Responses application to monitor and predict crude oil distillation rate using pneumatic control system on a furnace

In this paper, mathematical model were developed to evaluate the different types of responses for monitoring and predicting the furnace output temperature of crude oil at various time intervals. Result obtain reveals increase in furnace output temperature with increase in coefficient of time for different input signal at constant time. Similarly, as the time increases, it is observed that the furnace output temperature increases as well as presented in this research work. At constant coefficient of time, it is observe that the furnace output temperature increases with increase in time for step input, ramp input, and impulse. The order of magnitude in terms output temperature is ramp input > step input > impulse at constant time coefficient of 10 s -1 . The model developed was used principally to monitor and control the temperature of the crude oil entering the crude distillation column also to account for the effect of the variations in the finance fuel flow rate and the influence of the changes in the feed temperature and using the model dynamic open loop simulations are performed, and approximation based on parallel linear transfer function models are fitted to various input responses. The result obtained from the model was compared with existing furnace data of Nigerian Liquefied Natural Gas (NLNG) which indicates that step input response was used in the design of their furnace.


INTRODUCTION
Initially process control was envisioned primarily, as a means of controlling the quality of products in a given process.This vision further gave birth to automatic control, a means of reducing manufacturing cost by cutting down payroll expenses, increasing production and improving product quality (Ogoni and Ukpaka, 2004).Instrumentation in the engineering context deals with the physical construction, details and arrangement of instruments use for monitoring and controlling process streams in industries.
The production of desire product from the plant must meet market quality specification, set by consumers and it is the conscience of the engineers.The specifications may be expressed as chemical composition or physical properties, performance properties or a combination of equipment protection and smooth operation (Jegla, 2006;Busman and Guan, 2001).Process control contributes to good plant operation by maintaining the operating conditions required for excellent product quality.The pneumatic controller has been the predominant type, used in the process industries, during the past few years the electronic controller has found increasing application especially in new plants today.The basic purpose of a pneumatic controller is to supply controlled pressurized air to a pneumatic valve activator in response to an error signal, due to deviation of the measured variable from the *Corresponding author.E-mail: chukwuemeka24@yahoo.com.
The furnace burn fuel gas to heat the process liquid (crude oil) flowing through the tube in the fire box.Firing demand is determined by a temperature controller located on the process liquid as it exist the furnace (Cheng et al., 1999).As long as we use control algorithms with an integrating term (PI or PID), the upstream demand signal becomes the set point for both controllers and the desire ratio would be married (Hyun and Ko, 2000).For columns that use a low reflux ratio, feed enthalpy changes can significantly alter the vapor / liquid rates inside the column, causing a major significant upset in the product composition (Jegla et al., 2000;Williams, 1999;Wang et al., 2001).
The basic function of a crude distillation unit is to provide include separation of the crude oil feed mixture into the desired fractions to the further processed to achieve other useful components.A preheating furnace is one of the crude units quality of performance is depending on the functionality of its preheating furnace which in turn determine the performance of the unit"s operation of the process (Mir and Zahra, 2011).
The aim of this research is to develop a mathematical model which is set to achieve the following objectives such as: monitor and control the temperature of the crude oil entering the crude distillation column, account for the effect of variation in the furnace fuel flow rate and the influence of changes in the feed temperature and feed flow rate on the furnace effluent temperature monitor and predict the effect of temperature on crude oil distillation, monitor and the effect of combustion rate on furnace output temperature for effective separation mechanism of the products and finally monitor and predict the effect of combustion rate and furnace temperature on the function conversion of the products.The mathematical model developed from the research was simulated using various control response approach which can be attributed to safe, smooth, quality product and profitable output from distillation products.(Ogoni and Ukpaka, 2004, Bussman and Baukal, 2009, Li and Guan, 2001and Garg, 1999)

MATERIALS AND METHODS
The crude oil fed to the furnace is first preheated in the convection section by heat transfer with the exiting flue gases.From there it flows into the radiation section to be partially vaporized.The fuel (natural gas) is fed to the furnace burners, undergoes combustion whose products (flue gas) exits the furnace through the convection section.Several potential sources of accumulation may contribute to the dynamic response of the furnace: (a) the flue gas, (b) the tubes and the fluids in the convection section, (c) the tube and fluid in the radiation section, (d) the combustion zone gas and (e) the furnace walls.
The dynamics of the furnace are controlled by thermal accumulation in the furnace walls and the dynamic response of the fluid in the radiation section.Thus, our system is described by three dynamic equations, resulting from an energy balance on the furnace walls and from mass and energy balances on the crude flowing in the radiation section.
The model is based on the following assumptions: (i) The fluid carried through the furnace in the tube is assumed to be homogeneous.The tube walls are assumed to be wetted by this fluid at all times.
(ii) The heat flux into the tubes is assumed to be uniform around the tube circumference.This assumption therefore ignores the fact that part of the tube walls face away from the source of radiation.
This model therefore consists of two principal components: (a) A description of the heat distribution of the heat of combustion between the crude pipe bearing furnace walls and effluent flue gases.This part of the model will account for thermal accumulation of the furnace walls.
(b) A model describing the flow of crude oil in the radiation section of the furnace, resulting from mass and energy balances.

Mathematical model
In developing the mathematical model for the operating system, a constant volume system through which crude oil flows at a constant mass flow rate, because the incoming crude oil (process fluid) temperature may vary hence provision is made for heating up the crude oil within the furnace.The fuel gas composition is presented in Table 1.

Fuel gas combustion
In the combustion process, the rapid chemical combination of oxygen with the combustible portion of the fuel results in heat release.Combustion of fuel gas produces flue gases.It is vital that the fuel and air thoroughly mix; otherwise complete combustion cannot take place.Perfect combustion occurs when just enough air has been supplied to burn all the fuel.To ensure that all the fuel has been consumed, additional air is supplied.This extra air is called "excess air".A combustion process with high excess air increases the amount of fuel gas.When we reduce this excess air, we reduce the volume of flue gas and the hot gases spend more time in contact with the heat transfer surfaces.This reduces the exit flue gas temperature.So to reduce the mass of the flue gas, we reduce the excess air to the level so as to put the correct amount of combustion air into the process.If we supply too little air, we get incomplete combustion and the formation of carbon monoxide followed by smoke and solid emission.Gaseous fuels require minimum amount of excess air.The fuel gas combustion describing the molecular fraction and the chemical equation of combustion for various components is shown in

Distribution of energy of combustion
The energy balance equation for distribution of energy of combustion is given as: Total Energy Going into the system = Total Energy Going out of System + Total Energy stored within system (9) Substituting Equations ( 18) and ( 19) into Equation ( 16) gives: (20 Where QRad is the radiant heat transfer rate (W),  is Stefan-Boltzmann constant (W/m 2 K 4 ),  is absorption efficiency factor, Acp is cold plane area of tubes (m 2 ), F is radiation exchange factor, Tg is temperature of fuel gas (K) and Tt is tube surface temperature (K).
A given body can absorb or emit radiant energy.At thermal equilibrium the ratio of emissive power of a surface to its absorptivity is the same for all bodies.A perfect radiator has an emissivity of one.Such a surface must have an absorptivity of one and reflectivity of zero.This hypothetical surface is commonly referred to as a black body.The ratio of the emissive power of an actual surface to that of a black body is known as emissivity.At thermal equilibrium the emissivity and absorptivity of a body are identical.
A typical emissivity table shows value for the types of surface commonly used in processing.
The surface being studied here is Brick (Red) surface with an emissivity of 0.93.Total amount of energy stored in the furnace is neglected.
Substituting Equations ( 15) and ( 20) into ( 9) we have: Equation ( 22) is the mathematical model for the system and can be used to investigate the behavior of the system.

Energy balance
The mathematical model was formulated by considering the energy balance around the tubes using the necessary conditions and assumptions as presented in this project.Substituting Equations ( 24), ( 25) and ( 26) into (23), we have; Cancelling out like terms from RHS of Equation ( 27) gives; (28) Dividing both sides of Equation ( 45) by ℓACp gives Equation ( 31) For part of the tubular reactor which is situated in the radiant part of the furnace with the process fluid (crude oil) at a temperature lower than the furnace wall, heat transfer occurs mainly by radiation and the rate will be virtually independent of the actual temperature of the reaction mixture.For this part of the reactor, may be virtually constant. (32)

Mass balance inside the tube
Density and velocity can change as the fluid flows along the axial or z direction.There are now 2 independent variables; time "t", and position "z".ℓ and V are both functions of both t and z: ℓ(t,z) and V(t,z).Applying continuity equation: −     = The differential element is located at an arbitrary spot z down the pipe; it is dz thick and has an area equal to the cross-selection area of the pipe A.
Time rate of change of mass inside system = (34) Where is the volume of the system and is the density.
Mass flowing into the system through boundary at z is designated as; (35) Mass flowing out of the system through boundary at is given as; (36) The above expression for the flow at may be thought of as a Taylor Series expansion of a function .The value of the function at a spot away from z is: (37)

Ukpaka and Otabiri 221
If the is small, the series can be truncated after the first derivative term.Letting gives equation (36).
Substituting these terms into Equation (33) gives; (38) Cancelling out terms and assuming A is constant yields; (39) Liquid densities can be assumed constant in many systems unless large change in composition and temperature occurs.

Control system model
In developing the mathematical model for the operating system we considered a constant volume system through which crude oil flows at a constant mass flow rate, because the incoming crude oil (fluid) temperature may vary hence provision is made for heating up the crude oil (liquid) within the furnace.
With Figure 1 developing a mathematical model for the system by writing the macroscopic energy balance for the constituent parts, therefore for the liquid phase; Equation ( 43) constitutes the mathematical model for the system and can be used in investigating the behavior of the system.

Feedback control
From the model that has been developed, an energy balance at steady state around the heating process may be written as; The concept of using information about the deviation of the system from its desired state to control the system is called feedback control.Information about the state of the system is fed back to a controller which utilizes this information to change the system in some way.In the present case, the information is the temperature and the change is made in q. when the term (48)

Transient responses
The mathematical equation defining the transient response in relationship to changes in the functional parameters as presented below.
The   Therefore the time inverse of Equation ( 74) can be expressed as; (75) Inputting the value of β as represented in Equation ( 56) we have; Recall Equation 76and apply the necessary fundamental parameter to test for the value of at different "t" and "τ" value.

RESULTS AND DISCUSSION
The results obtained from the investigation are presented in Figures 2 to 7 and Tables 3 and 4. Figure 2 illustrates the output temperature T(t) response versus time for step input response.Increase in output temperature T(t) response was observed within a time range of above 0 to 20 s and after then a slight increase in output temperature was seen with increase in time.The variation in the output temperature T(t) response can be attributed to the variation in time.A linear change was observed within 0 and 20 s before experiencing functions that change instantaneously from one level to another within the range of 20 to 28 s.Comparing the results obtained from this investigation with desired value of 623 K  (which is the operating temperature for a functional furnace of Nigerian Liquefied Natural Gas (NLNG)), indicates that step input response characteristic or principle was used in designing the process temperature sensor in the furnace, which is close when compared to the calculated value of 585.1 K at 28 s from my investigation.For operating system of a furnace within the temperature range of slightly above 623 K and slightly below 623 k, a step input response is recommended for more accurate result.Figure 3 illustrates the output temperature T(t) response versus time for ramp input response.A temperature response T(t) similar to step input was observed within a time range of above 0 to 20 s just but this occurs at a higher temperature range and after then a slight increase in output temperature was seen with increase in time.The variation in the output temperature T(t) response can be attributed to the variation in time.A linear change was observed within 0 and 20 s before experiencing functions that change instantaneously from one level to another within the range of 20 to 28 s.Comparing the results obtained from this investigation with desired value of 623 K, it indicates that ramp input response characteristic or principle cannot be used in designing the process of temperature sensor for a crude oil preheating furnace but can be used in high temperature operating furnaces such as the one used in pyrolysis with its value of 15,002 K at 28 s.For operating system of a furnace within the temperature range of slightly above 15,000 K and slightly below 15,000 K, a ramp input response is recommended for more accurate result.From Figure 4, it is seen that increase in output temperature T(t) responses was observed with increase in time within the range of above 0 to 20 s.The optimum output temperature T(t) responses were experienced at 20 s with the value of T(t) at 84.31 K.A decrease in output temperature was observed with increase in time indicating that the variation in the output temperature T(t) can be attributed to the variation in time as shown in Figure 4.The Figure 4 illustrates the principle of the impulse function, that is, the dirac delta function, an infinitely high pulse whose width is zero and area is unity.For operating system of a furnace within a temperature range of slightly 85.0 K and below, an impulse response is recommended for the design of the furnace for effective utilization and for more accurate result to be achieved at the end of the process.time at constant coefficient of time as presented in Table 3.A coefficient of time interval of two steps incremental starting from 6 to 14 s -1 was used to monitor the drop in output temperature of the furnace using different types of response as presented in the research work at constant time of 10 s.
The result presented in Table 4 illustrates the output temperature of the feed in the furnace at different time coefficient interval with constant time.An increase in output temperature was observed with increase in time at constant coefficient of time.A time interval of two steps incremental starting from 20 to 28 s was used to monitor the drop in output temperature of the furnace using different types of response as presented in the research work with constant coefficient of time (10 s -1 ).

Conclusion
This work represents the first step in an overall study of the refinery separation train; a relatively simple non-linear model has been developed to describe the furnace dynamics.The dynamics of the furnace are controlled by thermal accumulation in the furnace walls and the dynamic response of the fluid in the radiation section.Thus, our system is described by three dynamic equations, resulting from an energy balance on the furnace walls and from mass and energy balances on the crude flowing in the radiation section.As a simplification the air supplied to the furnace has been considered as stoichiometric.
As an approximation to the non-linear model, linear   Stefan Boltzmann constant (W/m 2 k 4 ).
has the dimensions of time and is known as the time constant of the furnace.Equation


has the dimensions of time and is known as the time constant of the furnace.EquationThe term τ has the dimensions of time and is known as the time constant of the furnace.Equation (53) describes the way in which the effluent temperature changes in response to and of A and B into Equation (66), we have;(74) with the following parameters for the combustion zone and the process side;       = ṁ = 10,000/       =  = 800       =   = 2.13 × 10 3 /      =   = 623 To calculate the constant heat input into the system we apply Equation (45) which states; In putting the values, we have;   = 200/ 2  850 − 800 + 10,000/ × 2.13 × 10 3 / 850 − 800   = 3.834 × 10 6 / 2 Application of furnace output temperature to different types of responsesStep input response These are function that changes instantaneously from one level to another.If the step size is equal to 1, then it is called a unit step function.Considering a first order process control, at ῖ = 10,  =   = 623   = 20  − 28 Ramp input responseThese are functions that changes linearly with time.This is a direct delta function, an infinitely high pulse whose width is zero and area is unity.

Figure 3 .
Figure 3. Graph of Furnace Output temperature T(t) responses versus Time for Ramp Input Response.

Figure 5 .
Figure 5. Graph of Furnace Output temperature T(t) responses versus Time for Step Input Response using polynomial and linear trend.

Figure 5 Figure 6 .Figure 7 .
Figure5illustrates the polynomial expression of output temperature of crude oil to the furnace (K); Heat input to the furnace (KW/m 2 h)A cp :Cold plane area of tubes (m 2 )C L :Specific heat capacity of liquid (crude oil) (J/kgK)
Graph of Furnace Output temperature T(t) responses versus Time for Impulse Input Response.

Table 3 .
Computation of furnace output temperature of crude oil at different values of time and coefficient of time.

Table 4 .
Computation of furnace output temperature of crude oil at different values of time and coefficient of time.