Optimization of Unloading Operations in Petroleum Product Storage

Article pubs.acs.org/IECR

Optimization of Unloading Operations in Petroleum Product Storage Terminals Arun Srikanth, Sridharakumar Narasimhan,* and Shankar Narasimhan Department of Chemical Engineering, IIT Madras, Chennai, Tamil Nadu, 600 036, India ABSTRACT: Petroleum products such as propane, butane, liquified propane gas, and liquified natural gas are unloaded from ship carriers through pipelines to storage facilities located 10−12 kms inland. This process is an energy intensive and a timeconsuming operation. Unloading at high flow rates results in excessive boil-off gas (BOG) generation in the storage tank thereby resulting in increased cost of pumping the fluid and increased cost of compressing the resulting BOG. If the BOG generated exceeds the capacity of the compressors, then the excess gas has to be flared resulting in loss of valuable raw material, besides the associated environmental damage. But, when low unloading flow rates are employed, it results in longer berthing time of the ship to unload the product thus incurring demurrage. In this paper, efficient ways to minimize the total cost of an unloading operation are explored by solving a generalized simulation optimization model and the results are discussed. The strategies and the results presented in this work are valuable for industrial applications.

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INTRODUCTION Increase in demand for petroleum products and the consequent expansion of existing terminals and construction of new storage terminals has led to an increase in the frequency of unloading petroleum products. Unloading petroleum products in a storage terminal involves pumping refrigerated petroleum products from ship carriers berthed at the jetty through long insulated pipelines to storage tanks located 10−12 kms inland. A typical unloading operation lasts for about 10−16 h depending on the size of the parcel to be unloaded and the unloading flow rate. This operation is an energy intensive and a time-consuming operation and results in excessive boil-off gas (BOG) generation causing pressure build up in the storage tank. If the BOG generation in the tank exceeds the total compressor capacity, vapor is flared to maintain the pressure in the tank. The BOG generation is primarily due to the sensible heat added by the incoming liquid to the contents of the tank and depends on the temperature dynamics of the pipelines and the unloading flow rate. Unloading at high flow rates results in large inflow of energy into the tank and hence results in huge BOG generation and flaring of valuable material. Further it increases the pumping cost and cost of compressing the BOG. But when low unloading flow rates are employed, it results in longer berthing time of the ship to unload the required quantity of product, thus incurring demurrage to be payable to the transporter. Thus, energy efficient strategies and prudent BOG management that minimize the overall cost of an unloading operation have to be formulated. Studies related to energy efficient BOG management in storage terminals have been addressed in literature. Calculations of daily BOG generation in a liquefied natural gas (LNG) terminal and a detailed cost analysis for a combined LNG terminal and cogeneration plant have been presented.1 A new method for handling the BOG in LNG terminals based on sensitivity analysis has been reported.2 A design for efficient handling of BOG in LNG terminals by optimizing the retrofit design variables to maximize profitability has been proposed.3 A © 2014 American Chemical Society

control strategy for handling the BOG and optimizing the gas recondensation process has been reported.4 Other optimization studies relevant to storage terminals are focused on energy efficient operation of compressors used to handle the BOG. Optimal operation of compressors by solving a mixed integer linear programming (MILP) problem which minimizes the total power consumption in a LNG plant has been addressed in recent literature.5−7 A Nonlinear Programming (NLP) model to determine the optimal compressor operations for a refrigeration system in a LNG plant has been proposed.8,9 A dynamic model in ASPEN was used in an MILP formulation to determine the optimal operation schedule of compressors.10 Although the above optimization strategies are useful, they do not address the problem of optimal operating schedule when unloading a required quantity of product in the stipulated time taking into account the inherent transients involved during the unloading process. Studies related to optimal unloading operation are few in literature. An efficient, safe, and reliable procedure to unload petroleum products in terminals consisting of both above ground and in-ground storage tanks has been suggested.11,12 However, the emphasis is on efficiently carrying out the depressurization step which is performed prior to an unloading operation. A design based on thermodynamic analysis for flare minimization during unloading operations in LNG terminals has been addressed.13 They solve a rigorous simulation optimization model which minimizes the total energy consumption and provide a cost-effective flare minimization strategy; however, their optimization approach focuses mainly on the LNG regasification process. Heuristic strategies to minimize the total cost of unloading have been analyzed by the authors.14 Received: Revised: Accepted: Published: 13728

February April 28, April 30, April 30,

1, 2013 2014 2014 2014

dx.doi.org/10.1021/ie400389x | Ind. Eng. Chem. Res. 2014, 53, 13728−13735

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of a storage terminal showing precooling and unloading operations14

In the present work, we analyze energy efficient strategies to unload petroleum products by solving generalized simulation optimization models. We consider a case study of unloading a pure component petroleum product and demonstrate the efficacy of the developed strategies using this case study.

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Prior to an unloading operation, the pipelines are precooled by circulating the stored cold liquid petroleum product at a rate equal to mp. The circulated liquid is then recycled back to the same tank. The flow direction during unloading and precooling is also shown in Figure 1. The properties of the pipeline system used for the studies are provided in Table 1 and Table 2.

PROCESS DESCRIPTION

In this section the various specifications used in the optimization studies are presented. First, the details of a dynamic model for the unloading operation are presented which is then followed by the discussion on the cost considerations used in the optimization studies. Finally, the specifications of a case study of a typical unloading operation for which the optimal strategies are to be formulated and solved are presented. Modeling. A detailed description of the unloading operation, its mathematical modeling and validation has been presented elsewhere.14 An overview of the work is described here. Two parallel insulated pipelines UN1 and UN2, each of length L are used to transport the petroleum product from the ship to the storage tank as shown in Figure 1. The flow rate in each of the pipelines is denoted as m1 and m2. The storage tank and the pipelines form a connected system, and the temperature dynamics of the pipelines affect the dynamics of the storage tank and hence the BOG generated. The mathematical model for the unloading operation consists of a dynamic model of the storage tank coupled with a dynamic model of the pipeline, which includes the temperature dynamics of liquid flow, pipe wall, and the insulation. The model was tuned to predict the dynamic data obtained from an operating terminal during unloading of propane. Two or more compressors may be operated during unloading to withdraw the BOG generated in the tank so as to maintain the pressure in the tank at a desired level. If the BOG exceeds the available compressor capacities, it implies that the excess gas is flared.

Table 1. Geometric Properties of Pipeline length, L inner diameter thickness of steel thickness of insulation

5.8 km 0.434 m 11.1 mm 150 mm

Table 2. Thermophysical Properties of the Pipeline thermal conductivity

density

specific heat

material

W/(m K)

kg/m3

J/(kg K)

steel wall insulation

50.2 0.1

7700 192

500 1400

Cost Analysis. The overall operating cost involved in an unloading operation is the sum of compressor operating costs, cost of pumping the material through the pipelines, expense incurred due to flaring, and demurrage payable to the transporter, if the ship is made to wait at the jetty beyond the stipulated time to unload the product. The computations for the costs involved in the strategies to be analyzed in this work are given below. Cost of Pumping (CP). Since the pipelines, UN1 or UN2 are in parallel arrangement, the pressure drop is the same in each pipe. The cost of pumping the material in the pipelines is given by C P = ce 13729

∫0

K̅

1 ΔP dt m u (t ) ηp ρl

(1)



Article

where

C T(m u , K̅ ) = C P + CC + C F + C D

ΔP = ρl

8fLm u2(t ) ρl π 2d05

Unloading Operation. As mentioned in the introduction, BOG is generated in the tank due to the sensible heat added by the incoming liquid. Unloading at high flow rates results in large inflow of energy into the tank, significant BOG generation and consequent flaring of valuable material. It also results in increased pumping costs and cost of compressing the BOG. However, if lower flow rates are employed, it results in longer berthing time of a ship to unload the product, thus incurring demurrage to be payable to the transporter. In the following section, two major strategies are presented that are obtained by solving a generalized simulation optimization model for unloading petroleum products. These strategies are applied to a case study of typical unloading operation. The case study corresponds to unloading a 5000 t parcel of propane at −40 °C from a ship tanker berthed at the jetty in a stipulated time of 10 h. The available combined capacity of the compressors to compress the BOG is assumed to be 15 t/h. In the simulations, the value of the maximum precooling flow rate (which depends on the pump available at the terminal) is considered to be 130 t/h. The maximum unloading flow rate (which depends on the pump available in the ship) is considered to be 1000 t/h (ub) and lowest value of the unloading flow rate is considered to be 0 t/h (lb). The total unloading flow rate is split equally (m1 = m2) in the unloading lines. Prior to the unloading operation it is assumed that the stored liquid propane is circulated in the pipelines at the maximum flow rate of 130 t/h, and a steady state temperature profile prevails in the pipelines corresponding to this flow rate. The initial conditions in the tank prior to unloading are given in Table 3. The aforementioned specifications are summarized in Table 4.

(2)

and ΔP, mu, K̅ , ce, ηp, d0, f, ρl denote the pressure drop in the pipe, the unloading flow rate, the time for which the parcel is unloaded, the cost of electric power, pump efficiency, inner diameter of pipe, friction factor, and liquid density, respectively. The values ce, ηp, and f are taken to be 0.18 $/kWh, 0.85, and 0.002, respectively. Expense Incurred Due to Flaring (CF). The expense due to flaring can be computed using the formula

CF = M f cf

(3)

Vapor generated in the tank in excess of compressor capacity is flared. Hence, the rate of material flared is given by mf (t ) = max(0, m v (t ) − Ccc)

(4)

The total amount of material flared in an unloading operation carried out for a period K̅ is given by Mf =

∫0

K̅

m f (t ) d t

(5)

In the above equations, Mf, mf, mv, Ccc, and cf denote the amount flared, flaring rate, BOG generation rate, available compressor capacity at the terminal, and the cost of petroleum product per kg, respectively. The petroleum product is assumed to be propane, and its cost is taken to be $1.32 per kg. Cost of compression (CC). The cost of compressing the material can be calculated using the expression CC =

∫0

K̅

1 ceWc(t ) dt ηc

Table 3. Initial Conditions in the Tank Prior to Unloading

(6)

where the work done by compressor Wc(t) is given by γ − 1/ γ ⎡ ⎤ γmc(t )RTT ⎢⎛ P2 ⎞ − 1⎥ Wc(t ) = ⎜ ⎟ ⎥⎦ γ − 1 ⎢⎣⎝ P1 ⎠

mass of liquid mass of vapor temperature of tank contents pressure (gauge)

Table 4. Specifications of the Case Study total amount to be unloaded (U) stipulated time (N̅ ) unloading parcel temperature initial state of pipelines initial state of tank maximum precooling flow rate maximum unloading flow rate (ub) combined capacity of compressors

(8)

The above expression is based on the fact that the rate at which the material is compressed is always less than or equal to the total compressor capacity (excess vapor generated is flared) and is the minimum of the two quantities, namely, the BOG generation rate and the total compressor capacity. In this particular case study, we assume the pressure ratio to be 10, and γ = 1.15 and ηc = 0.85. Demurrage Incurred (CD). Demurrage charges are incurred if the ship is made to wait beyond the stipulated time (N̅ ) for unloading. For the following scenarios, demurrage is assumed to be charged at a rate of cd taken to be a value of $2000 per time period, Δt which is to be paid to the transporter. Thus, demurrage can be computed by the following equation. C D = cd(max(0, K̅ − N̅ ))

2051 t 56.459 t −40 °C 967.87 mmH2O

(7)

and mc(t ) = min(m v (t ), Ccc)

(10)

5000 t 10 h −40 °C steady state corresponding to 130 t/h refer to Table 3 130 t/h 1000 t/h 15 t/h

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OPTIMAL UNLOADING STRATEGIES In this section, the solution methodology adopted to solve the optimization formulations is presented followed by the mathematical formulations and the solution of the optimal unloading strategies. Finally, a brief comparison between the strategies is discussed and conclusions are drawn. Solution Methodology. The decision variables involved in the simulation-optimization model include the sequence of compressor operations, the unloading flow rate (mui) and the total time required for unloading (K̅ ). Among these, the unloading flow rate is assumed to be a continuous variable and

(9)

where N̅ and K̅ denote the stipulated time for unloading the parcel and the unloading time period, respectively. Total cost (CT). The total cost of an unloading operation is the sum of the above individual cost functions and is given by 13730



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Unloading Strategy (Strategy I). It is a usual practice in storage terminals, that soon after arrival of the ship, precooling operation (liquid recirculation in the pipelines) is ceased and unloading of the product commences. Unloading at high flow rates results in excessive BOG generation in the tank and flaring of material. By employing lower unloading flow rates, the time taken to unload the parcel may exceed the stipulated time thus incurring demurrage to be payable. A trade-off exists between the demurrage incurred and the expense due to flaring. To balance the trade-off, an optimization problem is formulated that seeks to minimize the overall cost of unloading operation by choosing appropriately the total time taken to unload the parcel and the unloading flow rate. The simplest operational strategy is to use a constant rate of unloading during the entire unloading period. We first consider the strategy in which a constant unloading flow rate is employed before considering a strategy in which the unloading flow rate is allowed to vary. Constant Unloading Flow Rate. Given a parcel of size U that is be unloaded, and the stipulated time of N̅ hours after which demurrage costs are incurred, the following optimization problem is formulated that seeks to minimize overall costs. As mentioned, the total unloading time is discretized into equal time periods (Δt) of 1 h. The average unloading flow rate mu is kept constant for all the time periods. The decision variables of the optimization formulation are then the constant unloading flow rate mu and the total number of unloading time periods K. The optimization problem is then given by

the compressor operation sequence and the unloading time are assumed to be integer variables. The compressor operation sequence further involves assigning several integer variables for the number of compressors in operation, time duration for each of the compressors in operation along with the load level on each of the compressors.5 This increases the number of decision variables, and since a distributed dynamic model is employed in this work, it becomes computationally intensive to solve the optimization problem. Thus, to reduce the computational burden, it is assumed that the compressors withdraw the BOG generated so as to maintain the pressure in the tank at a constant level throughout the unloading operation. Furthermore, the operation sequence can be easily calculated after obtaining the BOG generation of an unloading scenario and can be practically implemented if variable frequency drives are used to drive the compressors. The decision variable, total unloading time (K̅ ) which is an integer variable in the optimization formulations is divided into equal time periods, Δt. Thus, the total unloading time K̅ is given by KΔt with K denoting the total number of unloading time periods. Once the decision variables for optimization, namely, unloading flow rate and time periods for unloading are known, the simulation model can be run for determining the BOG, and hence the total cost can be computed. The total cost representing the objective function value is provided to the optimization routine for determining the updated guesses for the decision variables. The simulation model is thus impliclty embedded in the optimization procedure and is referred to as the simulation−optimization framework. The max (eq 4, eq 9) and the min functions (eq 8) involved in the cost computations are handled using if−then construction. The integrals in the cost functions (eq eq 1, eq 5, eq 6) are evaluated numerically. The total cost function CT is a nonlinear function of the decision variables, and since both continuous and integer variables are involved, the optimization problem to be solved is an MINLP problem. In general MINLPs form a class of challenging optimization problems, since the MINLP involves the difficulty of optimizing over integer variables with handling of nonlinear cost function and constraints.15 The MINLP problem is solved by converting it into a series of NLPs which is explained below. As mentioned, the only discrete variable is the number of unloading time periods. The optimal solution is obtained by solving a series of NLPs, for successive choices of the time periods. As the number of time periods increases, the cumulative demurrage increases, while the pumping and material flaring costs decrease (due to greater flexibility in the choice of the pumping flow rates). Thus, for each successive choice of the time period, the minimum overall cost can be determined. It can be shown that the optimum of the MINLP problem can be obtained by solving a finite number K* of NLPs, and an upper bound on K* can be determined a priori. It should be noted that this solution procedure will result in the optimal solution of the MINLP problem, if the global optimum solutions of the NLPs can be obtained. The NLPs were solved using the optimization routines supplied as a part of the optimization toolbox in MATLAB. The gradient-based solvers were used here, which employ trustregion, active-set, interior point algorithms. Optimtool has been used here, which is a graphical user interface (GUI) for selecting a toolbox function, specifying optimization options, and running optimization problems. The NLPs were tried with different initial guesses, and consistent solution was obtained.

min(mu,K ) C T

(11)

Subject to Km uΔt = U

(12)

K≥N

(13)

lb ≤ m u ≤ ub

(14)

The NLPs are solved for K = N, ..., K* and for the initial specifications provided in Table 4. It is found that the optimal time for which the parcel is to be unloaded is 15 h (K̅ ), and hence the time for which the ship had to wait beyond the stipulated time is calculated to be 5 h. The constant unloading flow rate is 333.33 t/h (mu). This scenario, incurred a demurrage of $10,000, since the ship was made to wait beyond the stipulated time for 5 h. The BOG withdrawal rate exceeded the compressor capacity (Figure 2), flaring resulted in an expense of $3,356. The overall cost sums up to $14,171. It may be observed that although it is possible to unload the entire

Figure 2. BOG withdrawal rate for constant unloading flow rate, strategy I. 13731



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Figure 3. Solution of NLPs.

Figure 4. (a) Optimal unloading flow rate sequence (K = 10); (b) BOG withdrawal rate. K

parcel within 10 h without incurring demurrage costs, this solution is not found to be optimal, since the BOG generated exceeds the capacity of the compressors and results in significant costs due to flaring of valuable material. Varying Unloading Flow Rate. Although it is simple to implement a constant unloading flow rate, we assess whether it is possible to further reduce the overall cost of unloading by varying the unloading flow rate. In this optimization problem, the decision variables are the unloading flow rate and the total time for unloading. The total unloading time (N̅ ) is discretized into equal time periods Δt of 1 h. The unloading flow rate is kept constant in each time period but allowed to change from one time period to the next. Thus, the solution given by the optimization formulation can be easily implemented in practice using variable frequency drives. The decision variables in the optimization problem are the total number of unloading time periods K and the sequence of unloading flow rates mui, where mui is the unloading flow rate in the ith time period. The total cost function to be minimized is

min(mui ,K ) ∑ [C Pi(m ui) + C Fi(m ui) + CCi(m ui)] + C D(K ) i=1

(16)

subject to K

∑ muiΔt = U

(17)

lb ≤ m ui ≤ ub

(18)

The above MINLP problem is solved as a series of NLPs for K = N + j, j = 0, 1, ..., K*, and for the initial specifications given in Table 4. The total optimal cost after solving the NLPs for K = 10 and K = 11 are shown in Figure 3. It can be concluded that solution of NLP for K = 10 gives the least total cost of $5,180, and hence gives the optimal scenario. The optimal unloading flow rate sequence (Figure 4a) and the total cost incurred in each time period are given in Table 5. The optimal scenario did not incur any demurrage, since the time taken to unload the parcel is equal to the stipulated time (K̅ = 10 h). When compared to the optimal solution obtained using a constant flow rate, there is more than 60% savings in cost obtained by varying the unloading flow rate. The BOG withdrawal rate for the optimal scenario is shown in Figure 4b. It can be seen that the BOG withdrawal rate exceeded the combined compressor capacity at various times during unloading and hence resulted in flaring. It can be inferred from Figure 4a and Figure 4b that when the flow rate is stepped up or stepped down, the BOG withdrawal rate also followed the same trend. This is mainly due to the fact

CT(m ui , i = 1,2...K , K ) K

=

i=1

∑ [CPi(mui) + CFi(mui) + CCi(mui)] + CD(K ) i=1

(15)

where the cost functions CPi, CFi, CCi denote the pumping, flaring, and compression cost for ith time period and are evaluated using the integral expressions given in section eq 10 over a period of Δt for the ith time period. The optimization problem becomes 13732



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flared. These costs can be calculated with the same expressions provided in section Table 2 but for the time during which the pipelines are precooled. Therefore, the total cost involved in strategy II is the total cost involved in precooling operation plus the total cost during unloading operation (CT). The decision variables involved in the optimization formulation are KI, KU, mu. The optimization formulation is given by

Table 5. Solution of NLP for K = 10 time interval (h)

flow rate (t/h)

CT (in US $)

0−1 1−2 2−3 3−4 4−5 5−6 6−7 7−8 8−9 9−10

325.65 344.77 312.19 333.70 561.91 625.08 624.16 624.16 624.16 624.16

88.90 671.38 630.53 1198.90 2248.90 84.54 67.58 63.82 63.15 62.81

min(mu , KI , K u) Cpre + C T

(19)

subject to

that stepping up or stepping down the unloading flow rate results in increase and decrease in inflow of energy into the tank, respectively, and hence affects the BOG withdrawal rate. Combined Precooling and Unloading Strategy (Strategy II). If the arrival of the ship is known well in advance, then there will be sufficient time to precool the pipeline, and the unloading operations can also be started soon after the ship’s arrival. In this case, the unloading operations can typically be completed without incurring demurrage costs. However, there are several instances when enough time is unavailable to precool the pipeline before ship’s arrival. Even in this case, if the option exists for varying the unloading flow rate, then unloading can start as soon as the ship’s arrival with a low unloading flow rate. This can be considered equivalent to precooling the pipeline using the ships’s parcel, which will typically be at a colder temperature. Once the pipeline has cooled sufficiently, the unloading flow rate can be increased to reduce demurrage costs. The optimal time varying unloading flow rate can be obtained as described in the preceding section. If the ship’s pump is not equipped with a variable frequency drive, then it is necessary to operate at a fixed unloading rate equal to the pump’s rated flow rate, which will be high. In this case, it is necessary to consider the option of continuing the precooling period (by using the recirculating pump at the terminal) even after the ship’s arrival, and delay the start of unloading operations to prevent excessive BOG generation and concomitant flaring. In this special case, it is necessary to consider the precooling and unloading strategy together. Although, it is possible to use a time varying flow rate during the precooling period, there is little incentive for this, since the pumping cost is negligible compared to other costs (compression, material flaring, and unloading). It may be noted that the recirculating pump capacity is generally an order of magnitude smaller than the ship’s pump. Furthermore, by using the maximum pumping rate during precooling, the pipeline can be cooled rapidly, thereby maximizing the time available for unloading. Thus, the only additional decision variable of interest when considering the precooling and unloading operations simultaneously is the additional time to be allocated for precooling the pipeline, after arrival of the ship. In the present case, the total time period during which the ship waits at the jetty is split into two parts KI and Ku, where KI is the number of time periods for which the precooling is continued at the maximum pumping flow rate after the ship arrives, and Ku is the number of time periods for which the parcel is unloaded. The total cost involved during a precooling operation (Cpre) involves the cost of pumping the material through the pipelines, cost of compressing the BOG that is generated during precooling, and flaring costs if any material is

K um uΔt = U

(20)

KI + KU ≥ N + 1

(21)

lb ≤ m u ≤ ub

(22)

KI ≥ 1

(23)

The above MINLP problem is solve for all feasible integral choices of KI and KU,KU = N,N + 1, ..., K*. The least value of CT is chosen to be the optimal solution. The above optimization problem is solved for the unloading scenario provided in Table 4. The optimal time for which the pipelines have to be precooled is 2 h (KIΔt), and the optimal time for which the parcel is unloaded is 14 h (KUΔt). Since the total time taken for unloading is 16 h (KΔt), the unloading operation incurred a demurrage of $12,000. The BOG withdrawal during unloading (Figure 5) exceeded the compressor capacity and resulted in

Figure 5. BOG withdrawal rate for constant unloading flow rate, strategy II.

flaring of material costing $2,908. The compressor operating costs and pumping costs during unloading is $774. The total cost involved during unloading is then $15,682. The total cost involved in precooling operation is $111.5 which includes the compressor operating costs and pumping costs during precooling. No material was flared during precooling operation. Therefore, the total cost involved in strategy II is $15,793. It can be observed that the total cost incurred during precooling operation is very less when compared to the costs involved during unloading. This is because precooling flow rates are low compared to unloading flow rates and hence resulted in zero flaring of material, low BOG generation, as well as low pumping costs.

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DISCUSSION The simulation optimization models using the constant unloading flow rate strategies (section Table 4, Figure 4) were computationally easier to solve, since it involved only fewer decision variables. Furthermore, the solution to these 13733



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constant unloading flow rate optimization models are practically easy to implement and provide a basis to compare with the solution obtained by solving a much more computationally intensive simulation optimization model which includes variations in the unloading flow rate as the decision variables. A cost comparison of all the strategies is shown in Figure 6. It is

*K C T* = min C T, K

(A.1)

C*T has two contributions C*ND which is the sum of pumping, compression, and flaring costs and cD(K* − N)Δt, the demurrage costs; that is, * + c D(K * − N )Δt C T* = C ND

(A.2)

Clearly, we have

*N C T* ≤ C T,

(A.3)

This can be rewritten as * + c D(K * − N )Δt ≤ C T, *N C ND

(A.4)

Since CND * is non-negative, we have * ≤ C T, * N − c D(K * − N )Δt 0 ≤ C ND

(A.5)

which provides the following a priori bound on K* as K* ≤ Figure 6. Total cost incurred in the optimal strategies.

* N + c DN Δt C T, cDΔt

(A.6)

Nomenclature

cd = demurrage charge per time period ce = cost of electric power consumption cf = cost of per kg of petroleum product CC = compressor operating cost CD = demurrage cost CF = cost incurred due to flaring of product CP = cost of pumping Cpre = operating costs during precooling Ccc = total compressor capacity of the terminal i = ith time period in the optimization model K̅ = total time for unloading K = total number of unloading time periods KI = number of time periods for which pipelines are precooled Ku = number of time periods for which the parcel is unloaded lb = lower bound L = length of the each unloading pipeline Mf = total amount of product that is flared mf = rate at which product is flared mc = rate at which product is compressed mv = rate of BOG withdrawal by compressors mw = product withdrawal rate mp = precooling flow rate m1 = mass flow rate in the pipeline UN1 m2 = mass flow rate in the pipeline UN2 mu = total unloading flow rate N̅ = stipulated time for unloading N = number of stipulated time periods for unloading P2/P1 = compression ratio t = time TT = temperature of tank contents ub = upper bound U = size of parcel to be unloaded Wc = work done by compressor

observed that by varying the unloading flow rate a significant reduction in overall costs can be achieved. A comparison of strategies in which a constant unloading flow rate is employed, extending the precooling even after the ship’s arrival, has reduced flaring costs but increased the demurrage costs. Although, for this example continuing the precooling operations even after ship’s arrival has not lowered overall costs, it is an option that has to be considered when a constant unloading flow rate constraint is imposed.

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CONCLUSIONS Optimal strategies to minimize the total cost of unloading petroleum products were anlayzed using a dynamic model for unloading operation. These optimal strategies were obtained by solving the MINLP formulations by converting them into series of NLPs. The results show that the use of a time varying unloading flow rate can result in substantial cost reduction. Although the present strategies were analyzed using a model for unloading involving only a single component, the cost considerations and the optimization formulations would be similar for unloading multicomponent mixtures, by using appropriate thermodynamic models. The proposed optimization strategies can be used to develop a decision support system for unloading petroleum products in storage terminals.

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APPENDIX A In this appendix, we formally show that an explicit upper bound on the optimal time period K* can be calculated a priori. Let N be the stipulated time period (minimum time period below which there is no demurrage cost) and let K, K ≥N be a chosen unloading time period. Assuming that the NLP can be solved to global optimality, let m*K be the vector of (sequence) optimal unloading flow rates during the time period of length K. Let CT,K * denote the optimal cost. CT,N * thus denotes the optimal cost incurred when the unloading is completed within the stipulated time period N which can be obtained by solving a NLP. Let K* denote the optimal time period over all time periods K, and CT* denote the corresponding optimal cost; that is,

Greek Symbols

ΔP = pressure drop in pipeline ΔT = temperature difference in liquid between the exit of pipe UN1 and UN2 Δt = time period

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ηc = compressor efficiency ηp = pump efficiency γ = heat capacity ratio ρl = density of liquid

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(15) Bonami, P.; Kinlinc, M.; Linderoth, J. Algorithms and Software for Convex Mixed Integer Nonlinear Programs; Technical Report No: 1664; Computer Sciences Department, University of WisconsinMadison: Madison, WI, 2009.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +91 (44) 2257-4177. Fax: +91 (44) 2257-4152. Notes

The authors declare no competing financial interest.

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REFERENCES

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Optimization of Unloading Operations in Petroleum Product Storage

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