Mathematical Modelling of the Atmospheric Crude Oil Distillation Unit.docx

Justine D. Daquioag BSChE Mathematical Modelling of the Atmospheric Crude Oil Distillation Unit

I.

INTRODUCTION Crude oil distillation is a multicomponent, continuous distillation process. It is the separation of hydrocarbons in crude oil into fractions based on their boiling points which lie within a specified range. The separation is done in a large tower that is operated at atmospheric pressure. The crude oil distillation systems, including distillation columns and their heat recovery systems, is the first stage of processing in a petroleum refinery. It is a highly energy intensive process, consuming fuels at an equivalent of 1% to 2% of the crude oil processed. As the price of energy increases, considerable effort has been made to reduce the energy requirement of the crude oil distillation process. At the same time, increasing concerns about the environment resulted in stricter regulations on the emission of green house gases. Consequently, both economic and environmental issues are important factors in the design of crude oil distillation system. Inside crude oil distillation systems, the distillation columns have strong interactions with the associated heat recovery systems. Compared to the conventional design approach of crude oil distillation systems, the heat-integrated design approach is more likely to and a better solution, from which the minimized energy consumption can be obtained. Less energy consumption also means less gas emissions, which is beneficial for the environment. The control of crude distillation units has always been of particular interest to researchers. Control of a process basically contains three steps; to measure, compare and adjust. In this regards, variables which are factors that can change the condition of the process are used.

Justine D. Daquioag BSChE

. Manipulated

Controlled

Disturbance

Heater Outlet Temperature

Heavy Diesel Pump Around

Feed to Atm. Column

(HADPA) Duty

Atm. Column Top Temperature

Heavy Naphtha 95% Distillation

Atm. Column Top Pressure

Kerosene Flash Point

Kerosene Draw-off Flow

Kerosene 95% Distillation

Light Diesel Draw-off Flow

Kerosene Stripper Level Control Valve Opening

Justine D. Daquioag BSChE Heavy Diesel Draw-off Flow

Light Diesel Stripper Level Control Valve Opening

Stripping Steam Flow

Heavy Diesel Stripper Level Control Valve Opening

Atm. Column O/H Drum Level Control Valve Opening

Atm. Column O/H Drum Pressure Control Valve Opening

Table 1: CONTROL VARIABLES OF CDU ATMOSPHERIC COLUMN

II.

MATHEMATICAL MODEL AND ASSUMPTIONS The Transfer function approach is valid only for the linear system and the state equation approach is valid for both, i.e., linear as well as non-linear systems. In reality, since all physical systems are non linear to some extent, in order to use transfer functions and linear state equations the system must first be linearized, or its range of operation be confined to a linear range. Although the analysis and design of linear control system have been well developed, their counter parts for non-linear systems are usually quite complex. Therefore, the control systems engineer often has the task of determining not only how to accurately describe a system mathematically, but more importantly, how to make proper assumptions and approximations, whenever necessary, so that the system may be adequately characterized by a linear mathematical model.

Professional engineering judgment and decisions are important when it comes to making assumptions related to chemical processes. Assumptions are made in order not to complicate matters unnecessary. The followings are assumptions that apply to CDU simulation based on Kumar et al. (2001), Luyben (1990) and Gabriel (2007): i) Crude oil compositions are expressed in terms of pseudo-components ii) Dynamic component of condenser and reboiler are negligible

Justine D. Daquioag BSChE iii) Ideal heat rate balance in absence of interface resistance iv) Equilibrium temperature is dependent variable v) Perfect mixing in column and the fluid is incompressible vi) Heat of mixing is negligible vii) Fluids are in thermal equilibrium but not phase equilibrium

viii) All streams are considered to be single phase

Overall Material Balance: d U Lj  dt

L

j 1

V

j 1

(1)

 L j V j  S j

For a particular Crude distillation column, the equation may be reduced to

U

L j

(2)

 f ' j ( L j , L j 1 )

Dynamic Component mass balance of stage n:

d (M n xn, j dt

 Ln1 xn 1, j  Vn1 y n 1, j  Fn z n, j  Ln xn, j  Vn y n, j  S n xn, j

(3)

Dynamic general Energy Balance of stage n:

d M n hn   Ln1hn1  Vn1 H n1  Fn h f  Ln hn  Vn H n  S n hn  QM  QS  Qloss dt

(4)

Equations of vapour liquid equilibrium: To model this system some assumptions have been used, such as, the binary system (two components) has constant relative volatility throughout the column and theoretical (100% efficient) trays. A 100% efficient tray is a tray, in which vapour leaving a tray is in equilibrium with the liquid on the tray. So, the simple vapour liquid equilibrium is used

Yn 

x n 1  (  1) xn

(5)

Where,

xn = Liquid composition on the nth tray (mole fraction more volatile component) Yn = Vapour composition on the nth tray (more fraction more volatile component)

 = Relative volatility If both phases are idea, the equation may be converted to Roult’s Equation:

Justine D. Daquioag BSChE

Pn  Pn1  P

(6)

V P  ( 0

(7)

K

)2

Where V0 the volumetric flow rate of live stream and K is the proportionality constant. Equations of condenser and reflux drum:

dM D x D  Vynt  ( L  D) xn dt

Equation of

n

th

(8)

Tray:

d ( M n xn )  Ln1 xn1  Ln xn  V y NT 1  V yn dt

(9)

Equation of Top Tray:

d ( M NT x NT )  Lx D  LNT x NT  VNT 1  Vy NT dt

(10)

Equation of feed Tray:

d ( M NF x NF )  LNF 1 x NF 1  LNF x NF  Vy NF 1  Vy NF  Fz dt

(11)

Equation of condenser:

d (M D xD )  Vynt  ( L  D) xn dt

(12)

Exergy Analysis of CDU:

 Ex  Ex

out

in

 ExLNaphta  ExHNaphta  Exker osene  ExDiesel  ExAGO  Exresidue  Excrude  Exsteam  Ex furnace  Exker osteam  Exdieselsteam  ExAGOsteam

(13) (14)

Enthalpy: Usually the enthalpy of the vapour and liquid stream should be calculated as function of temperature, pressure, and composition of each stream. However, because liquid are incompressible and if low to moderate pressure system is assumed, then the enthalpy is calculated as a function of temperature and composition based on linear fit of heat capacity with temperature.

hiL  AiLT  BiLT 2

(15)

Justine D. Daquioag BSChE

hiv  AivT  B vT 2  H iV

(16)

H iV implies pure component heat of vaporization at reference temperature(0˚F for this case) For multicomponent systems, mixing rules applies. The molar average of the pure component enthalpy is the vapour enthalpy while for liquid enthalpy, non idealities is accounted for by heat of mixing. L hmix   RT i xi

 ln i T

(17)

Vapour and liquid enthalpy for mixture therefore, is given as

III.

h v  i yi hiv

(18)

L h L  i xi hiL  hmix

(19)

SUMMARY Tray efficiency is a strong function of the physical properties of the vapour and liquid streams. It is also affected, to a lesser extent, by the Sow rates and tray layout. In the latter case, only hole diameter, hole area and weir height have a small inSuence on the tray efficiency. The optimum design, which gives the maximum number of equilibrium stages in a column, is often obtained at minimum tray spacing and minimum number of Sow paths that satisfy the hydraulic design criteria.

REFERENCES:

Osuolale, F. N. (2015). Energy Efficient Control and Optimization Techniques for Distillation Process.