Abstract:
Oil refinery is receiving its crude oil through a pipeline, which is
linked to docking station where oil vessels or any other's tankers
unloaded. The unloading schedule of these tankers is defend at
corporate level cannot be changed easily. This paper is focused on the
production scheduling optimization of operation modes concerning crude
oil vessel unloading, storage, blending and feed to crude distillation
units (CDUS). The model minimizes the operation cost for the total
system shown. The model is formulated using general notation and MILP
formulation, showing the possibility of using the model for a general
problem of this matter.
Key Words:
Oil Refinery, Oil Vessel, Crude oil, Unloading, Storage, Charging,
MILP Model.
1. Introduction:
This paper is focused on the production scheduling
optimization of operation models concerning crude oil vessel
unloading, storage, blending and feed to crude distillation units (CDUS)
[4].
The
model proposes the strategic operation for the system the strategic
operation for the system in accordance with the given condition and
the optimal operational cost calculated [7].
The strategic operation if it is feasible must follow the
proposed suitable unloading days for vessels and the proposed flow
rates among vessels and tanks, among storage and charging tanks and
among tanks and plants for keeping the optimal production scheduling
given by the model results [8]. This model can be used as a viable
tool not only for supporting the shipment planning also for
discovering system infeasibilities and for strategic decisions
concerning investments in storage and pumping systems [5], [9].
2. Problem Definition:
The crude oil is unloaded into storage tanks at the
docking station and the problem considers one preselected storage
tank per vessel that manages the same crude oil composition of the
vessel that manages the same crude oil composition of the vessel.
Then, the crude oil is transferred from storage tanks to charging
tanks. Each crude oil inside the charging tank must carry out to be
within a range of blended crude oil composition determined at the
planning level for the scheduling horizon. The fulfilment of this
blended composition range is made per tanks having in account the
material balance of the remaining volume and the different flows
coming in or coming out the tank with their different compositions per
time interval. Then, blended crude oils from charging tanks are
charged into the CDUS and whenever that it is optimally required feed
switches are done from one kind of blended crude oil to another for
each CDU. Finally, it is important to mention that whether a charging
tank is feeding a CDU; it must not be fed by any storage tank or vice
versa [3], [4], [8].
The problem will focus on determine the following
operating variables to minimum costs:
a)
Waiting time for each vessel in the sea after arriving.
b)
Unloading duration time for each vessel.
c)
Crude
oil unloading rate from vessels to storage tanks.
d)
Crude
oil transfer and blending rates from storage tanks to charging tanks.
e)
Inventory volumes of storage and charging tanks.
f)
Crude
distillation unit charging rates fulfilling the demand pee each CDU.
g)
Sequence of type of blending crude oil to be charge in each CDU in
accordance with the optimal model changeovers.
On the
other hand these are the following operating constrains that must be
met:
a.
Equipment capacity limitations; Tank capacity and pumping rate.
b.
Quality limitations of each blended crude oil; Range of component
concentration in each blended crude oil.
c.
Demand
per interval of time (day) of each CDU.
3. Nomenclature and Model Assumptions:
3.1.Set:
a.
VE =
{v = 1, 2, …V/ Crude Oil or Tankers}.
b.
ST = {i=1,
2, ...I/ Storage Tanks}.
c.
SCH
={t= 1, 2,…T/ Time intervals along the scheduling horizon}.
d.
CT=
{j, y = 1, 2, …J/ Charging tanks}.
e.
CDU =
{L= 1, 2,… L/ Crude distillation units}.
32.
Parameters:
CU_{V}
= Unloading cost of vessel v per unit time interval.
TARR_{V}=
Crude oil vessel arrival date to the docking station.
CSEA_{V}=
Sea waiting cost of vessel v per unit time interval.
CSINV_{i
}= Inventory cost of storage tank i per unit time interval.
CBINV_{j}=
Inventory cost of charging tank j per unit time interval.
CCHANG_{L}=Changeover
cost of CDU_{L}.
TLEA_{V}=
Crude oil vessel maximum departure date from the decking
station.
VS_{i}^{min}=
Storage tank minimum capacity.
VS_{i}^{max}=
Storage tank maximum capacity.
VB_{j}^{min}=
Charging tank minimum capacity.
VB_{j}^{max}=
Charging tank maximum capacity.
3.3
Variables:
3.3.1.Binary Variables
Z_{j,y,l,t}=
Variable to denote switch of the blended crude oil fed to
CDU_{L}
from charging tank j to charging tank y.
XF_{v,t}=
Variable to denote if vessel v starts unloading at time t.
XL_{v,t}=
Variable to denote if vessel v finishes unloading at time t.
D_{j,l,t}=
Variable to denote if the crude oil blended in charging tank
j
charges CDU_{L} at time t, otherwise charging tank j couldbe
being fed by
Storage tanks.
3.3.2Integer
Variables.
TL_{v}=
Vessel v unloading Completion time.
TF_{v}=
Vessel v unloading initiation time.
3.3.3Continuous Variables.
VS_{i,t}
= Volume of crude oil in storage tank i at time t.
VB_{j,t}
= Volume of crude oil in charging tanks j at time t.
FVS_{v,i,t
}= Volumetric flow rate from vessel v to storage tank i at time
t.
FSB_{i,j,t
} = Volumetric flow rater from storage tank i to charging tank j
at time t.
FBC_{j,L,t}
= Volumetric flow rate from charging tank j to CDU_{L} at time
t.
The
following are the assumptions for the proposed model:
1.Only
one vessel docking station for crude oil unloading is considered.
2. The
time applied for the changeovers are neglected and also the transient
flows
Generated during either start up or shut down when a changeover is
done.
3.
Perfect blending is assume for each charging tank while it is being
fed by different Crude oils, and additional blending time inside the
tank is not required before it Chargesthe CDU.
4.The
composition of the crude oil is decided by the amount of key Component
presented in the crude oil or in the blended crude oil. Ingeneral,
sulphur is at least one of the key components, for differentiating
between crude oils.
4.
Model Mathematical formulation:
The
model focus on minimizing the following operation cost of the system
for the operations of crude oil vessel unloading, storage, blending
and feeding to crude distillation units in an oil refinery [7], then
this is the main objective equation that represents the total
operation cost of the system:
The
above equation is subject to the following constrains:
4.1
Vessel Arrival and Departure Operation Rules.
Each
Vessel must arrive to the docking station for unloading only once:
Each
vessel leaves the docking station only once:
The unloading initiation time is:
The
unloading completion time is:
Each
vessel must start unloading either after or on the arrival time
established atthe planning level:
Each
vessel must finish unloading up to one interval of time before the
maximum
departure time established at the planning level:
Except
for the last vessel:
Minimum duration of the vessel unloading is two time intervals:
The
preceding vessel must finish unloading one time interval before the
next
vessel
in the sea arrives and start to unload:
4.2
Material Balance Equations for the Storage Tank.
The crude oil in storage tank i at time t+1
must be equal to the crude
oil in
storage tank i at time t plus the crude oil transferred from vessel v
to
storage tank i at time t taking a way the crude oil transferred to
charging
tanks
j at time t:
Volume
capacity limitation for storage tank i:
4.3
Material Balance Equation for the Charging Tank.
The crude oil blended in the charging tank j at timet+1
must beequal
to
the crude oil in the charging rank j at time t plus the crude oil
transferred
from
the storage tanks taking away the crude oil transferred to the CDU_{L}
at
time
t:
Volume
capacity limitation for charging tank j:
4.4
Operating Rules for Crude Oil Charging to Crude Distillation Units.
As it was stated above each CDU_{L}only
can be charged by one charging
tank j at time t:
On the
other hand, each charging tank j can charge at most one CDU_{L}at
time t:
If the CDU_{L} is charged by crude oil blended j
at time t and after is charged
by
crude oil blended y at time t+1 then, changeover cost must be
involved. The
following is the condition that confirms that changeover cost shall be
charged:
5. Numerical Example:
Table1.Shows the system information for
numerical example [2].
Scheduling Horizon (# of unit times : days) 
8 
No. of Vessel arrivals 
2 

Arrival time 
Amount of crude Oil 
Key component concentration 
Vessel 1 
1 
100 
0.01 
Vessel 2 
5 
100 
0.06 
No. of Storage Tanks 
2 
Storage Tanks 
Capacity 
Initial oil Amount 
Key component concentration 
Tank 1 
100 
25 
0.01 
Tank 2 
100 
75 
0.06 
No. of Charging Tanks 
2 
Charging Tanks 
Capacity 
Initial oil Amount 
Initial component concentration (MinMax) 
Tank 1 
100 
50 
0.02 (0.015–0.025) 
Tank 2 
100 
50 
0.05 (0.045 – 0.055) 
No. of CDUS 
1 
Unit Costs involved in vessel operation 
Unloading Cost = 8,
Sea waiting Cost = 5 
Tank Inventory Unit Cost 
Storage Tank = 0.08,
Charging Tank = 0.05 
Unit changeover cost for charged oil switch 
50 (independent of sequence and CDU) 
Blended oils demand from charging tanks To CDU_{S} 
Blended oil 1 : 100,
Blended oil 2 : 100,
Blended oil 3: 100. 
Maximum flow rate from vessel to one storage tank 
50 
Maximum flow from one storage tank to one charging tank 
40 
Maximum total flow rate from one storage tank to charging tanks
at any time 
40 
The
given data for quantifying volumes and flow rates are given in barrels
x 10,000 and barrels per time interval x 10,000 respectively,
changeover costs are given in US$ x 1.000; sea waiting costs and
unloading costs are given in US$ x1.000 per time interval (day) and
tank inventory unit cost are given in US$ x 0.1 per oil barrel.
Therefore, optimal value results will be in US$ x 1.000.
Table 2. Optimal Unloading Starting Date for Vessels.
Vessels 
Model A 
Model B 
1 
3 
2 
2 
7 
7 
Table
2. points out the comparisons of the optimal unloading starting up
date results from both models for numerical example vessel 1 stars to
unload on day (s) for model'A'; that is one day more than model 'B'which
considers this operation on day 2. Instead, for vessel 2 both coincide
starting unloading on day7.
The
optimization model Table 3.Involved36 discrete variables, 192 single
variables, and 331 constraints [2]. The modelling system G.A.M.S. [1].
Was used for setting up the optimization model and the numbers of
variables and constraints were reduced by considering the data
structure of binary variables. The problem was solved by OSL, IBM [6].
An IBM RS 6000 in 17.5 of CPU time.
Table 3. Comparison of Optimal Result
Items 
Model A 
Model B 
Optimal value (US$ X 1.000) 
217.667 
206.95 
Equations and constrains 
331 
552 
Single Variables 
192 
337 
Discrete Variables 
36 
116 
Iterations 
1.695 
4.393 
Solving time (second) 
17.1 
5.21 
The
optimal results generated by model 'B' with No omission of any data
given by model ‘A’ are shown and compared in advance with the optimal
results of model 'A' in table 3.
6.
Concluding Remarks:
1) The situations may be causing a big
part of the difference between both optimal value since the optimal
operational schedule of Model 'A' should be paying more money in
inventory total cost. On the other hand, Model 'A' results is paying
one day more of sea waiting cost (US $ 5,000) than model
'B' results as is indicated in table (2).
2)The optimal results for numerical
example are better for model 'B' indicating a total operational cost
saving for the problem conditions of US$ 10,717 (4.92%) cost
reduction with respect to model 'A' during the 8 day scheduling
horizon in accordance with the results showed in table (1).
References:
[1]
Brooke, D. Kendrick, A. Meeraus and R. Raman, "GAMS" (General
Algebraic Modeling system), a user's guide, Washington: GAMS
Development Corporation, (1997)
[2]
Annual Bulletin,“Oil, Gas and Minerals statistics," published
by ministry of oil and minerals, Republic of Yemen, pages 5055,
(2009).
[3]
F.D. Fagundez, A.E.Xavier, J.L.D. Faco,"Continuous Nonlinear
Programming Techniques to solve scheduling problems,” Informatica
journal,Vol. 20, No.2, pages 203216. (2009).
[4]
G.K.D.Saharidis and M.G.Ierapetritou,"Scheduling of Loading and
unloading of crude oil in a refinery with optimal mixture
preparation", Industrial and Engineering chemistry research,vol. 48,
No. 5, pages 26242633. (2009).
[5]
G. Robertson, A. Plazoglue and J.A. Romagnoli, "Multi Level
simulation approach for the crude oil loading/ unloading scheduling
problem'',Computer & chemical Engineering,Vol. 35, Issue 5,pages
817827,(2011).
[6]
IBM.OSL, "Optimization subroutine Library," Guide and reference
release 2, Kingston N.Y. (1991).
[7]
N. Shah, "Mathematical programming technique for crude oil
scheduling," computer and chemical Engineering,Vol.20, pages
S1227S1232. (1996).
[8]
R.M.Tahar, and W.K. Abduljabbar, “AnovelTransporting system
model for oil refinery," American journal of Engineering and applied
science. Vol. 3, No.1,pages 138143, (2010).
[9]
U. Yuzgec, A. Palazoglu and J.A. Romagnoli, "Refinery
scheduling of crude oil unloading storage and processing using model
predictive control strategy”, Computer and chemical Engineering, Vol.
34,pages 16711686, (2010).
[10]
J.A.Persson and M.G.Lundgren,"Shipment
planning at oil refineries using column Generation and valid
inequalities”, European journal of operational research, Vol.163,
pages 631 652, (2005).
