Computers and Chemical Engineering 35 (2011) 817–827

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journal homepage: www.elsevier.com/locate/compchemeng

A multi-level simulation approach for the crude oil loading/unloading

scheduling problem
G. Robertson a,∗∗ , A. Palazoglu b , J.A. Romagnoli a,∗
a
Louisiana State University, Baton Rouge, LA, USA
b
University of California, Davis, CA, USA

a r t i c l e i n f o a b s t r a c t

Article history: An integrated approach for refinery production scheduling and unit operation optimization problems is
Received 30 September 2010 presented. Each problem is at a different decision making layer and has an independent objective function
Received in revised form and model. The objective function at the operational level is an on-line maximization of the difference
27 December 2010
between the product revenue and the energy and environmental costs of the main refinery units. It is
Accepted 17 January 2011
modeled as an NLP and is constrained by ranges on the unit’s operating condition as well as product quality
Available online 18 February 2011
constraints. The production scheduling layer is modeled as an MILP with the objective of minimizing the
logistical costs of unloading the crude oil over a day-to-week time horizon. The objective function is a
Keywords:
Supply chain management
linear sum of the unloading, sea waiting, inventory, and setup costs. The nonlinear simulation model for
Refinery scheduling the process units is used to find optimized refining costs and revenue for a blend of two crudes. Multiple
Petroleum supply chain linear regression of the individual crude oil flow rates within the crude oil percentage range allowed by
Scheduling control the facility is then used to derive linear refining cost and revenue functions. Along with logistics costs, the
refining costs or revenue are considered in the MILP scheduling objective function. Results show that this
integrated approach can lead to a decrease of production and logistics costs or increased profit, provide a
more intelligent crude schedule, and identify production level scheduling decisions which have a tradeoff
benefit with the operational mode of the refinery.
© 2011 Elsevier Ltd. All rights reserved.

1. Introduction Production layer problems include the scheduling of process units

and blending problems. An overview of planning and scheduling
Supply chain management (SCM) is the oversight of materials, problems is outlined in Kallrath (2002). Operational layer prob-
information, and finances as they move in a process from suppliers lems are online problems including plant diagnosis, fault detection,
to manufacturers to wholesalers to retailers and then ultimately to and process unit optimization. Challenges to the integration of
consumers. Global solutions for supply chain problems can be com- problems in different layers are reconciling their different imple-
putationally burdensome due to the size of the problem and the mentation frequencies and the magnitudes of order of their cost.
number of alternatives. Therefore, both within and among com- Decomposition of problems both vertically and horizontally leads
panies, objectives are naturally separated horizontally along the to a feasible but not necessarily an optimal solution.
supply chain, with entities along the supply chain having their own Process industry supply chains are striving to improve efficiency
local objective. The decision making can also be separated vertically and profitability (Shah, 2005). Integrating different levels within a
into layers by the time horizons they consider. supply chains can improve profitability. Many planning problems
The longer the time horizon a decision considers, the less fre- have been addressed using managerial judgments where com-
quent the decision is made and the greater its ramifications. Here, plex interactions between different decision making levels were
we have broken down decision making into four layers (strategic, disregarded. Recent developments in mixed integer process opti-
tactical, production, and operational). Strategic level problems are mization provide new tools to help solve more complex problems
long term, around 5 years, and can include building or expanding of a company’s hierarchy (Puigjaner & Heyen, 2006). The deci-
a facility and contract negotiations. Within the time period of the sions made by planning, scheduling, and control functions have
strategic layer problem, many medium term tactical layer decisions a substantial economic impact on process industry operations –
are made such as resource allocation and transportation problems. estimated to be as high as US $10 increased margin per ton of feed
for many plants (Puigjaner & Heyen, 2006). Hence decision support
tools for scheduling and planning can have a profound effect on the
∗ Corresponding author. Tel.: +1 225 578 1377; fax: +1 225 578 1476. profitability of an enterprise.
∗∗ Co-corresponding author. Modern petroleum refining has become an extremely com-
E-mail addresses: grober8@lsu.edu (G. Robertson), jose@lsu.edu (J.A. Romagnoli). petitive business due to the deteriorating quality of crude oil

0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compchemeng.2011.01.030
818 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827

Nomenclature
f furnace efficiency (heat entering the stream per heat
Production scheduling model: (a) indices and sets released from fuel oil)
i = 1, . . ., ND docking stations b boiler efficiency (heat used to boil water per heat
t = 1, . . ., NP time periods released from fuel oil)
z = 1, . . ., NT storage tanks
j = 1, . . ., NO oil types
k = 1, . . ., NCDU crude distillation units
coupled with tighter product specifications and more stringent
environmental regulations. Furthermore, refineries today receive
(b) Parameters
shipments of crude from a variety of sources. These crude oils
CAP storage capacity of each tank
are of different quality and composition and usually blending can
Ei,j,t total quantity of crude type j in dock i for period t
improve the economics of the refinery. Therefore, refineries deal
Sk,t total demand of CDU k during period t
with a dynamic schedule of incoming crude which cause them to
amink,j,t minimum percentage of crude type j sent to CDU k
frequently change unit’s operating conditions to reduce operating
for period t
expenses including environmental impact. In this paper, we con-
amaxk,j,t maximum percentage of crude type j sent to CDU k
sider an integration of a production layer scheduling problem, the
for period t
crude oil unloading scheduling problem (CSP), with an operational
Invj inventory costs of crude j
layer process unit optimization problem of the main refinery units,
(c) Continuous variables the heat integration of the distillation units.
Xi,z,j,t amount of crude oil j sent from dock i to tank z during The traditional approach to the CSP for a refinery is a discrete
period t time optimization formulation where the scheduling horizon is
Yz,k,j,t amount of crude oil j sent from tank z to CDU k split into time intervals of equal size and binary variables are used
during period t to indicate if an action starts or terminates in the beginning of
Iz,j,t amount of crude oil j in tank z at the end of period t the associated time interval (Saharidis, Minoux, & Dallery, 2009).
Lee, Pinto, Grossman, and Park (1996) developed an MILP model
(d) Binary variables for short-term refinery scheduling with optimal inventory man-
Ci,z,t equal to one if connection between dock i and tank agement decisions. The objective minimizes the logistical costs
z is established during period t, 0 otherwise of the crude oil loading and unloading schedule including inven-
Dz,k,t equal to one if connection between tank z and CDU tory, changeover, unloading, and sea-waiting costs. Lee et al. (1996)
k is established during period t, 0 otherwise demonstrated a tradeoff between sea waiting and inventory costs.
SCi,z,t equal to one if connection is made between dock I This model was flexible in the consideration of different network
and tank z at the beginning of period t, 0 otherwise topologies as it included combinations of storage and blending
SDz,k,t equal to one if connection between tank z and CDU tanks. Including blending tanks improves the solution by having
k is made at the beginning of period t, 0 otherwise a means to account for feed-blend changes to the crude distillation
Fz,j,t equal to one if tank z is allocated to store type j unit (CDU). To overcome the bilinear term which arises from mix-
during time t, zero otherwise ing, individual key component flows are used as linear terms rather
than crude oil stream types. Saharidis et al. (2009) used crude oil
Operational refining objective: (a) indices and sets types as the linear terms within the model, but their model does not
f furnace take into account sea-waiting, unloading, and inventory costs. Also,
c condenser that model is not adaptable to all network topologies. The opera-
s steam stream tional purpose of a tank is assigned as either storage or blending
p product exclusively and there is no possibility for a combination of both.
PF profit function Pinto, Joly, and Moro (2000) and Joly, Moro, and Pinto (2002) also
RP revenue from the products studied the refinery operations in detail. These studies focused on
UC utility costs the planning and scheduling models for a refinery with only one
RM raw material costs type of tank which is used for both the blending and the storage
EC environmental costs of crude oil. Wu, Zhou, and Chu (2008) considered the short-term
SC sustainable credits refinery scheduling problem for crude oil operations and obtained a
SD sustainable debits target refining schedule from production planning as a constraint to
FDF total furnace heating duty of furnaces f create an executable schedule. The refinery system was modeled by
Ch cost of heating a hybrid Petri net and the proposed model was based on an efficient
CDc total condenser cooling duties of condenser c heuristic algorithm. Mendez, Grossmann, Harjunkoski, and Kabore
CC cooling costs (2006) presented a novel MILP-based method to simultaneously
Qs steam flow rates of steam stream s optimize the off-line blending and the short-term scheduling prob-
Cs cost to produce steam lem in oil-refinery applications. Abraham and Rao (2009) developed
PPp unit price of final products p an optimization model for production scheduling in an oil refin-
Qp flow rate of product p ery. In their study, for production scheduling operations of lube oil
TEFO theoretical electricity of fuel oil combustion section in the refinery, a binary ILP model was introduced by inte-
ce combustion engine efficiency (electricity produced grating the operations of the plant. A continuous approach to the
per heat of fuel oil combustion) scheduling problem has been addressed where the binary variables
FHR furnace heat requirement that are used to indicate if an action starts or terminates are allowed
SHR steam heat requirement at any point within the scheduling horizon (Jia & Ierapetritou,
FGEF fuel gas enthalpy flow 2004). Global optimization for scheduling refinery crude oil oper-
ations was implemented by Karuppiah, Furman, and Grossman
(2008). Yüzgeç, Palazoglu, and Romagnoli (2010) demonstrated the
 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827 819

Fig. 1. Petroleum supply chain nodes considered.

usefulness of scheduling solution approaches applied with a model manipulating the unloading amounts of crude from vessels to
predictive control strategy. storage tanks, transfer amounts from storage tanks to charging
The objective functions of the various mathematical models of tanks for blending, and mixed crude oil amounts from charging
the CSP include cost incurred for waiting sea vessels, unloading tanks to CDUs. Before crude can be transferred from one entity to
cost, inventory cost, and setup costs. Yet the blend of the crude another, the scheduler must establish a connection between the
affects the optimized refining cost even when within the opera- entities.
tional range allowed by the various models. The unit operation In our case study, one dock is used to feed one refinery CDU
and crude scheduling problems are currently solved independently. with four tanks as intermediate storage for incoming crude and
We propose a strategy that integrates these two optimization a blending manifold connecting the storage tanks and CDU. A
problems. Our approach will mathematically model and integrate list of initial conditions and process parameters is presented in
different nodes along the petroleum refining supply chains. In Table 1.
this paper, we present the development, implementation, and The following assumptions can be made for the case considered.
testing of an integration strategy for optimization models of There is only one vessel docking station for unloading of crude oil,
docks, tanks, and processing nodes along the petroleum supply crude oil is unloaded in a predetermined schedule and takes 36 h
chain. to unload (i.e., no sea waiting cost and constant unloading costs),
the amount of crude oil remaining in the pipeline is neglected,
2. Problem definition changeover times are neglected due to having small values in com-
parison with the scheduling horizon. It is assumed that there is
Our analysis focuses on nodes involved in unloading, storing, perfect mixing in the blending manifold. The inventory costs are
blending, and processing. A general description of the oil pro- equal for the crudes and will not play a role in the optimization,
duction system considered in our analysis is shown in Fig. 1. therefore, they are set to zero.
It consists of vessels, docks, storage tanks, and a separation Variables determined in our case study are: flow rates from ves-
train. sel to storage tank for each vessel, flow rates from storage tank to
A refinery is a system composed of docks, pipelines, a series CDU’s manifold for each storage tank; crude oil inventory levels in
of tanks to store crude oil (and prepare different blends), storage tanks for each time interval; series of crude oil blends to
CDUs, process units (such as reforming, cracking, alkylating, and be fed to the CDU, and periods where connections (or setups) are
hydrotreating), blenders and tanks to store intermediates and final established.
products (Saharidis et al., 2009). In a typical refinery system, crude
oil is shipped directly from overseas sources by tankers to dock- 2.2. The process: primary units of a crude oil refinery
ing terminals, which are connected to refineries through a pipeline
network. Crude oil is stored in tanks, blended in additional tanks or In the main refinery units, crude is separated by vapor pres-
a manifold, and then separated CDUs/VDUs. Separated crude cuts sures into fluids with differing properties. The separation train
are converted to various intermediate products in process units and considered in this study consists of a pre-fractionator, atmospheric,
blended into final products. Final products are sent to distribution and vacuum distillation columns (PDU, ADU, VDU) each with a
centers, and then transported by pipelines, trucks, or rail cars to preheat train ending with a furnace to elevate the feed temper-
customers (Kuo & Chang, 2008). ature of the column. Masila crude is blended with lighter Dubai
We identify two local objectives along the supply chain, mini- crude for refining. In the refinery in our analysis, the crude is first
mizing the logistical cost of unloading crude oil and maximizing the heated to 245 ◦ C before entering the PDU which has an overhead
main refinery unit’s (distillation units) operating conditions. The gas stream of light hydrocarbons and a light naphtha stream in
following sections briefly describe the refinery scheduling problem order to reduce the vapor load in the distillation column. The pre-
and the unit operational problem analyzed in this work. topped crude is then further heated before entering the ADU where
heavy naphtha, two kerosene grades, and diesel side draws are
2.1. Short term refinery scheduling problem removed. The bottoms are put under a vacuum, heated further and
separated in the VDU into a vacuum diesel stream, light vacuum
The CSP receives the shipping vessel’s schedule, arrival times gas oil, heavy vacuum gas oil, sour diesel and vacuum residuum.
and amounts, along with the CDU’s demand and blend range. The Steam is blown through each main column. Product draws from
scheduler of the crude unloading must decide how to store the the ADU are sent to side strippers which strip the side cuts with
incoming crude oil and feed the refinery distillation units a proper steam. In order to recover as much heat as possible from the dis-
blend of crude. The scheduler does so in a fashion which mini- tillation units, pumparound streams and product streams recover
mizes production level costs such as inventory holding, unloading, heat in the preheat trains for the column feeds. Some separated
sea waiting and setup. The scheduler achieves his/her goals by products are finished while others must be further treated, but
820 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827

Table 1
Initial conditions and process parameters of base case.

Initial conditions/process parameters Base case value

Time horizon 110 h (4.5 days)

Time interval 1h
Vessel1: 3rd time interval
Vessel2: 51st time interval
Arrival and departure times of vessels
Set up cost (includes more than just unloading cost but a penalty for an erratic schedule) $25,000
Crude type Vessel 1: Type 0
Vessel 2: Type 1
Crude amount in each vessel 90,000 m3
Number of docking stations/storage tanks/distillation units 1/4/1
Maximum/minimum amounts which can flow through a pipe during a time interval 5000–50 m3
Storage tanks/initial amounts/initial types/capacities T1/9.4 km3 /Type 0/100 km3
T2/42 km3 /Type 1/100 km3
T3/0 m3 /no type/100 km3
T4/0 m3 /no type/100 km3
Limitations of flow rates from tanks to CDU’s 5000–50 m3
CDU demand 765 m3 /h
CDU component concentration range 33.5–39 vol% Dubai
Inventory cost 0 Type 0: 0 Type 1

each can be assigned a value. Further information can be found in costs, RM. In refineries, the energy demand is met by burning side
Appendix B. products. Due to rising global warming concerns and with imple-
On the operational level, personnel must maximize the total mentation of emissions trading programs (“cap and trade”), the
value of product from the CDUs less the environmental impact triple bottom line (TBL) objective function given in Eq. (2) was used
costs of the refinery units by manipulating the steam side strip- in our approach. The objective function used accounts for costs
per, pump-around, and product stream flow rates as well as unit associated with the feed, products, utilities, and environmental
operating conditions. These variables have a complex impact on the effects.
performance of the refinery units. The crude oil pre-heat furnaces
PF = RP − UC − RM (1)
and stripping steam production have a significant environmental
impact due to generation of flue gases during fuel combustion pro- TBL = PF − EC + SC − SD (2)
cess. The main pollutants of the flue gas are CO2 , NOx , and SOx .
In Eq. (2), EC is the cost required to comply with environmen-
The heat integration strategy recovers as much heat as possible
tal regulations including permits, monitoring emissions, fines, etc.
from the distillation process; therefore, it recovers heat from final
SC represents the sustainable credits given to the processes that
products and column pump-around streams. The product streams
consume pollutants. SD represents the sustainable debits which
are valued differently and must meet certain specifications such as
penalize processes for producing pollutants. In this study, sulphur
density and compositions, but side cuts of the distillation columns
dioxide (SO2 ), carbon dioxide (CO2 ), and nitrogen oxides (NOx ) are
can be slightly manipulated to produce each amount within these
chosen as the environmental load (EL). The plant requires electric-
specification ranges. The complex heat integration schemes and
ity for the condensers, steam for stripping, and heat for elevating
the interactive nature of the process due to the presence of pump-
feeds generates releases to the environment which are considered
around and side-stripper distillation features make it difficult to
substantial debits. A portion of the net energy required is obtained
operate at the optimal conditions.
by using the overhead gas of the PDU as the fuel in the furnace
The decision variables of the operational level are the strip-
and the balance is met from fuel oil. From the environmental loads
ping steam mass flow rates, product flow rates, pump around
analysis, it is evident that the use of fuel gas in the furnace reduces
flow rates, overhead column flow rates, and atmospheric and vac-
the emissions to a greater extent but at the same time reduces the
uum furnace outlet temperatures. The constraints are the quality
quantity of the useful product making a negative impact on the
parameters such as the ASTM D86 95% temperature of the product
column economics (Yela et al., 2008).
flows and furnace duty and the bounds on the decision variables. A
  
more detailed process description can be found in Yela, Galán, and UC = FDf × Ch + CDc Cc + Qs ∗ Cs (3)
Romagnoli (2008).
f c s

3. Refinery simulation/optimization and MILP scheduling RP = PPp × Qp (4)
model p

This section provides a summary of the mathematical for- TEFO = (FHR + SHR) ∗ ce (5)

mulation of the refinery scheduling and operating optimization FDf − FGEF
f
problems including models and objective functions used as well FHR = (6)
f
as the approach to solving the optimization problem. 
s
Qs ∗ Specific heat
SHR = (7)
3.1. Operational level model/optimization b

Objective function: The goal in the operational planning level

  pollutant Pollutant

SD = FGEF ∗ + TEFO ∗
is maximizing operational revenue. Eq. (1) is the typical profit Duty Duty
Pollutants
function, PF, which is equal to the revenue from the products, RP,
minus the utility costs to produce them, UC, and the raw material ∗PenaltyPollutant (8)
 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827 821

Eq. (3) calculates the utility costs as the sum of the total furnace as a mixed integer linear problem.
heating duties, FDF , over all furnaces f multiplied by the cost of heat-
ing, Ch , the total condenser cooling duties, CDc , of all condensers c 
NT
Xi,z,j,t = Ei,j,t ∀i, j, t (9)
multiplied by the cooling costs, CC , and the steam flow rates, Qs ,
multiplied by the cost to produce steam, Cs . Eq. (4) is the revenue z=1

of products, RP , calculated as the multiplication of unit prices of final


NT 
N0
products (PPp ) and product flow rates (Qp ), summed over all prod- Yz,k,j,t = Sk,t ∀k, t (10)
ucts p. In Appendix A, pollution ratios are given as pollution amount
z=1 j=1
proportional to the electricity produced if the fuel had been used to
create electricity in a combustion engine. The available correlations 
ND

NCDU
relate the amount of pollutants released by the fuel burned to the Iz,j,t = Iz,j,t−1 + Xi,z,j,t − Yz,k,j,t ∀z, t, j (11)
electricity generated in combustion engines. The theoretical elec- i=1 k=
tricity of fuel oil (TEFO) is the electricity produced if the fuel oil used
in the process is converted to electricity. Eq. (5) calculates TEFO by NO

multiplying the fuel oil total heat requirement by the combustion 0≤ Iz,j,t ≤ Cap ∀z, t (12)
engine efficiency, ce . The fuel oil heat requirement is equal to the j=1
sum of the furnace heat requirement, FHR, and the heat necessary
to produce the steam, SHR (Eq. (6)). The FHR for the fuel oil is the 
NO

Ci,z,t ≤ Xi,z,j,t ≤ M ∗ Ci,z,t ∀i, z, t (13)

total heater duty heater duty minus fuel gas enthalpy flow, FGEF,
divided by furnace efficiency, f . Steam heat requirements, SHR, is j=1

equal to the total mass flow rate of the steam streams, QS , over all
steam streams s multiplied by the steam’s specific heat divided by

NO

Dz,k,t ≤ Yz,k,j,t ≤ M ∗ Dz,k,t ∀i, k, t (14)

the boiler efficiency,b , to produce the heat (Eq. (7)). This method
j=1
of calculating the pollution loads by finding a theoretical electricity
production is due to pollution data available and can be replaced

ND
by simply inserting a ratio of pollution amount to fuel oil required Ci,z,t + Dz,k,t ≤ 1∀z, k, t (15)
where that information is available. The sustainable debits, SD, are
i=1
then calculated as the pollutant amount multiplied by a pollution
penalty, calculated in Eq. (8). Ci,z,t−1 + SCi,z,t ≥ Ci,z,t ∀i, z, t (16)
In our study, feed costs are ignored since it is assumed that the
Dz,k,t−1 + SDz,k,t ≥ Dz,k,t ∀z, k, t (17)
incoming oil has already been purchased and raw water necessary
is proportional to feed costs. SC is equal to zero as no processes

NT
consume pollutants. EC are ignored because they are a function of Yz,k,j,t ≤ Sk,t ∗ amaxk,j,t ∀k, j, t (18)
feed flow rate and also do not affect the optimization problem. A
Z
100% conversion of the fuel gas enthalpy to electricity is assumed,
but this accounts for less than 2% of the total pollutants. The bulk of 
NT

the pollutants come from the theoretical electricity of fuel oil times Yz,k,j,t ≥ Sk,t ∗ amink,j,t ∀k, j, t (19)
the pollutant penalty per duty. Values necessary for operational Z
level optimization are available in Appendix B.
The modeling equations include thermodynamic relationships, 
NO
Fz,j,t = 1∀z, t (20)
mass balances, and energy balances obtained using HYSYS® . The
optimization model is a NLP solved with Frontline Systems’ Pre- j

mium Solver Platform® . The solver uses improved generalized Iz,j,t ≤ Cap(z) ∗ Fz,j,t ∀z, j, t (21)
gradient method capable of solving large scale nonlinear problems.
A bridge code is programmed in Visual Basic Application (VBA). The This model is specific to our base case with all storage tanks and
bridge code allows the user to import and export any selected vari- a blending manifold. Eq. (9) ensures that all the incoming crude
ables between the HYSYS model and Excel worksheet. Interaction type j into dock i at time t is transferred to some tank. Eq. (10)
with HYSYS uses object linking and embedding (OLE) automation. ensures the CDU k’s total demand during time t is met by some
The optimization process first takes the objects which are the type of crude from some tank. Eq. (11) balances the inventory of
variables of the triple bottom line objective function from the tank z during time t of crude type j. Eq. (12) bounds the capacity
HYSYS library for the operational layer model. The Visual Basic for of the tank z during any time period t. Eq. (13) bounds the flow
Applications (VBA) bridge code then embeds them into an Excel between the tank and dock to a maximum level when connected
spreadsheet where frontline chooses the next set of variables to and to zero when not. Eq. (14) bounds the flow between the tank
insert into the HYSYS model. In each of the iterations, the total cost and CDU to a maximum level when connected and to zero when
of the refinery operations is embedded into the Excel spreadsheet. not. Eq. (15) ensures that a tank cannot fill a CDU if it is receiving
After the objective function has reached a maximum, the cost of the crude from a dock. Eqs. (16) and (17) ensure tabs are being taken
profit optimized refinery are tabulated over the operational level when a connection is made. Eq. (18) ensures that the total crude
range. flow of type j feeding CDU k during time period t is less than the
maximum amount allowable. Eq. (19) ensures that the total crude
of type j flow feeding the CDU is more than the minimum amount
3.2. Scheduling solution approach allowable. Eqs. (20) and (21) make certain that there is no blending
in the tanks.
The model equations are constructed by combining material bal- The objective function can be described as the inventory costs
ances for the vessels and storage tanks, operating rules for arrival for storage, the setup cost of establishing a connection between two
and departure of vessels and for crude oil charging, and logistical entities, with refining cost associated to the crude sent to the CDU.
constraints. The loading and unloading scheduling model is stated In our scenario, this setup cost will dominate the objective function
822 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827

Table 2
Data from operational layer optimization.

Type 0 FLow (m3 /h) Type 1 flow (m3 /h) Vol. fraction Dubai Total flow rate Operational Operational Operational
(m3 /h) costs ($/h) revenue ($/h) profit ($/h)

298.10 467.1 0.3896 765.20 35,651.6 169,753 134,101

292.40 472.8 0.3821 765.20 35,688.5 169,705 134,016
286.60 478.6 0.3745 765.20 35,730.1 169,659 133,929
280.90 484.4 0.367 765.30 35,770.5 169,611 133,840
275.20 490.1 0.3596 765.30 35,817.2 169,558 133,741
269.40 495.9 0.352 765.30 35,858.1 169,512 133,654
263.70 501.7 0.3445 765.40 35,909.5 169,472 133,562
258.00 507.1 0.3372 765.10 35,950.3 169,425 133,475
252.20 513.2 0.3295 765.40 35,997.9 169,379 133,381

to be minimized. 4. Results and discussion


ND  
NT NP
 
NT NCDU NP
4.1. Operational layer optimization
min(setupPenaty ∗ ( SCi,z,t + SDz,k,t )
i z t z k t Table 2 shows the different individual crude flow rates inserted
into the operational layer simulation. Their total is equal to the CDU

NO 
NT NP
+ Invj ∗ Iz,j,t (22) demand and they are in the volume fraction blend range of the CDU.
The operational level was optimized to maximize profit and the
j z t
environmental and utility costs were tabulated. This information
was used to determine the relationship between the crude blends
GAMS optimization software with CPLEX solver was used to and refining operational cost and revenue.
solve the MILP. The objective function can be described as the The coefficients for the operational cost function were obtained
inventory costs for storage, the setup cost of establishing a con- using multiple linear regressions of columns 5 and 6 with column
nection between two entities, with refining cost associated to the 1. Both revenue and cost are positively related to the flow of Type
crude sent to the CDU. In our scenario, this setup cost will dominate 0. The more expensive crude blend to refine cost gave less rev-
the objective function to be minimized. enue. Therefore, there is an inexpensive profitable end of the blend
range and a more expensive less profitable end of the blend range.
The cost equations obtained from the regression of the above data
3.3. Integration of the two models
around one product flow are given below. The approach can be
extended for multiple crude types. The intercepts are readjusted
To account for the refining financial consequence of the blend
(weighted) to the same magnitude of order of the logistical costs.
entering the crude distillation unit, the operational revenue and
Eqs. (27) and (28) represent the difference in operational cost and
costs are tabulated for different blends within the range of feed
revenue.
blend. The revenue and costs tabulated have been optimized to
produce the maximum operating profit according to the method in $
Operation profit = 15.7 ∗ YType 0 − 350 k$ (28)
Section 3.1. After the optimized revenue and associated costs are m3
tabulated, each is regressed with individual crude feed flow rates,
Yz,k,jt , and expressed as a linear function. $
Operational costs = −7.7 ∗ YType 0 + 400 k$ (29)
m3
 
NP NCDU 
NT NO

Operation cost = cj,k Yz,k,j,t − A (23) 4.2. Blend range linearity

t k z j
Fig. 2 illustrates the residual plots (goodness of fit) for the oper-
ating profit function for the CDU feed composition (0.335–0.39 Type
 
NP NCDU 
NT NO

Operation revenue = pj,k Yz,k,j,t − B (24) 0.) As we can appreciate, the linear approximation works quite well
within the specified range. However, when the range is expanded
t k z j
more general approximations, such as piecewise linear approxima-
tion, may be needed, for better representation.
Total costs = Operation cost + Logistical costs (25)

The coefficients, Cj,k , pj,k in Eqs. (23) and (24) are determined by
multiple linear regressions around the range allowable for the pro-
duction facility. Parameters A and B are determined to ensure the
operating costs are of the same magnitude of order as the logistical
costs. Therefore, these equations represent the financial difference
across the blend range. It is only necessary to regress around the
total number of crude flows minus one. This method is capable of
expanding to any number of crude types. This refining cost func-
tion is embedded into the scheduling and planning MILP objective
function. This leads to two possible improved objective functions:

max(Operational revenue − Logistical costs) (26)

min(Total costs) (27) Fig. 2. Residual plot of profit function.

 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827 823

Fig. 3. Inventory levels under alternative objective functions.

The optimized financial parameters remain moderately linear. event outweighing operational cost or revenue difference across
As the amount of the lighter Type 0 crude is increased, the cuts the blend range.
are changed proportionally. This is due to the fact that the cuts In the base case, the initial tank Type 0 inventory can last for as
are much stronger function of composition than the degree of sep- short as 31.5 h or as long as 36.6 h depending on which end of the
aration. This causes the operational revenue function to be linear blend range the distillation unit is operating (high Type 0 or low
function of the feed composition. The costs remain more or less lin- Type 0). The Type 1 can last as short as 82.5 h or as long as 90 h.
ear as well. The furnace duties decrease linearly as the lighter crude The penalty for a set up establishment event on the production
is added as the specific heat of the mixture is a reasonably linear level is $25,000. The operation cost savings across the blend range
function of composition. This causes an equally linear decrease of is $324. By dividing the penalty of the production level event by the
sustainable costs as the amount of fuel oil required decreases with operational benefit across the blend range a minimum number of
the furnace duties. The condenser duties are proportional to the hours to justify a change in production cost for a change in operation
vapor load in the columns, which is proportional to the composi- cost is 77 h and for revenue profit difference to affect a changeover
tion. Despite the increases in the vapor load of the PDU, the ADU is 38 h.
and VDU condenser duties decrease. An overall decrease in the con- The base case study demonstrates a scenario when it is benefi-
densing costs occurs due to the fact that the condenser duties on cial to incur another logistical penalty of setting up a connection in
the ADU and VDU are larger. order to save operational costs. Fig. 3 is divided into three columns,
each corresponding to a different objective function (Eqs. (22), (26)
4.3. A tradeoff of operational mode and production layer event and (27)). Each column contains graphs of the feed composition
entering the CDU and inventory profiles of the four tanks. The first
Scenarios exist where the total costs (Eq. (25)) are higher when row is composed of the CDU compositions during the time horizon.
only the logistical costs are optimized. This scenario arises if a logis- The next two rows are inventories of Type 0 and Type 1 respec-
tical event can affect the feed composition for a sufficient amount tively. In all three cases, one of the inventory profiles of each crude
of time; the economic consequences of the unit operating costs will type is always decreasing. This is the one feeding the CDU the cor-
outweigh the logistical event’s penalty. Our base case is an exam- responding crude type. During hours 3–38, a shipment of Type 0
ple of a particular combination of the penalty for production level is to be loaded. During hours 50–85 an incoming vessel of Type 1
824 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827

Table 3 Table 4
Base case results of the scheduler using each objective function. Base case deviation results of the scheduler using each objective function.

Objective Logistical cost (k$) Total costs (k$) Profit (k$) Objective Logistical cost (k$) Total costs (k$) Profit (k$)

Min (log costs) 150 320 119 Min (log costs) 175 356 97
Min (total costs) 150 312 135 Min (total costs) 175 327 156
Max profit 175 327 156 Max profit 175 327 156

is to be loaded. During these times, one of the inventory profiles returned total cost and profit over the entire horizon are included
increases to accommodate the storage of these loads. in the table. The first row entries show the results when the sched-
The different objective functions have a different effect on the uler minimizes only the logistical cost, which is dominated by the
CDU composition. The logistical costs changed the composition setup cost in our scenario (number of setups is tabulated), while
between the extremes as needed to minimize the logistical setup still meeting the operational level blend specification. The second
costs. However, the logistical costs objective does not consider the row entries demonstrate the results when total logistical and refin-
operational costs, so the blend is indiscriminate as it does not affect ing costs are considered. In most cases, it was noted that a different
the objective function. The objective functions of maximizing profit total cost could arise when compared to min logistical cost refining
or minimizing total costs are inclined to keep the CDU feed com- cost even if the logistical costs were the same. This is true because,
position on the high Type 0 end (the inexpensive – profitable end) since the flow rates were decision variables to the CDU, they were
of the blend range. allowed to move freely within the blend range without affecting the
When considering only the logistical cost (column one in Fig. 3), objective function if they did not cause a change in connections.
Type 0 inventory in Tank 1 is completely consumed while the There was more than one arrangement possible. In other words,
incoming Type 0 crude is stored in an empty tank (Tank 4). Accord- there exists a solution space for the logistical objective function
ingly, the CDU is fed on the low end of Type 0 (the expensive less which was reduced when considering total costs.
profitable end of the blend range) to make Tank 1’s (initial Type 0) This is an example where giving the blend range a preferable
inventory stretch until the incoming crude is completely unloaded. side shrinks the solution space of the objective function. In the case
The tank has more than enough to accomplish this and the blend where the setup cost was minimized, the solver found no differ-
feed is changed to the high end for time periods 23–27. This change ence in the objective function to operate somewhere on either end
could have occurred at the end without changing the objective of the blend range, leading to a more fluid schedule than neces-
(during time periods 35–39). This would have reduced the num- sary (randomness increases as schedule complexity increases). The
ber of times the blend was switched back and forth. After time 39, optimizer does not consider blend changes within the CDU feed
the CDU feed operates at the high end of the feed range while in composition when minimizing setup costs and since the base case
the end (at time period 86) the CDU feed switches back to the low was selected to have preferable cost at either end of the blend range,
end for no apparent reason. This is a manifestation of the fact that large improvements can be expected when considering total cost
blending changes are not considered when blending in a manifold or profit.
occurs. This is due to blending changes being marked by connec- As shown in Table 4, minimizing total costs or maximizing total
tion establishment binary variables of the tanks to the CDU. The profit yields the same financial parameters, however, they have dif-
scheduler must note this shortcoming of the model and smooth it ferent schedules. Fig. 4 illustrates in keeping Type 0 flow rate high
over himself/herself by ensuring blend changes are not occurring to stay on the profitable inexpensive side of the blend range, the
unnecessarily. incoming Type 0 crude has to be shared among two tanks. Maxi-
When considering the total costs, the second column, the opti- mum profit formulation achieves this by using the two empty tanks,
mizer tries to keep the CDU on the high end of Type 0 to save then converting Tank 1 into a Type 1 tank for the incoming Type 1.
operational costs. This schedule does not include the unnecessary Minimum costs formulation achieves this by emptying the tank and
switch back to the low end at the end of the schedule. Before the then refilling it, which is a more desirable schedule as converting
39th period, the CDU composition does spend the same time in tank types requires a cleaning process. This scenario clearly shows
the expensive region (periods 23–27). This is the minimum time that using different objectives could result in superior scheduling.
before a connection would have been necessary to have enough In Figs. 3 and 4, the feed composition of the CDU was at either
Type 1 available to satisfy the CDU demand up to period 86. Once the high end or the low end despite the model allowing it move
again this time could have been during 35–39, avoiding two oper- freely within the blend range. Due to the objective’s linearity, oper-
ational mode changes. This is an example where operating at less ating somewhere in the middle of the blend range can only be as
than favorable conditions on the operational level can save total good or worse than operating at one of the ends of the blend range.
costs. Therefore, the linear solver will only check against the constraints
When the profit is considered, the optimizer places an addi- at either end of the blend range. From this perspective, it does not
tional connection to operate at the more profitable end of the blend matter how well the linear approximation describes the middle of
range. The two empty tanks share the incoming Type 0 while Tank the blend range, only the ends of the constraints. This remains true
1 is emptied quickly. The empty Tank 1 is then converted into a for multiple crude types (Fig. 4).
Type 1 Tank in order to store the incoming Type 1 crude. This is
an example where adding an extra connection is necessary to keep 5. Practical considerations
the operational mode of the tank in the profitable region (Table 3).
In this case study, a slight deviation of the base case is also 5.1. Choosing blend range possibilities
explored. The initial crude inventory in Tank 2 is 40,200 m3 . In this
case, there is not enough Type 1 to both operate on the low Type 0 Since the solver operates against a constraint, the scheduler is
end initially to ensure that Tank 1’s (Type 0) initial inventory can advised to begin with the operating point he/she is at and choose
last until the incoming crude is stored and Tank 2’s (Type 1) initial a second operating point that he/she deems has potential. Poten-
inventory can last until Type 1 is stored. In this case, three different tial could be perceived in various ways by process knowledgeable
schedules arise with the same logistical costs. Table 4 depicts the personnel. If inventory of a particular type is high and that crude is
results of the scheduler using the different objective functions. The pooling, inventory costs can be easily be incorporated in our objec-
 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827 825

Fig. 4. Inventory levels under alternative objective functions.

tive function. A potentially better operational point would consume Time constraints could be violated when the schedule is formu-
more of the pooling crude. If inventory of a particular product is lated. For example, establishing a connection is a time consuming
scarce, then there is a potential to cause many unwanted connec- process including:
tions as in the base case. A second operational point would use
less of this crude. If data or simulation shows a new feed blend • Configuring the pipeline network (e.g., opening valves, configu-
could improve the unit’s operational costs at the expense of hav- ration of pumps, etc.)
ing to change the unit’s operational condition, the more optimal • Filling pipelines with crude oil is a lengthy and dangerous proce-
condition could be the next point of interest. In any case, the sched- dure,
uler should set the ends of the blend ranges to describe the point • Sampling crude for chemical analysis, measuring crude oil stock
he operating, and the other end to be in the direction of interest. in tank before loading/unloading,
This will allow the scheduler to evaluate the tradeoff potential of • Starting loading/unloading,
changing the unit’s operating condition. • Stopping the loading/unloading.

5.2. Crude schedule control In the event that there are too many logistical events so that a
time constraints is violated, one has to first check cost shifters. If
Crude oil scheduling control is a natural extension of the work the production layer is not on the same order of magnitude as the
presented. The mathematical model does not account for all time operational layer, then the operational layer may drown out the
constraints, personnel opinions, as well as other factors are present production layer events leading to a very erratic schedule. Increas-
in a real world application of scheduling. Therefore, controlling ing the setup costs will decrease the number of times establishing
the crude oil scheduling is necessary. Parameters which are used connections occur. If there is only one undesirable production layer
to control the schedule include the shifting factors (A, B), opera- event, increasing that event’s penalty reduces the frequency with
tional costs coefficients, (cj,k , pj,k ), and penalties for production layer which it occurs. In our base case, a penalty of $31,500 for estab-
events such as penalty for setups. Based on the above described lishing connections will prevent the optimizer from establishing
strategy, a crude oil scheduling policy can be envisaged to take into another connection to maximize profit (i.e., the profit schedule will
account practical considerations. look like the min cost schedule).
826 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827

If there are many unwanted production layer events, reducing ing and feedstock selection problems, and will identify inventory
the benefit across the operational blend range using the operational and sea waiting tradeoffs in the schedule.
cost parameters can reduce the likelihood of a scenario where a pro-
duction layer event can affect enough time intervals to outweigh Appendix A.
the operational benefit. For example, the scheduler may tell the
operator to change a unit from optimal feed conditions in order to Tables A1 and A2.
save logistical costs of having that feed. The operator may be hesi-
tant and resist. The operator can then either increase the financial Table A1
consequence of changing to the less desirable feed or decrease the Sustainable costs.

penalty incurred on the logistical level. If the scheduler still gets the Environmental loads Fuel oil Fuel gas
same schedule, he/she can assert the operator change the operat-
CO2 Ton/GWH 657 439
ing conditions. If the scheduler finds that an insignificant change SO2 kg/GWH 1030 1
in the parameters leads to a schedule which pleases the opera- NOx kg/GWH 988 1400
tor, he/she may decide to allow the unit to remain at its current Engine efficiency 50% –*
condition. Special report of World Energy Council, July 04.
*
Assume that it is completely turned into heat in the preheat furnaces. The
sources of emissions are from steam generation from utility boilers, furnace flue
6. Conclusions and future work gas and electricity steam parameters. Assuming the heat to power ratio of 1.25 and
Mp steam @ 245 ◦ C as 13.5 MMKJ/h per ton of steam and the efficiency of the steam
furnace plant is 40%. Electricity combustion efficiency is 50%.
In summary, we found that in all cases it is important to consider
operational cost in the production layer scheduling. In most cases
the linear operation cost function narrowed the solution space
Table A2
of the previous models to the economically beneficial side of the Values for optimization of operational layer.
blend range. This led to a more intelligent schedule. A scenario
Pollutant Sustainable Debit Penalty for discharge
was identified where the overall costs were reduced despite incur-
ring higher production layer costs. The operational costs function is CO2 3.25 $/ton
able evaluate tradeoffs of production level events. Scenarios were SOx 192 $/ton
NOx 1030 $/ton
identified where operating the unit at unfavorable conditions and Product Price ($/m3 )
implementing a schedule that did not minimize the local logistical LN 300
costs could reduce the costs across the entire supply chain. We also CN 225
found shortcomings in the model that could be overcome by trying HN 240
Kerosene-1 265
different objective functions.
Kerosene-2 285
Lee et al. (1996) demonstrated a tradeoff between inventory and Diesel 250
sea waiting costs. This paper demonstrated a tradeoff between unit VDO 250
operation and production level events by adapting Saharidis model. LVGO 200
A natural extension of this work is to create model combining the HVGO 200
SD 165
advantage of the two aforementioned models. A model which (1) VR 165
uses crude oil types for linear terms (2) considers the sea waiting, Duty Price ($/MMKJ)
unloading, inventory, and refining costs, and (3) can account for Condenser duty 4
multiple tank types. These characteristics will allow the scheduler Furnace duty 75
Steam duty 75
to account for CDU blend changes, are compatible with both refin-

Table B1
Assay data for Dubai and Masila crude.

Properties Light end analysis TBP distillation

Density at 15 ◦ C, kg/m3 874 Component wt% vol% ◦

C wt% vol%

Masila crude
◦
API 30 Ethane 0.02 0.05
Propane 0.29 0.5 15 1.4 1.86
◦
Viscosity, cSt at 10 C 20 Iso-butane 0.23 0.36 149 15.6 19.2
Viscosity, cSt at 50 ◦ C 5.9 n-Butane 0.86 1.29 232 28.9 33.8
Pour point, ◦ C −30 342 48.6 53.9
362 53.4 58.5
509 74.4 78.3
550 79.3 82.7
Dubai crude
Density at 15 ◦ C, kg/m3 868
◦
API 31 Ethane 0 0
Propane 0.05 0.09 15 0.39 0.3
Viscosity, cSt at 10 ◦ C 22 Iso-Butane 0.14 0.22 32 1.09 1.28
Viscosity, cSt at 50 ◦ C 7.3 n-Butane 0.2 0.3 93 4.45 5.53
Pour point, ◦ C −9 149 12.4 14.9
182 17.7 20.8
260 30.8 34.8
371 52.8 56.9
427 59.9 63.8
482 70.1 73.6
538 78.1 81
550 80.4 83.2
 G. Robertson et al. / Computers and Chemical Engineering 35 (2011) 817–827 827

Table B2
Performance specifications for PDU, ADU and VDU.

Decision variable Low Optimization example High

Prefractionator
Vapor flow rate, m3 /h 3 3.23 4
Light Naphtha flow rate, m3 /h – 68.6 –
Bottom steam rate, Kg/h 4500 6009 8000
Atmospheric distillation column
Vapor rate, m3 /h 0 0 0
Distillate rate. m3 /h 4.5 6
CN rate, m3 /h – 12.0525 –
HN rate, m3 /h 26 30
Kerosene-1 rate, m3 /h 95 98.5738 99
Kerosene-2 rate, m3 /h 44 46.1232 49
Diesel rate, m3 /h 102 106.031 107
HN P/A rate, m3 /h 325 330.303 335
Kerosene P/A rate, m3 /h 385 390 390
Diesel P/A rate, m3 /h 390 394.367 395
HN steam rate, kg/h 300 654.662 1000
Kerosene-I steam rate, kg/h 2000 3229.3 5000
Kerosene-2 steam rate, Kg/h 500 997.872 2000
Diesel steam rate, Kg/h 1000 2194.79 4000
Bottom steam rate, Kg/h 4000 6022.41 8000
ADU feed temperature, ◦ C 372 372 385
Vacuum distillation column
VDU feed Temperature deg C 398 398 410
Vapor to ejector, m3 /h 4.5 5.22402 6
VDO rate, m3 /h 18 20.6416 23
LVGO rate, m3 /h 15 16.6767 18
HVGO rate, m3 /h 105 110.776 112
SD rate, m3 /h 19 21.1926 24
VDO P/A rate, m3 /h 168 171.57 174
LVGO P/A rate, m3 /h 58 61.2264 63
HVGO P/A rate, m3 /h 175 177.602 180
Bottom steam rate, Kg/h 3000 3000 5000

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