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 exchangers is realized with specialized programs within problem, the models being classified by the type of these being included HTRI and Unisim Heat Exchanger [4, dynamic regime (stationary models and dynamic models) 5]. For example, within the simulator Unisim Heat and by the special distribution of the parameters (models Exchanger there is the option Unisim FPH that is used for with concentrated parameters and models with distributed the design or simulation of a tube exchanger. The inlet data parameters). refer to the focus geometry, fuel, the convection section An example of a model with parameters distributed in geometry and the heated fluids. The simulator calculates stationary regime is realized by Diaz - Mateus [1]. The model the heat transfer, the temperature and the distribution of proposed is made of two different tub-models, one for the pressures in the heating system and the parameters of the flow that passes through the tubes (the heated flow) and outlet flows. the other for the flow of the burning gases. The model of An approach based on considering the heat exchanger the heatedflow treats the process as a distributed as a system with concentrated parameters was realized parameters-system, special attention being paid to the by the author [6, 7]. The developed models allow for a fast liquid- vapours balance for the oil products. The model of estimation of the outlet temperatures of the heat exchanger, the heat transfer for the burning gases is based on being especially useful in exploiting the heat exchangers. differential relations of the heat transfer through radiation Adapting the last type of model to the convection heater that uses the temperature at the outlet defined by Hottel represents the main element of the research work [2]. The linking element between the two sub-models is presented in this article. the temperature of the tube surface. Since this variable is the inlet variable in the twosub-models, its initialization The structure of heat exchanger in the convection and recalculation are necessary, the numerical solution of section the entire model being iterative. Regarding the heat transfer, the convection section of In the paperwork [3], there is presented a dynamic the tube heater is a heat exchanger, with a circulation in model for a heat exchanger from an energetic group. crossed counter-flow, (fig. 1a). Through the model is dynamic, the exchanger is treated The hot fluid is represented by the burning gases that as a system with concentrated parameters, the relations leave the radiation section of the heater, while the cold used being the energy balance equation and Peclet’s law. fluid is defined by the feedstock (preheated crude oil). The The design and checking of certain types of industrial heat 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

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REV.CHIM.(Bucharest)♦67♦No. 8 ♦2016 http://www.revistadechimie.ro 1599 α Th1, Qhot - the inlet temperature and the hot fluid (burnt ps - the surface of the convection area walls, gases); T , Q - the inlet temperature and the cold fluid corresponding to a row of tubes; cl cold α (the crude oil). The outlet variables are: Th2 - the outlet is - the exposed surface of a row of tubes. temperature of the hot fluid and T - the outlet temperature The coefficient of heat transfer by the mechanism of c2 α of the cold fluid. convection, cg , is calculated with the relation The mathematical model of the convection section in the tube heater (5) The mathematical model of the heat exchanger Reynolds and Prandtl criterions having the expressions: 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; (6) -the heat exchanger is operated in a stationary regime; -the heat transfer with the surrounding environment is neglected. (7) The elaborated mathematical model contains a heat balance equation associated to the two material flows, The physical properties of the burning gases, the Qhot and Qcold, and as well as the expression of the transferred dynamic viscosity and the heat transfer coefficient heat flow, expression derived out of Newton’s law [7- 10]. calculated as ponderal rates of the properties of the chemical compounds that make up the burning gases,

respectively, CO2, H2O, N2, O2 and CO, at the average temperature of the burning gases. The equivalent hydraulic

(1) diameter used in the relation (6) has the value de of a tube diameter in the convection section, The coefficient of heat transfer by radiation from the For the heat flow transferred in the heat exchanger, the burning gases to the tubes is calculated with the relation global heat transfer coefficient has the next expression [8]: known in literature [8]: (8) According to the same source, the transfer coefficients (2) corresponding to the two chemical compounds with radiant properties have the expressions: where: α in represents the convection coefficient within the tube; (9) 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. (10) The mathematical model of the heat transfer at the tube the parameter significance being the following: outlets ee - the emission coefficient of the screen; The mathematical model of the heat transfer at the tube PCO2, PH2O - the partial pressures of the compounds; outlets considers the cumulated effect of the two heat s - the thickness of the gas layer calculated with the transfer mechanisms, of convection and radiation, relation respectively, and has the expression [8] (3) (11)

s1 - the space between the tubes, horizontally; the significance of the variables being as follows: s – the space between the tubes, vertically. α 2 cg - the coefficient of the heat transfer by radiation, from the burning gases to the tubes screen; The value of the power in the relation (10) is calculated α rg - the coefficient of the heat transfer by convection, with the expression from the burning gases to the tubes screen; z - a term that considers the radiation of the convection (12) area walls, a term defined by the expression: 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] (4) [J / m2hK] (13)

The geometrical variables introduced in the relation (4) are: The mathematical model of the heat transfer within the α tubes rp- the coefficient of the heat transfer by radiation from walls to tubes; Considering the fact that the flow within the tubes is the crude oil and also viewing industrial realities, the

1600 http://www.revistadechimie.ro REV.CHIM.(Bucharest)♦67♦No. 8 ♦2016 mathematical model of the heat transfer within the tubes The adoption of the mathematical model represents the implies the next simplifying by hypotheses: operation of specificating the numerical constant values -the flowing regime is turbulent, without axial dispersion; that interfere within the structure of the mathematical -the following is just mono-phasical. model. These constant values can be classified as follows: For the type of mono-phasical flowing, without axial -the constant values that are specifically to the heater dispersion, the criterial relation [11] may be applied: geometry; -the constant values that are specifically to the used (14) fuel; -the constant values to the heater flow; -the constant values to the specific to the burning gases. The criteria Reynolds and Prandtl in the relation (14) have the expressions: The constant values specifically to the heater geometry Geometrically, the convection section of the analyzed (15) 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 (16) section. The constructive parameters of the convection section are presented in table 1. Based on the geometrical The physical properties of the fluid within the tubes are data previously presented, there have been calculated the calculated at the average temperature of the fluid: geometrical constants specific to the heater convection section, constant values presented in table 2. (17) Constant values specifically to the used fuel the value of the heat transfer coefficient within the tubes In the atmospheric distillation plants, liquid fuel is used, resulting from the relation (14) 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]: (18) -relative density, d = 0.9404; The adaptation of the mathematical model -carbon mass fraction, c =0.99081; Table 1 -caloric power, qinf =40946.1kJ/kg; THE GEOMETRIC CHARACTERISTICS OF THE CONVECTION -fuel enthalpy at 80 C, hcomb=150.3 kJ/kg. SECTION 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 [m3]

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 Fig. 4. The enthalpy dependence on temperature 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 (19) the vapour phase with the temperature. The enthalpy calculus algorithm is widely presented in (20) [13] and contains the following phases: a)The construction of the discrete function associated The enthalpy of the partially vaporized oil product at the to the PRF curve by using lab data. heater outlet is calculated with the relation: b)The construction of the discrete function associated to the curve of average percentages - density. (21) c)The calculus of the VE curve at atmospheric pressure. d)The calculus of the temperature on VE curve In figure 4 there is presented the dependence of the corresponding to 50% distillated volume and operating enthalpy on temperature, at the absolute pressure of 1.5 pressure. bar. e)The calculus of the distillated volume for the operating Althrough for the domain [50…400] oC the enthalpy pressure and temperature. varies nonlinearly with the temperature, for subdomains f)The calculus of the liquid phase density (depending on of 100oC, the enthalpy may be estimated by an the residual volume) and of the density in the vapour phase approximation function under the form: (depending on the distillated volume). g)The calculus of the enthalpy in liquid and vapours phases by using the relations [8]: [kJ/kg] (22)

1602 http://www.revistadechimie.ro REV.CHIM.(Bucharest)♦67♦No. 8 ♦2016 By using the polynomial regression, [14], there have a)Selecting the thermodynamic model for the oil been determined approximation functions of the crude oil products; enthalpy for various domains of temperature, (table 4). b)Introducing into the Simulator the lab analyses of the Table 4 oil product; THE COEFICIENTS OF THE APPROXIMATION FUNCTION OF THE c)Calculating the pseudo-components; CRUDE OIL ENTALPHY 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 The heat conductivity. For the oil products, products similar crude oil experimental density value. The implementation to the crude oil, the conductivity in liquid phase may be of these experimental data is achived by the next estimated with the relation [8] : specifications of Assay menu: - Bulk Properties = Used -Assay Data Type = TBP (23) - Light Ends = Ignore - Molecular Wt. Curve = Not Used The dynamic viscosity - Density Curve = Independent The crude oil viscosity is treated in a detailed way in the - Viscozity Curves = Not Used paperwork [15]. Based on the diagram of the dynamic C. Calculating the pseudo-components. Determining the viscosity variation with the temperature and density, there pseudo-components takes place in two stages [16]: has been determined the next approximation function: -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 (24) close as the experimental one, while the calculated density where d is the relative density; T - temperature in °C. of the pseudo-components mixture is equal to the crude In the table 5 there are presented the coefficients of the oil experimental density. The gap between the two curves approximation function. is very small and for this reason decompose of the crude oil in pseudo components is validated. In figure 5 there is Determining the crude oil heat properties by using UNISIM presented the composition between the two PRF curves Simulator (experimental and calculated). The heat properties of any oil product may be calculated Figure 5 Comparison between the PRF curve, calculated by using Unisim Design Simulator. The use of Unisim Design based on the pseudo-components, and the PRF curve Simulator for oil products is conditioned by undergoing the calculated by experimental data. following configuration phases [16]: 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 pseudo- components) 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 In table 8 there are presented approximation functions calculus of their concentration, the next phase is exploited of viscosity, caloric capacity and conductivity of the these data within the list of chemical compound. The following chemical components: carbon dioxide, water, material flow that will use these pseudo-components is nitrogen, oxygen and carbon monoxide. specified and by activating the commands specific to Unisim Design Environment, the control of the program Simulation of the convection section of the will return in the simulation menu, the material flow atmospheric distillation heater previously defined becomes active, the user being able to The mathematical model of the convection section is pass to defining the thermodynamic conditions of this one. defined by the system of equations (1), where the unknown E. Simulation of liquid-vapour equilibrium. The crude oil variables are Tc2 and Th2. Due to the nonlinear interactions subject to heating in the convection section of the heater between the two variables and the global heat transfer in the atmospheric distillation plant is characterized by the coefficient, the system (1) is a nonlinear system under the pressure of 7 bar and temperatures ranged between the form: domain [200…300] oC. The simulation of the liquid-vapour equilibrium under these conditions generated the values of the heat properties presented in table 6. A specific (26) problem of this simulator is the value of enthalpy. The where the two functions have the expressions: simulator Unisim Design calculates the value of the enthalpy in other standard conditions as compared to the (27) classical system. This specific aspect results in a difference between the enthalpy numerical values calculated in Unisim Design simulator and the numerical values (28) calculated in classical standard conditions (pressure of o 1bar and temperature of 0 C. Table 8 The absolute variations of the enthalpy aren’t different THE COEFICIENTS OF THE APPROXIMATION FUNCTION OF THE in comparison to the standard condition assumed within BURNING GASES 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 re- calculation of the results obtained with Unisim Design Simulator using the value of 438.5 kJ/kg of the enthalpy determined at 200oC [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).

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 The simulation of the convection section of the heater equations is Newton-Raphson [18]. A particular aspect of in the atmospheric distillation plant prints at three purposes. this algorithm is represented by Jacobean matrix The first purpose aimed at is the validation of the associated to the nonlinear system of equations (26) 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. (29) By comparing the calculated value of crude oil outlet temperature, 276.9oC, with the value calculated in the project, 272.0oC, there results a very good closeness of the For the numerical evaluation of the Jacobean matrix values, a fact that validates both the proposed model and there has been used the relation 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 (30) the results obtained for the two versions of calculating the crude oil properties. The most significant difference, 30% For the current point the variation being defined: compared to the calculated value by using Unisim Design simulator, is registered for the crude oil viscosity. This (31) difference in the estimation of the crude oil properties Based on the previously presented algorithm there manifests especially at the crude oil outlet temperature, havebeen realized two versions of calculus programs for respectively 8.9%. simulating the convection section: a version that uses The third purpose of the simulation is the calculus of the emirical relations for calculating the crude oil propertiesand static characteristics of inlet-outlet type of the tube heater the second version based on the simulator Unisim Design. convection section. For the simulation there have been Both programs have been tested by using the following varied two variables: the feedstock inlet temperature and heater design data: the burnt gases inlet temperature. As the heat exchanger -crude oil flow is a multivariable system, changing an inlet variable will -the crude oil inlet temperature generate changes of both outlet variables. The feedstock -fuel flow inlet temperature generates a linear variation of the -the coefficient of the air quantity. feedstock outlet temperature and burnt gases temperature. As far as the temperature of the burning gases at the The linear static characteristics obtained indicate a good inlet of the tube heater convection section is concerned, design of the convection section of the analyzed tube heater the value of 800oC is adopted [8, 11]. 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 Notations the simulation program under the conditions of change of Th1 – hot input fluid temperature; the burnt gases inlet temperature. The variation of the Tc1 – cold input fluid temperature; feedstock outlet temperature has a same linear character Qhot – hot flowrate; but burnt gases outlet temperature has a slight nonlinear Qcold – cold flowrate; character, figure 6. Thot2 – hot output fluid temperature;

Tcold2 – cold output fluid temperature;

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

Manuscript received: 25.01.2016

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