of inside and outside tubes, the model adaptation and numerical simulation. In the first part there is treated the system of the convection heater zone of the tubular heater. Also there have been identified the input and output variables. The convection heater mathematical model is based on thermal balance equations and newton s law. For the model adaptation process there have been identified four constant types: heater geometrical constants, fuel constants, heated flow constants and burn gases constants. To calculate the heated flow constants there have used two methods. First method uses the empirical relations and the second method uses the Unisim Design simulator. The comparison between the numerical simulation results and the design data there has validated the proposed model. There has been studied the crude oil properties estimation method influence to simulation results. The study has permitted the convection heater zone statically input-output characteristics prediction. Keywords: convection heater zone, thermal balance equations, Unisim Design simulator The modeling of the tube heaters represents a complex problem, the models being classified by the type of dynamic regime (stationary models and dynamic models) and by the special distribution of the parameters (models with concentrated parameters and models with distributed parameters). An example of a model with parameters distributed in stationary regime is realized by Diaz - Mateus [1]. The model proposed is made of two different tub-models, one for the flow that passes through the tubes (the heated flow) and the other for the flow of the burning gases. The model of the heatedflow treats the process as a distributed parameters-system, special attention being paid to the liquid- vapours balance for the oil products. The model of the heat transfer for the burning gases is based on differential relations of the heat transfer through radiation that uses the temperature at the outlet defined by Hottel [2]. The linking element between the two sub-models is the temperature of the tube surface. Since this variable is the inlet variable in the twosub-models, its initialization and recalculation are necessary, the numerical solution of the entire model being iterative. In the paperwork [3], there is presented a dynamic model for a heat exchanger from an energetic group. Through the model is dynamic, the exchanger is treated as a system with concentrated parameters, the relations used being the energy balance equation and Peclet s law. The design and checking of certain types of industrial heat exchangers is realized with specialized programs within these being included HTRI and Unisim Heat Exchanger [4, 5]. For example, within the simulator Unisim Heat Exchanger there is the option Unisim FPH that is used for the design or simulation of a tube exchanger. The inlet data refer to the focus geometry, fuel, the convection section geometry and the heated fluids. The simulator calculates the heat transfer, the temperature and the distribution of pressures in the heating system and the parameters of the outlet flows. An approach based on considering the heat exchanger as a system with concentrated parameters was realized by the author [6, 7]. The developed models allow for a fast estimation of the outlet temperatures of the heat exchanger, being especially useful in exploiting the heat exchangers. Adapting the last type of model to the convection heater represents the main element of the research work presented in this article. The structure of heat exchanger in the convection section Regarding the heat transfer, the convection section of the tube heater is a heat exchanger, with a circulation in crossed counter-flow, (fig. 1a). The hot fluid is represented by the burning gases that leave the radiation section of the heater, while the cold fluid is defined by the feedstock (preheated crude oil). The heat exchanger is characterized by four inlet values and two outlet values, (fig. 1b). The inlet values are as follows: Fig. 1 The heat exchanger associated to the convection section of the tube heater: a) structure; b) block diagram * email: c.patrascioiu@upg.ploiesti.ro; Tel.: (+40)0244573171 REV.CHIM.(Bucharest) 67 No. 8 2016 http://www.revistadechimie.ro 1599

T h1, Q hot - the inlet temperature and the hot fluid (burnt gases); T cl, Q cold - the inlet temperature and the cold fluid (the crude oil). The outlet variables are: T h2 - the outlet temperature of the hot fluid and T c2 - the outlet temperature of the cold fluid. The mathematical model of the convection section in the tube heater The mathematical model of the heat exchanger associated to the convection section of the tube heater is conceived based on the next simplifying hypotheses: -the heat exchanger is considered a system with concentrated parameters; -the heat exchanger is operated in a stationary regime; -the heat transfer with the surrounding environment is neglected. The elaborated mathematical model contains a heat balance equation associated to the two material flows, Q hot and Q cold, and as well as the expression of the transferred heat flow, expression derived out of Newton s law [7-10]. For the heat flow transferred in the heat exchanger, the global heat transfer coefficient has the next expression known in literature [8]: where: α in represents the convection coefficient within the tube; α out - the convection coefficient at the tube outlet; A - the heat transfer area of the heat exchanger. The mathematical models used for the calculus of the convection coefficient at the tube inlet and the outlet, respectively, are presented in the next part. The mathematical model of the heat transfer at the tube outlets The mathematical model of the heat transfer at the tube outlets considers the cumulated effect of the two heat transfer mechanisms, of convection and radiation, respectively, and has the expression [8] the significance of the variables being as follows: α cg - the coefficient of the heat transfer by radiation, from the burning gases to the tubes screen; α rg - the coefficient of the heat transfer by convection, from the burning gases to the tubes screen; z - a term that considers the radiation of the convection area walls, a term defined by the expression: (1) (2) (3) (4) α ps - the surface of the convection area walls, corresponding to a row of tubes; α is - the exposed surface of a row of tubes. The coefficient of heat transfer by the mechanism of convection, α, is calculated with the relation cg Reynolds and Prandtl criterions having the expressions: The physical properties of the burning gases, the dynamic viscosity and the heat transfer coefficient calculated as ponderal rates of the properties of the chemical compounds that make up the burning gases, respectively, CO 2, H 2 O, N 2, O 2 and CO, at the average temperature of the burning gases. The equivalent hydraulic diameter used in the relation (6) has the value d e of a tube diameter in the convection section, The coefficient of heat transfer by radiation from the burning gases to the tubes is calculated with the relation [8]: (8) According to the same source, the transfer coefficients corresponding to the two chemical compounds with radiant properties have the expressions: (5) (6) (7) (9) (10) the parameter significance being the following: e e - the emission coefficient of the screen; P CO2, P H2O - the partial pressures of the compounds; s - the thickness of the gas layer calculated with the relation s 1 - the space between the tubes, horizontally; s 2 the space between the tubes, vertically. (11) The value of the power in the relation (10) is calculated with the expression (12) The coefficient of the heat transfer from walls to tubes, through the radiation mechanism is calculated with Monrad relation, depending on the tubes temperature [11] [J / m 2 hk] (13) The geometrical variables introduced in the relation (4) are: α rp - the coefficient of the heat transfer by radiation from walls to tubes; 1600 http://www.revistadechimie.ro The mathematical model of the heat transfer within the tubes Considering the fact that the flow within the tubes is the crude oil and also viewing industrial realities, the REV.CHIM.(Bucharest) 67 No. 8 2016

mathematical model of the heat transfer within the tubes implies the next simplifying by hypotheses: -the flowing regime is turbulent, without axial dispersion; -the following is just mono-phasical. For the type of mono-phasical flowing, without axial dispersion, the criterial relation [11] may be applied: (14) The criteria Reynolds and Prandtl in the relation (14) have the expressions: (15) (16) The physical properties of the fluid within the tubes are calculated at the average temperature of the fluid: (17) the value of the heat transfer coefficient within the tubes resulting from the relation (14) (18) The adaptation of the mathematical model Table 1 THE GEOMETRIC CHARACTERISTICS OF THE CONVECTION SECTION The adoption of the mathematical model represents the operation of specificating the numerical constant values that interfere within the structure of the mathematical model. These constant values can be classified as follows: -the constant values that are specifically to the heater geometry; -the constant values that are specifically to the used fuel; -the constant values to the heater flow; -the constant values to the specific to the burning gases. The constant values specifically to the heater geometry Geometrically, the convection section of the analyzed atmospheric distillation heater is described in the figure 2 and 3. In figure 2 there is presented an overall view of the section seen from above, while in figure 3 there is a side section. The constructive parameters of the convection section are presented in table 1. Based on the geometrical data previously presented, there have been calculated the geometrical constants specific to the heater convection section, constant values presented in table 2. Constant values specifically to the used fuel In the atmospheric distillation plants, liquid fuel is used, many times, this being the far obtained in the atmospheric distillation column. The analyses effectuated for this fuel type led to the next average values [7]: -relative density, d = 0.9404; -carbon mass fraction, c =0.99081; -caloric power, q inf =40946.1kJ/kg; -fuel enthalpy at 80 C, h comb =150.3 kj/kg. Constant values specific to crude oil Fig. 2 Tubes placement in the convection section of the tube heater Fig. 3. Side section of the convection section REV.CHIM.(Bucharest) 67 No. 8 2016 http://www.revistadechimie.ro 1601

Table 2 GEOMETRICAL CONSTANT VALUES ASSOCIATED TO THE CONVECTION SECTION [m 3 ] Table 3 PROPERTIES OF THE CRUDE OIL SUBJECT TO PROCESSING [12] For the heaters in the atmospheric distillation plant, the feedstock subject to heating and vaporization is the crude oil. This is characterized by the PRF curve, table 3 [12]. The properties of the crude oil used at the calculus of the heat transfer in the convection section of the tube heater are enthalpy, caloric capacity, heat conductivity and dynamic viscosity. In order to determine these properties, two methods have been used: a)the empirical relations; b)the simulator for chemical properties. Determining the crude oil heat properties by using empirical relations Crude oil enthalpy. This property can be calculated based on three elements: -liquid - vapour balance determined by Edmister- Okamoto model; -the empirical relation of the enthalpy dependence in the liquid phase with the temperature; -the empirical relation of the enthalpy dependence in the vapour phase with the temperature. The enthalpy calculus algorithm is widely presented in [13] and contains the following phases: a)the construction of the discrete function associated to the PRF curve by using lab data. b)the construction of the discrete function associated to the curve of average percentages - density. c)the calculus of the VE curve at atmospheric pressure. d)the calculus of the temperature on VE curve corresponding to 50% distillated volume and operating pressure. e)the calculus of the distillated volume for the operating pressure and temperature. f)the calculus of the liquid phase density (depending on the residual volume) and of the density in the vapour phase (depending on the distillated volume). g)the calculus of the enthalpy in liquid and vapours phases by using the relations [8]: Fig. 4. The enthalpy dependence on temperature (19) (20) The enthalpy of the partially vaporized oil product at the heater outlet is calculated with the relation: (21) In figure 4 there is presented the dependence of the enthalpy on temperature, at the absolute pressure of 1.5 bar. Althrough for the domain [50 400] o C the enthalpy varies nonlinearly with the temperature, for subdomains of 100 o C, the enthalpy may be estimated by an approximation function under the form: [kj/kg] (22) 1602 http://www.revistadechimie.ro REV.CHIM.(Bucharest) 67 No. 8 2016

By using the polynomial regression, [14], there have been determined approximation functions of the crude oil enthalpy for various domains of temperature, (table 4). Table 4 THE COEFICIENTS OF THE APPROXIMATION FUNCTION OF THE CRUDE OIL ENTALPHY The heat conductivity. For the oil products, products similar to the crude oil, the conductivity in liquid phase may be estimated with the relation [8] : (23) The dynamic viscosity The crude oil viscosity is treated in a detailed way in the paperwork [15]. Based on the diagram of the dynamic viscosity variation with the temperature and density, there has been determined the next approximation function: (24) where d is the relative density; T - temperature in C. In the table 5 there are presented the coefficients of the approximation function. Determining the crude oil heat properties by using UNISIM Simulator The heat properties of any oil product may be calculated by using Unisim Design Simulator. The use of Unisim Design Simulator for oil products is conditioned by undergoing the following configuration phases [16]: a)selecting the thermodynamic model for the oil products; b)introducing into the Simulator the lab analyses of the oil product; c)calculating the pseudo-components; d)defining the simulation window. e)simulating the liquid- vapour balance. A. Selecting the thermodynamic model. For the oil products, the use of Peng-Robinson thermodynamic model is recommended the model being based on the state equation with the same name, elaborated in the year 1976. B. Introducing into the Simulator the lab analyses of the oil product. The experimental data consists in temperature and density values of all the distillated fractions and the crude oil experimental density value. The implementation of these experimental data is achived by the next specifications of Assay menu: - Bulk Properties = Used -Assay Data Type = TBP - Light Ends = Ignore - Molecular Wt. Curve = Not Used - Density Curve = Independent - Viscozity Curves = Not Used C. Calculating the pseudo-components. Determining the pseudo-components takes place in two stages [16]: -In the first stage there are selected the theoretical pseudo-components included between the first and the last distillation temperature of the PRF distillation curve. -The second stage contains the calculus of the concentration of each pseudo-component, so that the PRF curve calculated on the basis of pseudo-components is as close as the experimental one, while the calculated density of the pseudo-components mixture is equal to the crude oil experimental density. The gap between the two curves is very small and for this reason decompose of the crude oil in pseudo components is validated. In figure 5 there is presented the composition between the two PRF curves (experimental and calculated). Figure 5 Comparison between the PRF curve, calculated based on the pseudo-components, and the PRF curve calculated by experimental data. D. Defining the simulation window. After having undergone the operation referring to the selection of the Table 5 THE COEFICIENTS OF THE APPROXIMATION FUNCTION Fig. 5 Comparison between the PRF curve (calculated based on the pseudocomponents) and the PRF curve calculated by experimental data REV.CHIM.(Bucharest) 67 No. 8 2016 http://www.revistadechimie.ro 1603

Table 6 THE CRUDE OIL HEAT PROPERTIES (UNISIM DESIGN) Table 7 THE COEFICIENTS OF THE POLYNOMIAL REGRESSION pseudo-components associated to the crude oil and the calculus of their concentration, the next phase is exploited these data within the list of chemical compound. The material flow that will use these pseudo-components is specified and by activating the commands specific to Unisim Design Environment, the control of the program will return in the simulation menu, the material flow previously defined becomes active, the user being able to pass to defining the thermodynamic conditions of this one. E. Simulation of liquid-vapour equilibrium. The crude oil subject to heating in the convection section of the heater in the atmospheric distillation plant is characterized by the pressure of 7 bar and temperatures ranged between the domain [200 300] o C. The simulation of the liquid-vapour equilibrium under these conditions generated the values of the heat properties presented in table 6. A specific problem of this simulator is the value of enthalpy. The simulator Unisim Design calculates the value of the enthalpy in other standard conditions as compared to the classical system. This specific aspect results in a difference between the enthalpy numerical values calculated in Unisim Design simulator and the numerical values calculated in classical standard conditions (pressure of 1bar and temperature of 0 o C. The absolute variations of the enthalpy aren t different in comparison to the standard condition assumed within the two methods. As the other heat properties used within the mathematical model are calculated based on the classical standard conditions, there was necessary a recalculation of the results obtained with Unisim Design Simulator using the value of 438.5 kj/kg of the enthalpy determined at 200 o C [15]. By using the data in table 6, there have been calculated the coefficients of the approximation functions for caloric capacity, heat conductivity, dynamic viscosity and mass enthalpy, (table 7). In table 8 there are presented approximation functions of viscosity, caloric capacity and conductivity of the following chemical components: carbon dioxide, water, nitrogen, oxygen and carbon monoxide. Simulation of the convection section of the atmospheric distillation heater The mathematical model of the convection section is defined by the system of equations (1), where the unknown variables are T c2 and T h2. Due to the nonlinear interactions between the two variables and the global heat transfer coefficient, the system (1) is a nonlinear system under the form: where the two functions have the expressions: (26) (27) Table 8 THE COEFICIENTS OF THE APPROXIMATION FUNCTION OF THE BURNING GASES (28) Constant values specific to the components existing in the burning gases The fourth phase of adaption of the mathematical model is represented by determining the approximation function of the physical properties of the components existing in the burning gases. For all these properties there has been used data in the literature [17] and based on it there were generated approximation functions under the form: (25) 1604 http://www.revistadechimie.ro REV.CHIM.(Bucharest) 67 No. 8 2016

The algorithm used for solving the systems of nonlinear equations is Newton-Raphson [18]. A particular aspect of this algorithm is represented by Jacobean matrix associated to the nonlinear system of equations (26) (29) For the numerical evaluation of the Jacobean matrix there has been used the relation For the current point the variation being defined: (30) (31) Based on the previously presented algorithm there havebeen realized two versions of calculus programs for simulating the convection section: a version that uses emirical relations for calculating the crude oil propertiesand the second version based on the simulator Unisim Design. Both programs have been tested by using the following heater design data: -crude oil flow -the crude oil inlet temperature -fuel flow -the coefficient of the air quantity. As far as the temperature of the burning gases at the inlet of the tube heater convection section is concerned, the value of 800 o C is adopted [8, 11]. The simulation of the convection section of the heater in the atmospheric distillation plant prints at three purposes. The first purpose aimed at is the validation of the mathematical model. Taking into consideration the design old age, the first test have been realized with the version that uses empirical relations for the calculus of the crude oil properties. By comparing the calculated value of crude oil outlet temperature, 276.9 o C, with the value calculated in the project, 272.0 o C, there results a very good closeness of the values, a fact that validates both the proposed model and the adaption phase of the model. The second purpose of the simulations is the study of the influence of the estimation way of the crude oil properties. In table 9 there are comparatively presented the results obtained for the two versions of calculating the crude oil properties. The most significant difference, 30% compared to the calculated value by using Unisim Design simulator, is registered for the crude oil viscosity. This difference in the estimation of the crude oil properties manifests especially at the crude oil outlet temperature, respectively 8.9%. The third purpose of the simulation is the calculus of the static characteristics of inlet-outlet type of the tube heater convection section. For the simulation there have been varied two variables: the feedstock inlet temperature and the burnt gases inlet temperature. As the heat exchanger is a multivariable system, changing an inlet variable will generate changes of both outlet variables. The feedstock inlet temperature generates a linear variation of the feedstock outlet temperature and burnt gases temperature. The linear static characteristics obtained indicate a good design of the convection section of the analyzed tube heater that is subject to analysis. Table 9 RESULTS OBTAINED AT THE CONVECTION SECTION SIMULATION T gaze_iesire Fig. 6 The dependence of the outlet burning gases temperature versus the burn gases inlet temperature REV.CHIM.(Bucharest) 67 No. 8 2016 http://www.revistadechimie.ro 1605

The second set of results has been obtained by unfolding the simulation program under the conditions of change of the burnt gases inlet temperature. The variation of the feedstock outlet temperature has a same linear character but burnt gases outlet temperature has a slight nonlinear character, figure 6. Conclusions The paperwork presents the results of the research related to the elaboration and adaption of a mathematical model destined to the simulation of the convection section of the tube heater in an atmospheric distillation plant. For the convection section of the furnace, which is a heat exchanger with countercurrent flow, the input and output variables are defined. The structure of the mathematical model for this section is based on heat balance and Newton s Law. The expressions of the heat transfer partial coefficients were found in the literature. A special attention was paid to the mathematical model adaptation. Thus, there were defined four stages of the adaptation process related to the calculation of the following type of constants specific to: the furnace geometry, the used fuel, the heated flow and the burning gases. The heated flow and burning gases specific constants are nonlinear approximation functions of the temperature related properties. Regarding the heated flow constants there were used two methods. First method uses empirical relations and graphical correlations from the literature. Second method is based on the use Unisim Design environment for calculation of the properties on different temperatures. From mathematical point of view, the simulation of the convection section of the atmospheric distillation furnace represents the numerical solving of a nonlinear equation system, and the chosen solving option was the Newton- Raphson algorithm and the Jacobian matrix calculation through numerical derivation. The simulation of the convection section had three objectives: mathematical model validation, study of the oil properties estimation influence on the simulation results, and determination of input-output characteristics. The comparison of the simulation results with the design data led to the validation of the proposed mathematical model. Regarding the oil properties estimation influence, the results emphasized the following deviations: Oil output temperature 9%; Prandtl criterion 58%; Convection partial coefficient in tubes interior 18%. There is estimated that the calculation of the properties influences the convection section output temperature. A better approach of this problem can be done only by comparing the numerical results with measured data. This study allowed the determination of the input-output characteristics for the convection section of the furnace. Except for the characteristic output temperature of the burning gases related to input temperature of the same gases (nonlinear characteristic), the other three characteristics are linear. This conclusion is useful for the development of a simplified model for the convection section of the furnace. Notations T h1 hot input fluid temperature; T c1 cold input fluid temperature; Q hot hot flowrate; Q cold cold flowrate; T hot2 hot output fluid temperature; T cold2 cold output fluid temperature; K ed global heat transfer coefficient; α in - inlet tube partial heat transfer coefficient; α out - outlet tube partial heat transfer coefficient; µ - dynamic viscosity; λ - heat transfer coefficient; c p heat capacity. References 1.DIAZ-MATEUS, F., A., CASTRO-GUALDRON, J., A., Mathematical Model for Refinery Furnaces Simulation, Ciencia, Tecnologia y Futuro, 4, No. 1, 2010, p. 89. 2.HOTTEL, H., C., First estimates of industrial furnace performancethe one-gas-zone model re-examined, Heat Transfer in Flames, 1974. 3.RAFAL L., KRZYSZTOF W., Comparison of two simple mathematical models for feed water heaters, Journal of Power Technologies 91, no. 1, 2011, p. 14. 4.* * * www.htri.net/software.aspx 5.* * * www.htri.net/unisim-fired-process-heater-modeler.aspx 6.PATRASCIOIU, C., IOAN, V., The Steady-State Modeling and Simulation of a Heat Exchanger, Petroleum-Gas University of Ploiesti Bulletin, LXI, No. 3, 2009, p.187. 7.PATRASCIOIU, C., NEGOITA, L., The Convection Heater Numerical Simulation, XII International Conference on Thermal and Fluids Engineering, International Science Index, 8, No. 4, 2014, p. 335. 8.DOBRINESCU, D., Thermal transfer Processes and Specifically Devices, Editura Didactica si Pedagogica, Bucuresti, 1983. 9.PATRASCIOIU, C., RADULESCU, S., Prediction of the outlet temperatures in triple concentric - tube heat exchangers in laminar flow regime: case study, Heat and Mass Transfer, 51, 1, 2015, p. 59. 10.PATRASCIOIU, C, RADULESCU, S., Modeling and Simulation of the Double Tube Heat Exchangers. Case Studies, 10th WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment, 2012, p. 35. 11.SUCIU, GH., TUNESCU, R., Ingineria prelucrãrii hidrocarburilor, vlog II, Editura Tehnicã, Bucureºti, 1985. 12.RADULESCU, G., A., Proprietatile titeiurilor romanesti, Editura Academiei Romane, 1961. 13.PATRASCIOIU, C., PASCU, C., Numerical Modeling of Vapor-Liquid Equilibrium by using the Edmister - Okamoto Model, Rev.Chim.(Bucharest), 60, no. 7, 2009, pp. 728-734. 14.PATRASCIOIU C., Metode numerice aplicate in ingineria chemicals Aplicatii in PASCAL, Editura MatrixRom, Bucuresti, 2005. 15.BERGHOFF, O., W., Erdolverarbeitung und Petrochemie Tafeln und Tabellen, VEB Ditcher Velar fur Grundstoffindustrie, Lepzig, 1967. 16.PATRASCIOIU, C., POPESCU, M., Sisteme de conducere a processor chimice, Editura Matrix Rom Bucuresti, 2013. 17.KUZMAN, R., Tables ºi diagrame termodinnamice, Editura Tehnicã, Bucureºti, 1978. 18.PATRASCIOIU, C., MARINOIU, C., The applications of the non-linear equations systems algorithms for the heat transfer processes, Proceedings of 12th WSEAS International Conference on MATHEMATICAL METHODS, COMPUTATIONAL TECHNIQUES AND INTELLIGENT SYSTEMS, Tunisia, 2010, p. 30. Manuscript received: 25.01.2016 1606 http://www.revistadechimie.ro REV.CHIM.(Bucharest) 67 No. 8 2016