An Overall Velocity Distribution and Optimization Method for Crude Oil

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An overall velocity distribution and optimization method for crude oil fouling mitigation in heat exchanger networks Yufei Wang, Ruonan Liu, Xiao Feng, and Shihui Zhan Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01569 • Publication Date (Web): 12 Sep 2017 Downloaded from http://pubs.acs.org on September 17, 2017

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Industrial & Engineering Chemistry Research

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An overall velocity distribution and optimization

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method for crude oil fouling mitigation in heat

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exchanger networks

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Yufei Wang,*,† Ruonan Liu,† Xiao Feng,‡ and Shihui Zhan†

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†

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Beijing 102249, China

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‡

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China

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ABSTRACT: Fouling problem can seriously affect heat exchanger network (HEN) efficiency

10

and its normal operation. From fouling threshold model, a higher velocity can effectively

11

mitigate fouling. There are two ways to change velocity in a heat exchanger. One is to adjust

12

flow rate distribution in parallel structure of heat exchangers, the other is to modify detailed heat

13

exchanger structure. However, there is no such research to consider both ways simultaneously to

14

mitigate fouling. Fluid velocity is also an important factor that related to heat transfer and

15

pressure drop. But this point is also ignored in most of work. In this paper, a new method is

16

proposed to promote the HEN performance with consideration of fouling, pressure drop and heat

17

transfer simultaneously by an overall optimization of velocity. The problem is analyzed in the

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entire operation time horizon, and it is divided into several time intervals to describe the dynamic

State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing),

School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049,

ACS Paragon Plus Environment

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nature of the fouling problem. All variables are established in each time interval, and adjacent

20

intervals are linked by the fouling resistance. Simulated Annealing (SA) is used in optimization

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method. A case study is illustrated to show the capacity of method. From results, it can be noted

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that the optimal solution reduces the utility consumption and total annual cost significantly.

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INTRODUCTION

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Heat integration technologies in HEN have been studied for several decades to satisfy energy

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saving in process industries. One commonly used method is Pinch Analysis, which combines

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process logistics via HEN to achieve heat recovery, and another method for HEN synthesis is

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mathematical programming1.

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Fouling in heat exchangers will severely affect the performance of a HEN, resulting in a

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reduction in energy recovery and operation stability. Since the concept of fouling was proposed

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for fouling mitigation by Ebert and Panchal2, fouling mitigation has been a research hotspot,

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especially for crude oil preheat train. Regular cleaning of fouled heat exchange units is a

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responsive mitigation strategy to minimize the losses due to fouling. Ishiyama et al.3 firstly

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proposed a new methodology to identify optimum cleaning cycles and optimal cleaning time

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between plant shutdowns by idealizing the foulant deposit as two layers, fresh and aged. In their

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work, they considered two available cleaning methods, chemical clean and mechanical clean,

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and introduced economic competition between the two methods. Pogiatzis et al.4, 5 successively

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established a nonlinear programming (NLP)-based approach and a mixed-integer nonlinear

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programming (MINLP) model to optimize the schedule of cleaning actions of a heat exchanger

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subject to fouling and aging, considering the combinations of chemical clean and mechanical

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clean. Smaïli et al.6, 7 extended the scheduling problem for a large continuously operating HEN,

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and a mixed-integer nonlinear programming (MINLP) model was introduced to optimize the


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cleaning schedule with the objective of minimizing the total operating cost. Aforementioned

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papers are focused on the cleaning schedule problems, but this method cannot mitigate fouling,

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and the interaction between fouling and network characteristics is ignored. More recently,

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optimization of cleaning cycle is further combined with more features of crude oil preheat train.

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Rodriguez and Smith8 put forward a new proactive method exploiting the effects of wall

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temperature on fouling to depress the occurrence of fouling deposition. The method combines

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the optimization of wall temperature with the optimal management of cleaning actions applied to

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an existing HEN, of which the results indicated higher energy savings, lower operational costs

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and fewer disturbances to the background process, compared with optimizing cleaning schemes

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only. The mean idea for optimization of wall temperature is to make more crisscross match to

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reduce wall temperature, although it reduces fouling, it also reduces heat recovery when all heat

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exchangers are clean. Ishiyama et al. combined the desalter inlet temperature control9 with the

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cleaning schedule optimization to aid fouling management by using hot stream bypassing. They

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considered hydraulic behavior10 in their continuous paper, where they developed a highly

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flexible preheat train simulator in MATLABTM/ExcelTM to accommodate variable throughput

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in scheduling the cleaning operations. Biyanto et al.11 developed an improved optimization

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problem for the cleaning schedule of heat exchangers in a crude preheat train considering the

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hydraulic impact of fouling through the additional pressure drops and proposed recent stochastic

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optimization methods to solve the problem.

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The utilization of heat transfer enhancement devices in the HEN synthesis is another effective

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strategy for fouling mitigation. Wang and Smith12 proposed a method based on simulated

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annealing to solve HEN retrofit problems on the basis of heat-transfer enhancement by

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considering fouling. The method applied to HEN retrofit under fouling was optimized with


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different kinds of crude oils. Pan et al.13 developed a new mixed-integer linear programming

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(MILP)-based iteration method for HEN retrofit considering fouling effects by implementing

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tube-side intensification. They extended the work for more practical problems in a retrofitted

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HEN within the operating period, addressing fouling effects and pressure drop constraints in

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their continuous work14. In addition, some researchers have found that sol-gel coating can be

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used for fouling mitigation in heat exchangers, which focus on the material and the interaction

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between crude oil fouling and network characteristics is not considered15, 16.

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Several researchers found that optimizing flow velocity can be applied to fouling mitigation.

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Assis et al.17 developed a constrained nonlinear programming formulation for fouling

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management considering the hydraulic behavior of a HEN. In their work, velocity is

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redistributed through optimizing split ratio of parallel structure in HEN design. In another work,

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the work is further extended to consider dynamic nature of fouling18. In the work of Ishiyama et

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al.19, flow rates optimization is incorporated with cleaning of parallel heat exchangers. The

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thermo-hydraulic effects of fouling is discussed in their following work20. Wang et al.21 proposed

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a velocity optimization method to mitigate fouling of heat exchangers over the entire operating

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cycle through optimizing the velocity distribution with the consideration of heat transfer and

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pressure drop simultaneously. In this work, velocity is no longer changed through flow rate

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redistribution in parallel structure but by changing detailed design of heat exchangers. By doing

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this, velocity in heat exchangers in series structure can be also optimized. Tian et al.22 further

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extended fouling mitigation approach by optimizing velocity and cleaning schedule

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simultaneously.

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Based on the literature review, velocity is an important factor that can mitigate fouling. It can

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be changed through both adjusting flow rate ratio in parallel structure and modifying detailed


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design of heat exchangers. Adjusting flow rate ratio in parallel structure is a very easy and

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economical way to be operated, but with an increased flow rate in one branch, flow rate in the

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other branch will be reduced, leading to a lower heat transfer coefficient and anti-fouling

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capacity. Additionally, it can be only applied in parallel structure. For modifying detailed design

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of heat exchangers, it can be applied in both series and parallel structure, and the velocity change

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in one heat exchanger will not affect the velocity in other heat exchangers. But this method leads

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to higher pressure drop, and in retrofit, it is expensive and sometime not easy to be implemented.

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The focus of this paper is to propose a method to promote refinery HEN performance by

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optimizing velocity through both ways aforementioned with comprehensive considerations of

97

fouling, heat transfer and pressure drop. Split ratio adjustment is considered for both hot and cold

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stream. Fouling, heat transfer and pressure drop are all correlated to velocity. To describe

99

dynamic nature of fouling, the investigated time horizon is divided into several intervals and all

100

relevant parameters are recalculated at each interval using the connections with fouling

101

resistance. The objective function is to minimize total annual cost (TAC) including hot utility

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cost, pumping cost and detailed structure modification cost.

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MODEL FORMULATIONS

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Fouling Rate Model. The new approach proposed in this paper considers the effects of fouling

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in tube-side of heat exchangers on HENs’ performance. Polley fouling threshold model is used to

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describe the impact of the variation of the operating variables on fouling rate, which is presented

107

in eq 123. The fouling rate of heat exchanger can not be less than 0.

108

   -E  dRf = max α Re−0.8 Pr -0.33exp  - γ Re0.8 , 0  RT  dt    g w

(1)


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where Rf is fouling resistance, Re and Pr are Reynolds number and Prandtl number, α and γ are

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model parameters, E is activation energy, R is gas constant, and Tw represents wall temperature

111

of heat exchanger.

112

As deposition layer accumulates with time, fouling problem is a dynamic optimization

113

problem. To handle the dynamic nature of fouling, the investigated time is divided into several

114

time intervals, as shown in eq 2. Adjacent intervals are linked by the fouling resistance, which

115

can be calculated by eq 3. τ=

116

t m

(2)

Rfn+1 = Rfn + (dRf / dt)n ⋅τ

117

(3)

118

where τ is time interval width, t is investigated operation period, m is number of time interval, n

119

is the index for time interval.

120

Fouling rate in each time interval is assumed as constant, all variables are recalculated in each

121

time interval. More details about the relationship between fouling resistance and other variables

122

can be found in the work presented by Zhan et al21.

123 124

Heat Exchanger Equations. The convective heat transfer coefficient (HTC) for tube side is changing with time during the operational period, which is calculated by eq 4-618, 24.

125

The shell side convective heat transfer coefficient is assumed constant along the HEN, because

126

streams prone to fouling normally flow through tube side. Eq 7 is given to calculate the overall

127

heat transfer coefficient K.

128

hT = hT ,n=0 (vn / vn=0 )0.8

(4)

0.8

0.4

129

λ  d v ρ   µ Cp  hT ,n=0 = 0.023  n=0 n=0   d µ   λ 

130

v n = v n = 0  d / ( d − 2δ ex , n −1 

2

(5)

(6)


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−1

1 1  K =  + + RfT + RfS   hS hT 

131

Tw = Tcbulk +

132

hS × (Thbulk − Tcbulk ) hS + hT

(7)

(8)

133

where hT and hS are convective heat transfer coefficient for tube and shell side of heat exchanger,

134

d is the inner diameter (ID) of tubes, λ is fluid heat conductivity, v is fluid velocity of tube side, ρ

135

is fluid density, µ is fluid viscosity, δ is the thickness of foulant layer, which can be calculated on

136

the basis of fouling rate, RfS is the shell side fouling resistance, subscript n=0 means the starting

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point of operation time period, Tcbulk and Thbulk are bulk temperature of cold and hot streams,

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subscripts S and T represent shell side and tube side.

139

For parallel heat exchangers, the initial velocity vn=0 of tube side is co-determined by the

140

detailed design modification of the heat exchanger and the mass flow rate in the optimization, as

141

shown in eq 9. The shell side convective heat transfer coefficient for parallel heat exchanger is

142

related to mass flow rate, presented in eq 10.

143

vn=0 = vmodify (MT ,optimized / MT ,base )

(9)

144

hS = hS ,base (M S ,optimized / M S ,base )0.6

(10)

145

where vmodify is the velocity of heat exchanger considering only the detailed design modification,

146

M is the mass flow rate, subscripts base and optimized represent base case before optimization

147

and optimized case.

148

P-NTU method is used to calculate heat transfer of heat exchanger in this work, which is

149

always directed to one stream, without depending on the minimum heat capacity of stream. The

150

heat exchangers considered in this paper present counter flow with single shell pass and two tube

151

passes, the corresponding P-NTU expression is shown as eq 11. And the related stream by the

152

method is cold stream in this work.


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 1 + exp  − NTU n (1 + Rn 2 )1/ 2   2 1/ 2 P = 2 1 + Rn + (1 + Rn ) ×  1 − exp  − NTU n (1 + Rn2 )1/ 2   

153

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-1

(11)

154

where P is the thermal effectiveness, R is heat capacity ratio of cold stream and hot stream and

155

NTU is heat transfer unit, which are described in eq 12-14.

Tcout − Tcin Thin − Tcin

156

P=

157

Rn =

158

NTU n =

(12)

M c , n Cpc , n

(13)

M h , n Cph , n

Kn A M c ,nCpc, n

(14)

159

where Th and Tc are respectively temperature of hot streams and cold streams, the superscript in

160

and out are inlet and outlet, A is heat transfer area of a heat exchanger, Cp is the specific heat

161

capacity of a stream, subscripts c and h are cold and hot streams.

162

Pressure Drop. As the deposition of fouling in tube-side, the actual fluid flowing area

163

constantly decreases, which promotes the fluid velocity and results in higher pressure drop. The

164

total pressure drop for the tube side ∆Pf of a heat exchanger consisting of three parts can be

165

calculated by eq 15.

∆Pfex,n=0 = ∆Psex,n=0 + ∆Plex,n=0 + ∆Pnex,n=0

166 167

where ∆Psex,n ,

168

resistance. The three resistances can be calculated by eqs 16-1925.

(15)

∆Plex,n and ∆Pnex,n represent straight pipe resistance, local resistance, and nozzle

L ρ vex,n=0 ∆Psex,n=0 = ξex,n=0 N d 2 2

169 170

171

ξex ,n=0 = 0.01227 + ∆Plex,n =0 = ζ

0.7543 0.38 Reex,n=0

ρ vex2 ,n=0 2

N

(16)

(17)

(18)


8

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∆Pnex,n=0 = 1.5 ×

172

ρvex2 ,n=0

(19)

2

173

where ξ is friction coefficient, which can be calculated by eq 17 proposed by Gu26. Subscript ex

174

means heat exchanger, L is the length of tubes, N is the number of tube passes, and ζ in eq 18 is

175

the local resistance coefficient, it values 3~4 for multiple tube passes, while it equals to 2 for

176

single tube pass.

177 178

Once the initial pressure drop is known, change of pressure drop under fouling over the investigated time can be obtained from the correlation shown in eq 20.

∆Pfex,n

179

∆Pf ex,n=0

 δ  = 1 − ex,n  d  

−5

(20)

180

In this paper, pipeline pressure drop is not considered, thus, the total pressure drop ∆PT for a

181

HEN is the sum of pressure drop of heat exchangers in series and pressure drop of parallel heat

182

exchangers, shown in eq 21.

183 184

∆PT = ∑ ∆Pfex,series + ∑ ∆PT , parallel ∆PT , parallel = max {∆PT ,branch ,1 , ∆PT ,branch ,2 ,L , ∆PT ,branch ,i }

(21) (22)

185

where ∆Pfex,series is the pressure drop of a heat exchanger in series, ∆PT,parallel represents the

186

pressure drop of parallel heat exchangers, which is depended on which branch gets the maximal

187

pressure drop, as shown in eq 22, where ∆PT,branch,i is the accumulation of pressure drop for all

188

heat exchanger on branch i. For branches with lower pressure drops, throttle valves will be

189

installed in these branches to make pressure drops of all branches are equal.

190

Optimization Constraints. The main optimization constraints are composed of bounds for

191

velocity in tube side of a heat exchanger, bounds for mass flow rate of each branch, mass and

192

energy balances, heat exchanger equations and fouling rate model equations. To keep heat

193

exchangers working away from vibration and abrasion problems, fluid velocity must be limited


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to the lower and upper bounds, which is represented by eq 23. Generally, the maximum flow

195

velocity in a tube and shell heat exchanger can reach 3 m/s, while the minimum value cannot be

196

less than 0.5 m/s, so the limitations for velocity variations are set to be 0.5~3 m/s. The

197

constraints for mass flow rate of each branch is shown in eq 24.

198

vLB ≤ v ≤ vUB

199

MLB ≤ Mbranch ≤ MUB

200

(23) (24)

where the subscripts UB and LB represent the upper and lower bound.

201

The constraints for inlet and outlet temperatures of cold and hot streams of every heat

202

exchanger are given by eq 25-28. The outlet temperature of cold streams in hot utility heat

203

exchanger must be equal to target temperature of cold streams, and the outlet temperature of hot

204

streams in cold utility heat exchanger must be equal to target temperature of hot streams, as

205

shown in eq 29-30.

206

Tcout ≤ Thin ≤ Thsupply

(25)

207

Thtarget ≤ Thout ≤ Thin

(26)

208

Tcsupply ≤ Tcin ≤ Thout

(27)

209

Tcin ≤ Tcout ≤ Tctarget

(28)

210

Tcexout,hu = Tctarget

(29)

211

Thexout,cu = Thtarget

(30)

212

where subscripts supply and target represent the supply temperature and target temperature of

213

the streams, subscripts ex,hu and ex,cu are hot utility and cold utility heat exchangers.

214 215 216

Eq 31-34 show the mass balances and energy balances for splitters and mixers.

∑M = ∑M ∑M = ∑M in SP

in MX

out SP

(31)

out MX

(32)


10

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∑(MCpT )

in SP

217

∑(MCpT )

in MX

218 219

= ∑(MCpT )out SP

= ∑(MCpT )out MX

(33) (34)

where subscripts SP represents the splitter and MX represents the mixer.

220

Objective Function. The objective function in this work is to minimize the total annual cost,

221

which is the sum of energy cost, power cost (electricity charges for pumps), equipment capital

222

cost and detailed structure modification cost for heat exchangers, as shown in eq 35.

obj = CQ + Cpower + Cpump + Cex,modify

223

(35)

224

where CQ, Cpower, Cpump, and Cmodify are annual cost for hot and cold utility, power, pump

225

investment and detailed structure modification.

226 227

Eq 36-37 are the calculations of hot utility Qhu and cold utility Qcu respectively, the price of utility CQ can be calculated by eq 38. Qhu =

228

∑  M Cp × (Tc c

ex , hu

Qcu =

229

∑  M

ex , cu

h

− Tcexin , hu ) 

(36)

Cph × (Thexout, cu − Thexin, cu ) 

(37)

c

out ex , hu

CQ = ∑[ hu × Qhu + cu × Qcu ]

230

(38)

t

231

where subscripts ex,hu and ex,cu represent hot and cold utility heat exchangers located at the end

232

of cold and hot streams, hu and cu represent the unit price of hot utility and cold utility.

233 234

Power cost is related to volume flow rate of fluid and pressure drop, which can be calculated by eq 3927.  V × ∆PT  C power = ∑  pc × η  t 

235

(39)

236

where pc is the unit electricity cost, η represents the pump efficiency, V is volumetric flow rate

237

for a stream.


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Page 12 of 29

238

Pump investment meets exponential function of the flow rate and pressure drop, annualized

239

pump capital cost Cpump is calculated by eq 4027. Heat exchanger annualized capital cost Cex is

240

related to its heat exchange area and device lifetime, which can be calculated by eq 41. Eq 42 is

241

used to calculate detailed structure modification cost Cex,modify for optimized cases.

242

C pump =

2.365 + 0.151 × (V × ∆PT , n = m ) 0.86 Yrpump

Cex =

243

a + bA β Yrex

Cex,modify = ∑Cex ⋅θ

244

(40)

(41)

(42)

ex

245

where Yrpump is pump lifetime, subscript n=m indicates the last time interval of the operational

246

time horizon, Yrex is lifetime of heat exchanger, θ is structure modification cost coefficient, and

247

a, b and c are model parameters.

248

OPTIMIZATION ALGORITHM

249

The proposed method is to minimize total annual cost by overall velocity distribution

250

optimization to simultaneously correlate fouling, heat transfer and pressure drop of heat

251

exchangers. Accounting for the highly nonlinear property of fouling problems, simulated

252

annealing (SA) algorithm is used to solve the optimization problem in this paper. The proposed

253

method can be used for both retrofit and design problems.

254

Figure 1 presents the flowchart for HEN optimization of the proposed method. The

255

optimization variables in this method are velocity of heat exchangers and the split ratio of each

256

splitter for both cold and hot streams. The former refers to changing velocity through detailed

257

design modification of heat exchangers. Obviously, the velocities for heat exchangers in series

258

can be only changed by detailed design modification, while both split ratios optimization and

259

detailed design modification are considered for parallel heat exchangers. These two control


12

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260

variables jointly determine the initial velocity distribution, which can be seen from Figure 1. The

261

objective function is to minimize annual total cost with trade-off between fouling, heat transfer

262

and pressure drop. Therefore, the optimal velocity distribution can be eventually obtained for

263

each heat exchanger by simultaneously adjusting fluid velocity in heat exchanger and split ratio

264

in splitters when objective function reaches the minimum value. Input the original HEN in base case

Simulated annealing algorithm (SA) Randomly selected by SA

Randomly changes velocity distribution (detail structure modification)

Randomly changes the split ratios

The constraints of velocity are satisfied

The constraints of split ratio are satisfied

NO

NO

YES

YES

Calculate detail structure modification cost

Synthesis the HEN in the first time interval, n=1 Calculate fouling resistance, utility cost and power cost in time interval n Calculate velocity distribution in next time interval, n=n+1 If n >the number of investigated time interval ?

NO

YES Calculate pump investment cost and the objective function NO

The constraints in SA are satisfied YES Output the optimization results

265 266

Figure 1. Flowchart for HEN optimization.

267

CASE STUDY


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268

Basic Data for The Crude Oil Preheat Train. This section illustrates the application of the

269

proposed optimization approach by using a simplified crude oil HEN, as shown in Figure 2. The

270

case is based on the work presented by Smaïli et al.7, which is composed of nine shell-and-tube

271

heat exchangers, four splitters and four mixers. The HEN can be considered as two sections. The

272

section upstream the flash contains three heat exchangers in series and the section downstream

273

the flash contains six heat exchangers aligned equally in two parallel branches. The temperature

274

change in flash is neglected, while there is a loss of 5 ~10% in flow rate7. In Figure 2, SP is the

275

index for splitter and MX is the index for mixer. The stream split ratios of base case for all

276

splitters are equal to 0.5 over the whole operational period7. gas E4

E5

E6

Flash

Crude Oil

MX-H1

MX-H2

H6

MX-H3 H4

H5

Branch A E2A

E1A

E3A

MX-C SP-C

FIT

Furnace

Branch B

SP-H1 H1

277 278

E3B

E2B

E1B

SP-H2 H2

SP-H3 H3

Figure 2. Flowsheet of crude oil preheat train for case study.

279

The mass flow rates, temperatures and heat capacities of the process streams are presented in

280

Table 1. The prefix H represents hot streams. Crude oil is the only cold stream in this case. The

281

heat capacity of the hot streams are assumed constant along the HEN, while the heat capacity of

282

crude oil upstream the flash is 2.3 kJ/(kg K) and crude downstream the flash has a heat capacity


14

Page 15 of 29

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283

of 2.4 kJ/(kg K). The other physical properties of crude oil are displayed in Table 2. The heat

284

capacity and other physical properties of process streams are assumed constants along the HEN.

285

Table 1. Streams data

286

287

Streams

Mass flow rate (kg/s)

Specific heat (kJ/(kg K))

Tsupply (°C)

Ttarget (°C)

H1

142.0

2.8

327

200

H2

127.0

2.9

292

200

H3

127.5

2.8

282

180

H4

63.2

2.9

251

150

H5

68.5

2.6

233

120

H6

70.9

2.8

205

100

Crude

95

2.3/2.4

135

385

Table 2. Physical properties of crude Density (kg·m-3)

Viscosity (Pa·s)

Thermal conductivity (W·m-1 K-1)

800

1×10-3

1×10-4

Table 3. Heat exchangers data Exchangers

ID (mm)

Area (m2)

Heat duty (kW)

E1A

15.4

310

E1B

15.4

E2A

Initial velocity (m/s)

Shell side HTC

Base case

Optimized case

(kW/m2/K)

2648

1.5

2.84

0.451

360

2673

1.4

2.94

0.451

15.4

300

2388

1.4

2.12

0.523

E2B

15.4

350

2634

1.2

1.77

0.523

E3A

15.4

200

2400

1.1

1.55

0.482

E3B

15.4

250

2787

1.1

1.66

0.482

E4

15.4

600

5642

1.1

1.10

0.590

E5

15.4

300

5034

2.4

0.82

0.653

E6

15.4

400

5872

1.8

0.58

0.653

288

Table 3 displayed the other detailed data of the heat exchangers. The size of heat exchangers in

289

Branch B are larger than heat exchangers in Branch A. The heat duties of heat exchangers in

290

Table 3 are the average heat duties during the operational time period. Fouling in heat

291

exchangers is mainly due to deposition of crude oil, and crude always flows in the tube side of

292

heat exchangers in this case. So only the tube side fouling is considered in this case, which is

293

calculated by Polley’s model. In Polley’s model, the values of parameters are the same for all


15


294

heat exchangers in this case study: α = 8×105 m2·K·kW-1·h-1, E= 55 kJ/mol, γ = 2×10-9

295

m2·K·kW-1·h-1. All heat exchangers are clean at the beginning of the operational time. The

296

thermal conductivity of fouling resistance is 0.5 W·m-1 K-1. Fouling resistances in shell side are

297

assumed constants along the HEN in the investigated time period. Several optimizations are

298

carried out under different values of detailed structure modification cost coefficient to determine

299

the optimal value. The detailed structure modification cost coefficient for heat exchangers is set

300

to be 0.02 through comparing the effect of different values on the optimization results and

301

referring to the practical cost.

300

E2B E3B E3A

250

Temperature(°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 29

E1B E1A

Threshold Fouling Curve

E2A

E4 200

E5 E6

150

100

50

0 0

1

2

3

4

5

Velocity(m/s)

302 303

Figure 3. Fouling threshold curve and exchangers condition in base case.

304

Figure 3 presents conditions for all heat exchangers in the base case compared with the

305

threshold fouling condition. The fouling threshold curve is corresponding to the wall temperature

306

and velocity, which can be determined at condition when fouling rate is equal to zero. Fouling

307

condition of heat exchangers can be judged from the comparison of positions for the

308

corresponding temperature and velocity points with the threshold fouling curve. Fouling is going

309

to develop when the position is above curve, and fouling will not occur and the heat exchanger


16

Page 17 of 29

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310

surface will remain clean during the operation time when the position is below the curve. Higher

311

wall temperature and lower velocity positively lead to more fouling deposition formed in the

312

operation period. In Figure 3, the points are corresponding to the conditions for the nine heat

313

exchangers in the base case, and it can be seen that all the heat exchangers are above the fouling

314

threshold curve. Moreover, heat exchanger E1A and E1B are far from the threshold curve,

315

indicating that these two heat exchangers will be severely fouled. The reason is that E1A and

316

E1B are located at the hot end of cold stream, the wall temperatures are high and the initial

317

velocities are low. Meanwhile, heat exchanger E5 and E6 are closed to the threshold fouling

318

curve, because both heat exchangers are far from the hot end of the preheat train, the wall

319

temperature for both heat exchangers are too low to lead to severe fouling.

320

Optimization Results. The optimization results of stream split ratios over the whole

321

operational period are described in Table 4. The split fractions are based on the streams directed

322

to the heat exchangers in Branch A. For example, the split ratio for SP-H1 is 0.466, representing

323

that 46.6% of the mass flow rate of hot stream H1 is distributed to the heat exchanger E1A at

324

Branch A. As we can see that the values of split ratio for all splitters after optimization decrease

325

compared with the base case. For crude oil, the split ratio is mainly depended on the difference

326

of fouling resistances and heat duty between the parallel branches. Although all the heat

327

exchangers in this case are clean at the initial time, heat exchangers present different fouling

328

rates due to different velocity and wall temperature. The average fouling resistances of Branch A

329

and Branch B during the investigated time horizon are 4.91 m2K/kW and 5.29 m2K/kW. This

330

indicates that Branch B is easier to get fouled, so more mass flow rate is required to increase

331

velocity for fouling mitigation. Moreover, the increase in mass flow rate can positively affects

332

the convective heat transfer coefficient for both shell and tube side besides mitigating fouling.


17


333

The average heat duty of Branch B is higher than that of Branch A in base case, which indicates

334

that with same increasing percentage of heat transfer coefficient, the increase of heat duty in

335

Branch B is larger than that of Branch A.

336

Table 4. Stream split ratio in base case and optimized case Splitters

SP-C

SP-H1

SP-H2

SP-H3

Split ratio (base case)

0.5

0.5

0.5

0.5

Split ratio (optimized case)

0.475

0.473

0.493

0.468

3.5

base case optimized case detailed design modification

3.0

Initial Velocity(m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

2.5 2.0 1.5 1.0 0.5 0.0 E6

E5

E4

E3A

E3B

E2A

E2B

E1A

E1B

Exchangers

337 338

Figure 4. Initial velocity distribution in base case and optimized case.

339

Figure 4 presents the initial crude oil velocity distribution in base case and optimized case. It

340

can be seen from the figure, for heat exchangers upstream the flash, the initial velocities of heat

341

exchangers E6 and E5 after optimization decrease sharply. This is because E6 and E5 are far

342

from fouling region, and no severe fouling is going to occur in E6 and E5 even with low

343

velocities. Thus, the velocities are decreased to save pump capacity for increasing velocity in

344

other heat exchangers prone to fouling. It is needed to emphasize that velocity have to be kept at

345

a reasonable value to maintain heat transfer efficiency. For E4, the initial velocity in optimized

346

case is the same as that in base case mainly because it is near optimal value in base case when


18

Page 19 of 29

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347

considering trade-off between fouling, pressure drop and heat transfer. For parallel heat

348

exchangers downstream the flash, velocities for heat exchangers after flash are increased not

349

only by changing the split ratios, but also detailed structure modification of heat exchangers,

350

because the wall temperature is high, velocity tends to be high to avoid fast fouling after

351

optimization, especially for E1A and E1B (with the highest wall temperature). The case is a

352

simplified preheat train, in industrial case, the velocity of heat exchanger with low wall

353

temperature will reduce to save pump power.

354

exchangers E3A to E1B represents the optimal velocity distribution with detailed structure

355

modification only (cold stream split ratio is set to be 0.5). The difference between the values of

356

the second columns and the third columns is helpful for us to see clearly the contribution of split

357

fractions and detailed structure modification to the initial velocity of parallel heat exchangers.

358

For example, the second columns are generally higher than the third columns for heat exchangers

359

in Branch B due to the increase of the mass flow rate of crude oil in Branch B after optimization.

360

It is worth noting that the initial velocities of heat exchangers in Branch A are improved after

361

optimization even with a reduction in crude oil split fraction, which offset the defect of method

362

only considering the optimization of split ratio in parallel structure of heat exchangers.

In Figure 4, the third column for parallel heat


19


7000

base case(X) base case(average)

6000

optimized case(X ) optimized case(average)

5000

Heat duty(kW)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

4000 3000 2000 1000 0

E6

E5

E4

E3A

E3B

E2A

E2B

E1A

E1B

Exchangers

363 364

Figure 5. Initial and average heat duty of heat exchangers in base and optimized case.

365

Figure 5 shows the initial and average heat duty of heat exchangers in both base case and

366

optimized case. The index X represents the difference between initial and average heat duty of

367

every heat exchanger. Heat duty reflects heat recovery and it is directly related to the cost of

368

utility, which is the major component of total cost. In Figure 5, both initial and average heat duty

369

of E6 and E5 in optimized case decrease compared with base case owing to the reduction in

370

velocities. For E4, both initial and average heat duty increase after optimization even without

371

change in velocity. This is because the up and down streams relation between heat exchangers.

372

The inlet temperature of crude oil in E4 is dropped due to the reduction of heat duty in E6 and

373

E5, so that the heat transfer driving force in E4 is increased to have a larger heat duty. The

374

reduction in duty of E1A can be also explained by the up and down streams relation between

375

heat exchangers. In addition, the decrease in flow rate in branch A makes temperature for both

376

hot and cold streams change more significantly, result in a reduction of heat transfer driving

377

force. On the contrary, the increase in flow rate of branch B makes the increase in heat duty of

378

heat exchangers in branch B after optimization larger than that in branch A.


20

Page 21 of 29

379

It is known that the heat duty of a heat exchanger decreases with time due to fouling in the

380

operational period, so the difference (X) between initial and average heat duty can represent the

381

severity of fouling in heat exchangers. It can be seen that the difference between initial and

382

average heat duty of the parallel heat exchangers decrease after optimization due to the fouling

383

mitigation.

384

Figure 6 presents the fouling rates of E6 and E1B during the investigated time both in base and

385

optimized case. It can be seen in Figure 6 that the fouling rate of E1B is much higher than that of

386

E6, and it decreases rapidly with time. This is because the increase of deposition of foulant leads

387

to a decline of the wall temperature and an increase in velocity, and both aspects positively

388

decrease the fouling rate. It can be predicted that the fouling rate will eventually tend to be a

389

fixed value if the investigated period is long enough. It can be also seen that the fouling rate of

390

E1B after optimization presents an apparent reduction mainly due to the increase in velocity of

391

E1B. On the contrary, the fouling rate of E6 in both case are almost horizontal and on the verge

392

of zero, which indicates that fouling problem is almost not going to occur in E6.

E6-base E1B-base E6-optimized E1B-optimized

0.0010

Fouling rate(m2•K•kW-1•h-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0008

0.0006

0.0004

0.0002

0.0000 0

1

2

3

4

5

6

7

8

9

10

11

12

Time (months)

393 394

Figure 6. Fouling rates of E6 and E1A both in base and optimized case


21


310

base case optimized case

305 300

Temperature(°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 29

295 290 285 280 275 270 0

1

2

3

4

5

6

7

8

9

10

11

12

Time(months)

395 396

Figure 7. Comparison of FIT in base case and optimized case

397

Furnace inlet temperature (FIT) profile is an important indicator for the performance of crude

398

oil preheat train, which can estimate the fuel consumption to meet target temperature of crude

399

oil. Figure 7 shows the comparison of FIT profile between base case and optimized case over the

400

operational period (12 months). It can be seen that the trend of two curves are similar, which are

401

decrease with time due to fouling. The decline rate of FIT profile also gradually decrease with

402

time, which can be explained based on the interaction with fouling rates of heat exchangers. FIT

403

decreases from 304.5 °C to 281.2 °C by 23.3 °C during the operational period in optimized

404

case, while FIT changing from 302.2 °C to 273.9 °C by 28.3 °C before optimization. The

405

comparison of FIT profile clearly indicates a better HEN performance and appreciable energy

406

savings after optimization.

407

Table 5. Cost related data Items

Value

Power cost ($/kW• y)

400

Cold utility ($/kW• y)

11.8


22

Page 23 of 29

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Hot utility ($/kW• y)

118

Pump efficiency (%)

70

408 409

Table 5 presents the cost related data. Utility cost used in this paper refers to the work of

410

Panjeshahi and Tahouni28 , power charge refers to current price. Table 6 presents the annualized

411

cost in base case, optimized case, and two reference cases. For the optimized case, compared

412

with the annualized cost in base case, the power cost and cold utility cost after optimization

413

change slightly, but utility cost decreases sharply by 193.03 k$/y. The lifetime for all pumps and

414

heat exchangers is set to be 5 years. The total annual cost is reduced from 4677.87 k$/y to

415

4535.00 k$/y, saving about 142.87 k$/y. Two reference cases are performed to compare the

416

optimization results. Reference case 1 is based on the method proposed by Assis et al.17, which

417

choose stream split ratios both for cold and hot streams as optimization variables and the hot

418

utility cost is treated as objective function without considering the cost for power and pump.

419

From the results, it can be seen that the total annual cost has increased when compared to the

420

base case even with a reduction in the utility cost. This is because the changes in mass flow rate

421

of the two parallel branches can cause very high pressure drop which is not considered in this

422

case. Reference case 2 is based on the work of Wang et al.21, which mitigates fouling by

423

optimizing velocity only through modifying detailed design of heat exchangers, saving about

424

128.44 k$/y compared with base case as shown in Table 6. Considering overall velocity

425

distribution, the proposed method in this work has a higher economic efficiency.

426

Table 6. Economic efficiency in different case Base

Optimized

Reference

Reference

case

case

case1

case2

Utility cost(k$/y)

4423.51

4230.48

4410.20

4266.35

Power cost(k$/y)

16.73

19.08

20.62

17.48

Pump capital cost(k$/y)

237.62

272.00

282.95

252.15

Items


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

427 428

Page 24 of 29

Detailed structure modification cost(k$/y)

0

13.44

0

13.44

Total cost(k$/y)

4677.87

4535.00

4713.77

4549.43

CONCLUSIONS

429

This paper presents a method to mitigate fouling in crude oil preheat train by optimizing

430

overall velocity distribution. Accounting for that fluid velocity can correlate fouling, heat

431

transfer and pressure drop, the new method can make design for the HEN more practical

432

compared with traditional optimization of flow rate distribution. In this work, velocity can be

433

changed through detailed structure modification of heat exchangers and adjusting spilt ratio of

434

splitters. A simplified crude oil pre-heat train is used to illustrate the application of the proposed

435

method. From the analysis for the optimization results, it is found out that the optimal initial

436

velocity distribution is apparently affected by the initial fouling behavior of each heat exchanger,

437

which is related to the detailed design modification of heat exchanger and the crude split

438

fraction. The optimal split ratios are determined by the difference of fouling resistance and heat

439

duty between the parallel branches. The optimization results show that the annual total cost is

440

decreased from 4677.87 k$/y to 4535.00 k$/y through optimizing overall velocity distribution.

441

Meanwhile, optimization results of two reference cases mitigating fouling respectively by

442

optimizing split fractions and velocity are presented to prove the practicability of proposed

443

method. Reference case 1 considers hot utility cost as objective function ignoring the effects of

444

pressure drop. Hence, the total annual cost is more than that in base case. The savings of

445

reference case 2 is less than the optimized case. The whole investigated time horizon is divided

446

into 12 time intervals to describe the dynamic nature of fouling for all case. Fouling rate in each

447

interval is treated in steady state, all related variables are recalculated in each interval and

448

adjacent intervals are linked through fouling resistance.


24

Page 25 of 29

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449

AUTHOR INFORMATION

450

Corresponding Author

451

*E-mail: [email protected]

452

Notes

453

The authors declare no competing financial interest.

454

ACKNOWLEDGMENTS

455

Financial support from the National Natural Science Foundation of China under Grant No.

456

21306228 and Science Foundation of China University of Petroleum, Beijing (2462017BJB03)

457

are gratefully acknowledged.

458

NOMENCLATURE a A b c cu C Cp d ex E h hu hS hT K L LB m M MX n N NTU obj pc P

= = = = = = = = = = = = = = = = = = = = = = = = = =

equation parameter heat exchange area, m2 equation parameter index for cold streams cold utility cost coefficient, $/(kW y) cost, $/(kW y) specific heat capacity of stream, kJ/(kg K) inner diameter of tubes, m index for heat exchanger activation energy, kJ/mol index for hot streams hot utility cost coefficient, $/(kW y) shell side convective heat transfer coefficient, kW/(m2 K) tube side convective heat transfer coefficient, kW/(m2 K) overall heat transfer coefficient, kW/(m2 K) tube length, m

lower bound number of time interval mass flow rate, kg/s index for mixer index for time interval tube passes heat transfer unit objective function, k$/y unit electricity cost, $/(kW y) thermal effectiveness


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Pr Q R Re Rf Rg S SP t T Tc Th Tw UB v V Yr

= = = = = = = = = = = = = = = = =

Page 26 of 29

Prandtl number index for utility consumption, kW heat capacity ratio of cold stream and hot stream Reynolds number fouling resistance, m2•K/kW gas constant, kJ/(mol K) index for shell side index for splitter Time index for tube side cold stream temperature, K hot stream temperature, K wall temperature, K

upper bound fluid velocity, m/s volume flow rate, m3/s lifetime of equipment, y

Greek symbols α β γ τ δ ξ ζ ρ η µ θ

△Pf △Pl △Pn △Ps △P T

= = = = = = = = = = = = = = = =

model parameter, m2•K/(kW•h) model parameter model parameter, m2•K/(kW•h) time interval length thickness of foulant layer, m friction coefficient local resistance coefficient fluid density, kg/m3 pump efficiency Fluid viscosity, Pa·s structure modification cost coefficient total pressure drop for a heat exchanger, kPa local resistance, kPa connection pipe resistance, kPa straight pipe resistance, kPa total pressure drop for a HEN, kPa

459 460

REFERENCE

461 462 463 464 465 466 467 468 469 470 471 472 473

(1) Klemeš, J. J.; Varbanov, P. S.; Kravanja, Z., Recent developments in Process Integration. Chemical Engineering Research and Design 2013, 91, (10), 2037-2053. (2) Ebert, W.; Panchal, C. Analysis of Exxon crude-oil-slip stream coking data; Argonne National Lab., IL (United States): 1995. (3) Ishiyama, E. M.; Paterson, W. R.; Ian Wilson, D., Optimum cleaning cycles for heat transfer equipment undergoing fouling and ageing. Chemical Engineering Science 2011, 66, (4), 604-612. (4) Pogiatzis, T.; Ishiyama, E. M.; Paterson, W. R.; Vassiliadis, V. S.; Wilson, D. I., Identifying optimal cleaning cycles for heat exchangers subject to fouling and ageing. Applied Energy 2012, 89, (1), 60-66. (5) Pogiatzis, T. A.; Wilson, D. I.; Vassiliadis, V. S., Scheduling the cleaning actions for a fouled heat exchanger subject to ageing: MINLP formulation. Computers & Chemical Engineering 2012, 39, 179-185.


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536 537


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Page 29 of 29

538

For Table of Contents Only Input the original HEN in base case

Simulated annealing algorithm (SA) Randomly selected by SA

Randomly changes velocity distribution (detail structure modification)

Randomly changes the split ratios

The constraints of velocity are satisfied

The constraints of split ratio are satisfied

NO

NO

YES

YES

Calculate detail structure modification cost

Synthesis the HEN in the first time interval, n=1 Calculate fouling resistance, utility cost and power cost in time interval n Calculate velocity distribution in next time interval, n=n+1 NO

If n >the number of investigated time interval ? YES Calculate pump investment cost and the objective function NO

The constraints in SA are satisfied YES Output the optimization results

3.5

310

base case optimized case detailed design modification

3.0

base case optimized case

305 300

2.5

Temperature(°C)

Initial Velocity(m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.0 1.5 1.0

295 290 285 280

0.5

275

0.0

270

E6

E5

E4

E3A

E3B

E2A

E2B

E1A

E1B

0

1

2

3

4

539

5

6

7

8

9

10

11

12

Time(months)

Exchangers Initial velocity distributions

FIT profile


29

An Overall Velocity Distribution and Optimization Method for Crude Oil

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