Investigations into Optimization Models of Crude Oil Distillation Column in the Context of Feed Stock and Market Value

doi:10.4236/aces.2012.24058

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Advances in Chemical Engineering and Science, 2012, 2, 474-480

http://dx.doi.org/10.4236/aces.2012.24058 Published Online October 2012 (http://www.SciRP.org/journal/aces)

Investigations into Optimization Models of Crude Oil

Distillation Column in the Context of Feed Stock

and Market Value

Lekan T. Popoola1, Jamiu A. Adeniran2, Solomon O. Akinola3

1Department of Petroleum and Chemical Engineering, Afe Babalola University, Ado-Ekiti, Nigeria

2Department of Chemical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Nigeria

3Department of Computer Engineering, Afe Babalola University, Ado-Ekiti, Nigeria

Email: [email protected]

Received July 14, 2012; revised August 25, 2012; accepted September 3, 2012

ABSTRACT

This paper proposes optimization models of crude oil distillation column for both limited and unlimited feed stock and

market value of known products prices. The feed to the crude distillation column was assumed to be crude oil contain-

ing naphtha gas, kerosene, petrol and diesel as the light-light key, light key, heavy key and heavy-heavy key respec-

tively. The models determined maximum concentrations of heavy key in the distillate





HK and light key in the

bottom



for limited feed stock and market condition. Both were impurities in their respective positions of the

column. The limiting constraints were sales specification concentration of light key in the distillate [





LK



LK ],

heavy key in the bottom [

HKHK ] and an operating loading constraint of flooding above the feed tray. For

unlimited feed stock and market condition, the optimization models determined the optimum separation [



HK and





Boo

] and feed flow rate (

)that would give maximum profit with minimum purity sales specification constraints

of light key in the distillate and heavy key in the bottom as stated above. The feed loading was limited by the reboiler

capacity. However, there is need to simulate the optimization models for an existing crude oil distillation column of a

refinery in order to validate the models.

Keywords: Feed Stock; Crude Oil Distillation Column; Constraints; Market Condition; Reboiler; Crude Composition;

Optimization

1. Introduction

While the use of distillation dates back in recorded his-

tory to about 50 B.C., the first truly industrial exploita-

tion of this separation process did not occur until the 12th

century when it was used in the production of alcoholic

beverages [1]. Crude oil distillation is the separation of

the hydrocarbons in crude oil into fractions based on

their boiling points which lie within a specified range [2].

The separation is done in a large tower (Crude Oil Dis-

tillation Column) that is operated at atmospheric pressure.

The tower contains a number of trays where hydrocarbon

gases and liquids interact. The liquids flow down the

tower and the gases up [3]. The fractions that rise highest

in the column before condensing are called light fractions,

and those that condense on the lowest trays are called

heavy fractions [4]. The portion of the column above the

feed iscalled the rectifying section and below the feed,

the stripping section.Globally, more than 80 million bar-

rels of crude oil are refined daily. In the US, 146 refin-

eries operate, employing over 65,000 people and pro-

ducing a total value that exceeds $151 billion [5]. Figure

1 gives a schematic representation of the process over-

view of a crude oil distillation column.

Crude Distillation Units (CDUs) are key process plants

in a petroleum refinery as changes in these units have a

great impact on product yield and quality. It is recom-

mended to operate these units at optimal conditions from

technical and economical points of view. Mathematical

modelling has become very common to develop these

optimization studies [6]. Many conventional ways of

optimizing crude oil distillation column such as total

L. T. POPOOLA ET AL. 475

Figure 1. Process overview of crude oil distillation column.

energy requirement, heat integration, enhanced crude

blending, crude oil energy consumption, operating condi-

tions, products specification and many more had been

discovered by previous researchers. Yu et al. [7] pro-

posed an on-line soft-sensor for the quality control and

energy optimization of crude distillation column. A

two-stage soft sensor was developed for the estimation of

internal liquid and vapour loads, and product quality

specifications of side streams. The measurements of the

soft-sensor were used to derive the constraints of the en-

ergy optimization system as well as feedback to the qual-

ity control system. Gadalla et al. [8] developed optimiza-

tion framework which included shortcut models for the

simulation of the existing distillation column and a retro-

fit shortcut model for the heat exchanger network. The

process was optimized by changing key operating pa-

rameters while simultaneously accounting for hydraulic

limitations and design including the performance of the

existing heat exchanger network. A reduction in energy

consumption and operating costs of over 25% was

achieved. In 2003, Okeke et al. [9] proposed the design

and optimization of a crude distillation unitat the Nigeria

Port Harcourt refinery in the context of total energy re-

quirement. The modelling procedure used was a stage-

wise approach to determine opportunity for optimization

using sequential quadratic programming (SQP). They

concluded that the programming technique was ideal for

solution of the algorithm achieving quick convergence

and 8% gasoline yield increment. Domijan et al. [10]

made improvement on research done by Yu et al. [7] and

Okeke et al. [9] by considering off-line energy optimiza-

tion model for crude distillation unit. The CDU model

was a non-stage-by-stage, steady-state model and cor-

rected by real process values. The model calculated the

yields and properties of the products based on feed in-

formation and product specifications. The optimal solu-

tion obtained showed that the energy consumption could

be decreased 3.2% over the normal operating condition.

Fazlali et al. [11] also considered an energy saving op-

tion in refinery industry but used operating conditions to

optimize the distillation columns. The atmospheric dis-

tillation unit of Iran-Arak-Shazand petroleum refinery

was subjected to optimization efforts using a simulator

with theaim to earning more overhead products. Results

demonstrated that changes in the real operating condi-

tions increased the overhead products with desirable

quality. Kozarev et al. [12] investigated the optimization

of crude distillation units using the knowledge of com-

puter aided steady state control to optimize the mode of

operation of a crude oil column with respect to the prod-

uct prices, energy consumption and standard require-

ments of products compositions. A simple non-iterative

L. T. POPOOLA ET AL.

476

mathematical model of a crude oil distillation tower to-

gether with an appropriate technique was presented. The

results revealed that a good separation at considerably

low quantity of reflux could be realized. The use of the

short-cut model made the optimization procedure to be

very fast. Benyoucef [13] worked on oil refining plan-

ning under price and demand uncertainties using Algeria

as a case study. His paper aimed at analysing the Alge-

rian refining industry development in the presence of

uncertainties for both domestic products demand and the

international markets. Considering multiple uncertainties

on demand and oil price, the model provided the produc-

tion levels, the rate units running and the foreign trade of

products by the year 2030. Hassan et al. [14] improved

on the work done by Benyoucef [13] by using linear pro-

gramming modelling to improve oil refinery productivity

but through enhanced crude blending. The objective of

their study was to develop a mathematical programming

model for solving a blending problem in a major refinery

Alexandria, Egypt with the objective of maximizing

naphtha productivity. Their study showed that the devel-

oped linear programming model for the blending prob-

lem yielded better overall naphtha productivity for the oil

refinery studied as compared to the results obtained from

the commercial software.

2. Proposed Optimization Models

The optimization models proposed are applicable for

known product prices of crude oil distillation column in

order to obtain the specified separation for the least oper-

ating cost under the conditions of both limited and

unlimited market and feed stock. It is impossible to

maximize the profit without knowing the prices of ter-

minal products of the distillation column and taking into

account all other aspects of the overall plant in which the

column is a part. The feed to the crude distillation col-

umn is assumed to be crude oil containing naphtha gas,

kerosene, petrol and diesel as the light-light key, light

key, heavy key and heavy-heavy key respectively. The

limited market and feed stock optimization models are

presented for the conditions in which the top products are

more valuable than the bottom products and vice versa.

2.1. Product Prices Known with Limited

Market and Feed Stock

Condition 1: Top products are more valuable than the

bottom prod ucts

Since it is assumed that the top products have the

highest unit prices, they must be produced at minimum

specified purity such that the heavy key component in the

top product (HKD) is the impurity present in the distillate

and hence, the control component. The maximum con-

centration of the heavy key in the distillate is calculated

thus (see below):

where





HK = Optimum concentration of heavy key in the

distillate, mol/m3,

LKF = Concentration of the light key in the feed,

mol/m3,



= Concentration of the light key in the bottom,

mol/m3,

LLKF = Concentration of the light-light key in the feed,

mol/m3,

(LKD)ss = Sales specification concentration of light key

in the distillate, mol/m3.

When the change in operating cost equals the change

in product worth,



() i

PD PBCL

LK LK



 





 





 



(2)



 

where

PD = Price of the distillate, ₦/sec,

PB = Price of the bottom, ₦/sec,

D = Distillate concentration, mol/m3,

CLi = is the unit cost of operation per unit of internal

reflux, ₦(s/m3),

Li = internal reflux, m3/s,

= Concentration of the light key in the bottom,

mol/m3.

The simultaneous solution of Equations (1) and (2) gives

the the optimum values of HKD and LK

. The light key

in the distillate (LKD) is the purity component in the top

product and thus, its purity concentration must not be

less than that of the sales specification. Hence, the limit-

ing constraint equation for Equations (1) and (2) above is:



 

LK LK (3)

where (LKD)ss is the sales specification concentration of

the light key in the distillate, mol/m3.

Condition 2: Bottom products are more valuable than

the top products

When the bottom products are assumed to be more

valuable than the top products, light key in the bottom

(LKB) becomes the impurity and its maximum concentra-

tion in the bottom products should be determined as the

ontrolling component. Thus, we have c







FFDFF

DoB

LK LKLLKLKLLK LK LK

HK LK LK

 



 (1)

L. T. POPOOLA ET AL. 477

 











max

FF FFF

oss

HK LLKLKHKHKLLKLK

LK LK HK

 





 









(4)

where



HK = Optimum concentration of heavy key in

the distillate, mol/m3,



= Sales specification concentrationof heavy

key in the bottom, mol/m3,

K= Concentration of heavy key in the feed,

mol/m3,



max

LK = Maximum concentration of the light key

in the bottom, mol/m3.

Other variables are as stated for Equations (1) and (2)

above.

The heavy key in the bottom



K is the purity

component in the bottom product whose concentration

must not be less than that of the sales specification.

Hence,







HKHK (5)

The column is assumed to approach an operating con-

straint of flooding above the feed tray (because of exces-

sive entrainment of liquid in the vapour) as





HK o

determined from Equations (1) and (2) above is lowered.

The loading equation for this constraint is given as:



13 2

aaPFa 110









(6)

where

a1, a2 and a3 = Coefficients of experimental loading

equation,

P = Column pressure, Pa,

F = Feed flow rate, m3/s,

L = Li = Liquid flow rate in column at the point at

which flooding occurs, m3/s,

Li/F and B/F are obtained from the operating control

equations for reflux and bottom product flow rate.

B = Bottom flow rate, m3/s.



HKDo is reduced from optimum, Li/F and B/F

change. The value of



will be obtained at a



point where Equation 6 is equal to zero. That value of



HK is used in Equation 4 to obtain



max

LK . The

flow chart algorithm for limited market and feed stock is

shown in Figure 2.

2.2. Product Prices Known with Unlimited

Market and Feed Stock

For an unlimited market, the feed flow rate and separa-

tion resulting in maximum profit rate for the existing

products must be determined. Operation for a column

under this condition will always be against an operating

constraint because of the unlimited market and feedstock.

The overall optimization problem involves determining

the optimum separation [i.e.





and



feed flow rate (i.e.





) and column pressure [] that

will give maximum profit. The optimum concentrations

of the separation,





HK and



, are calculated



using Equations (1) and (4) above but with the following

minimum purity constraints:





DDB B

sss

LKLKHK HK (7)









max max

,DD

LK LKHKHK (8)

The maximum feed flow rate is calculated by using:



max12 12

31 2

FaaddPT

addP TBL



 











(9)

where

a1, a2 and a3 = coefficients for condenser-loading

equation that are determined by column tests

d1 and d2 = coefficients determined off-line from cor-

relation of data obtained from flash calculations at the

average composition of the existing overhead vapour.

P = Column pressure, Pa,

Tc = Temperature of the coolant to overhead vapour

condenser, ˚C,

B = Bottom product flow rates from the output of op-

erating control equation, m3/s,

L = Reflux flow rates from the outputs of operating

control equation, m3/s,

Fmax = Maximum feed flow rate required to load the

condenser for optimum separation, m3/s.

For Equation 9 above, the temperature of the overhead

vapour (To) is a function of column pressure only while

other independent inputs are negligible.

Assuming the feed loading is limited by the reboiler

capacity, the column must then be operated at minimum

value in order to gain maximum reboiler capacity. Hav-

ing known the optimum separation and column pressure,

the the feed rate can now be increased up to the maxi-

mum capacity of the reboiler which gives the most prof-

itable operation. The feed flow controller set point that

gives the maximum reboiler heat input rate is calculated

thus:

L. T. POPOOLA ET AL.

478

Figure 2. Flow chart optimization algorithm of crude oil distillation column for limited market and feed stock.



max

iFv

FLKT fB



 















(10)

where

F = Feed flow controller set point, m3/s,

max = maximum reboiler heat input rate, J/s,

= a constant equal to the specific heat of the feed

divided by the heat of vaporization,

T = Temperature of vapour above the feed tray, ˚C,

T = Temperature of the feed at column entry, ˚C,

and B are obtained from the operating control

equations used to achieve a suboptimum operation (Fig-

ure 3).

3. Discussion

The existences of the feed stock and market situation

which may be limited or unlimited are among major fac-

tors in the determination of process optimization of crude

oil distillation column. The proposed modelling equa-

tions are applicable for the process optimization of crude

oil distillation column with products purity specification.

Hence, the products prices and their purity specifications

from customer need be known for this goal to be

achieved. For known products prices of crude distillation

column with limited market and feed stock, the simulta-

neous solution of Equations (1) and (2) gives the optimum

values of the heavy key in the distillate (petrol) and light

key in the bottom(kerosene). Assuming the top products

are more valuable than the bottom, then the light key in

the distillate (kerosene) is the purity component in the

top product and thus, its purity concentration must not be

less than that of the sales specification. Equation 3 is then

the limiting constraints for the simultaneous solution of

Equations (1) and (2). When the bottom products are as-

sumed to be more valuable than the top products under

the same condition of limited market and feed stock, the

light key (kerosene) becomes the impurity in the bottom

L. T. POPOOLA ET AL. 479

Figure 3. Flow chart optimization algorithm of crude oil

distillation column for unlimited market and feed stock.

and thus, its maximum concentration is calculated by

using Equation (4). However, the heavy key (petrol) in

the bottom becomes its limiting constraint whose con-

centration must not be less than that of the sales specifi-

cation (Equation (5)). To get the value of



HK o to be

used in Equation (4), the column is assumed to approach

an operating constraint of flooding above the feed tray.

The loading equation for this constraint is stated as Equa-

tion (6). As the value of



Do gotten from Equation

(1) is reduced from optimum, the values of Li/F and B/F

change. Thus, the value of



HK that satisfies Equa-

tion (6) is obtained to solve for



max

LK in Equation

(4) while other variables are stated. When unlimited

market and feed stock exist with known product prices,

the optimum separation [i.e.





HK and



LK ] is

determined using Equations (1) and (4) but with the lim-

iting purity constraints stated in Equations (7) and (8).

The maximum feed flow rate that gives maximum profit

rate is determined using Equation (9) in which the tem-

perature of the overhead vapour (To) is a function of the

column pressure. If the feed loading is assumed to be

limited by the reboiler capacity instead of the column

pressure, the feed flow controller set point that gives the

maximum reboiler heat input rate is evaluated using

Equation (10). The proposed optimization models can be

used to simulate an existing crude oil distillation column

of a refinery.

4. Conclusion and Recommendation

The optimization of crude oil distillation column in the

context of feed stock and market condition can be

achieved using the stated models. The products prices

from the crude oil distillation column must be known and

the consumers’ products specification were put into con-

sideration using the products limiting purity constraints.

Also, the effect of operating cost on the products worth

was considered by assuming that the change in operating

cost equals the change in product worth. Nevertheless,

the proposed optimization modelling equations are ap-

plicable for both the conditions of limited and unlimited

feed stock and market situations for known product

prices. The situation in which either the top products or

bottom products being valuable than each other for the

condition of limited feed stock and market condition had

been examined. However, it is recommended that the

point of introducing the feed into the column be known

to validate the assumption of flooding above the feed tray.

Finally, the proposed models should be tested on an ex-

isting crude oil distillation column of a refinery for future

research in order to validate the applicability.

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