FPSO Chapter V

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CHAPTER V.

EXAMPLE PROBLEM: DEVELOPING A HIERARCHICAL PRODUCT PLATFORM FOR A

FAMILY OF GRAVITATIONAL SEPARATORS .......................... ........................... ................ 114

5.1 THE GRAVITATIONAL HYDROCARBON SEPARATOR – AN INTRODUCTION.............115

5.1.1 The Separator Basics......................................................................................115

5.1.2 Flexibility: Scaling and Leveraging................................................................. 118

5.1.3 The Appropriateness of This Example Problem...............................................119

5.2 EXEMPLIFICATION OF PHASE I: DEFINE.........................................................................122

5.2.1 Step I.1 – Select OTUs, Characters, and Assembly Levels...............................122

5.2.2 Step I.2 – Obtain and Select Samples.............................................................. 126

5.2.3 Step I.3 – Record Data ...................................................................................127

5.2.4 Step I.4 – Cluster Data...................................................................................131

5.2.5 Step I.5 – Evaluate Clustering......................................................................... 131

5.3 EXEMPLIFICATION OF PHASE II: MODEL........................................................................133

5.3.1 Step II.1 – Select Taxonomic Levels (TL).......................................................133

5.3.2 Step II.2 – Partition Realization Processes5- ........................... ......................... 137

5.3.3 Step II.3 – Determine Design Rules for each TL..............................................138

5.3.4 Step II.4 – Model Relationships ...................................................................... 141

5.3.5 Step II.5 – Formulate c-DSP........................................................................... 145

5.4 EXEMPLIFICATION OF PHASE III: SOLVE........................................................................148

5.4.1 Step III.1 – Establish Scenarios ...................................................................... 148

5.4.2 Step III.2 – Solve for each Scenario ................................................................ 149

5.4.3 Step III.3 – Decide on Hierarchical Product Platform......................................160

5.4.4 Step III.4 – Critically Evaluate Hierarchical Product Platform.........................162

5.5 A LOOK BACK AND A LOOK AHEAD................................................................................165


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LIST OF FIGURES

Figure 5-1 Typical Gravitational Inlet Separator, with Internals.............. ........................... ....... 117

Figure 5-2 Scaling and Leveraging of Gravitational Separators.... ........................... ................ 117

Figure 5-3 The Simplified Gravitational Separator and its Variables. ........................... ............ 125

Figure 5-4 Visualization of Parameter Ranges......................... ........................... ..................... 128

Figure 5-5 Baffle Plate Clusters @ AL 1......................... ........................... ........................... ... 132

Figure 5-6 Baffle Rack Clusters @ AL 2......................... ........................... ........................... ... 132

Figure 5-7 The Hole Diameter Values as a Function of Clustering.................. ......................... 135

Figure 5-8 The Perforation Area as a Function of Clustering .......................... ......................... 135

Figure 5-9 The Plate Spacing as a Function of Clustering ......................... ........................... ... 136

Figure 5-10 The Separator Lengths as a Function of Clustering ......................... ..................... 136

Figure 5-11 The Partitioned Baffle Plate / Rack Realization Process........................... ............ 140

Figure 5-12 The Plate Rack Standardization Concept ........................... ........................... ....... 140

Figure 5-13 Design Time and Retooling Discounting Profile ........................... ......................... 142

Figure 5-14 Rack Installation Discounting Profile................................... ........................... ....... 144

Figure 5-15 Solution Algorithm.......................... ........................... ........................... ................ 150

Figure 5-16 Standardization of Baffle Plate Design .......................... ........................... ............ 151

Figure 5-17 Performance of Baffle Plates....................... ........................... ........................... ... 151

Figure 5-18 Standardization of Plate Rack Design............................ ........................... ............ 152

Figure 5-19 The System Performance.......... ........................... ........................... ..................... 154Figure 5-20 The Solution Spaces for Scenario 1 through Scenario 8, see Table 5-11.............. 157

Figure 5-21 Suggested Plate Clustering by each Scenario ........................ ........................... ... 159

Figure 5-22 Suggested Rack Clustering by each Scenario ........................ ........................... ... 159

Figure 5-23 The Gravitational Separator Hierarchical Product Platform................................... 161

LIST OF TABLES

Table 5-1 The Example Correctness’ Impact on the METHOD Verification.............................. 121

Table 5-2 OTUs and Characters for the BAFFLE Plate Standardization Example.................... 123

Table 5-3 Typical Separation Train for Production Capacities below 50.000 bbl/day................ 126

Table 5-4 The Ranges of the Parameters....................... ........................... ........................... ... 127

Table 5-5 The Coding Scheme for Baffle Plates and Racks ........................... ......................... 129

Table 5-6 The Entries of the Baffle Plate / Rack Database........................ ........................... ... 129

Table 5-7 Baffle Plate Input Parameters for Separator Example Problem ........................ ....... 130

Table 5-8 Baffle Plate Clustering Analysis @ AL 1 / TL 26 ....................... ........................... ... 133


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Table 5-9 Baffle Rack Clustering Analysis @ AL 2 / TL 26 ........................ ........................... ... 134

Table 5-10 The Nominal Values for Fixed Design and Process Parameters ......................... ... 141

Table 5-11 Scenarios Representing Various Customer Types ........................ ......................... 148Table 5-12 Baffle Plate Families for Gravitational Separators ........................ ......................... 160

Table 5-13 Quantification of HPP Benefits .......................... ........................... ......................... 162

Table 5-14 Quantification of HPP Benefits .......................... ........................... ......................... 163


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CHAPTER V

5. EXAMPLE PROBLEM: DEVELOPING A

HIERARCHICAL PRODUCT PLATFORM FOR A

FAMILY OF GRAVITATIONAL SEPARATORS

NumTax TechDiff c-DSP HPPRM Demonstrating Internal

consistency of the HPPRM

and usefulness of NumTax

and compromise DSP

x

x x xx x x

The principal objective in this chapter is to test the Structural Validity of the HPPRM, and to

test the Performance Validity of Numerical Taxonomy and the compromise DSP. We do this by using

tailored input that is anticipated to give a certain output, hence, comparing the actual output to the

anticipated output we get a feel for:

§ Numerical Taxonomy’s ability to reveal the inherent order in a data set;

§ the usefulness of using the compromise-DSP as our multi objective decision model;

§ the adequacy of HPPRM to develop Hierarchical Product Platforms for this type of problems;

In addition, this exemplification serves as an illustration of how to implement the conceptual

framework presented in Chapter III, and hence, it also serves as a means of improving the framework

through learning-by-doing. Therefore, we assert that this chapter substantiates our claim that the HPPRM

is Structural Valid, and that Numerical Taxonomy and the compromise DSP are valid within the HPPRM

and adds value to it. Hence, this chapter adds to the Performance Validation as well.

“It is comm on s ense to take a method and try i t . If i t fai ls , admit i t frankly

and try anoth er. Bu t abov e al l , try som ething”

– Franklin D. Roosevelt


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CHAPTER V

Example Problem: Developing a HPP for a Family of Gravitational Separators

115

5.1 THE GRAVITATIONAL HYDROCARBON SEPARATOR –

AN INTRODUCTION

The objective in this section is to demonstrate the appropriateness of the example problem, and

we start in Section 5.1.1 by presenting the basics of the gravitational hydrocarbon separator in terms of

context, application and composition. Then, in Section 5.1.2 we present the specific challenge associated

with introducing flexibility in Hierarchical Product Platforms. Based on this, we demonstrate the

appropriateness of this example problem in Section 5.1.3.

5.1.1 The Separator Basics

The context in which a Hierarchical Product Platform is developed for a family of gravitational

separators is Marginal Fields in the North Sea. A marginal field is defined as ‘economical infeasible to

develop with current designs’ due to too small amounts of oil to pay for the investment

et al. 1997). One way of making these fields economical feasible is to recover oil and gas reserves from

several fields with the same production facility. This implies flexible production systems able to handle a

variety of different production profiles and oil compositions. A major component in the production system

is the separator, where the well stream is separated into gas, oil and water. If the separation system is

gravitational based, this is normally done in several separators (or stages). In the first separator (the inlet

separator) water, sand and some gas are removed from the oil before sending it to subsequent separator(s)

for further separation of gas from the oil, by gradually reducing the pressure to atmospheric pressure and

adjusting the temperature to optimize the oil output.

In Figure 5-1 a typical gravitational inlet separator is given in terms of its outer shape and its

internals. The industry separator norm is pressure vessels with circular cross sections and semi-spherical

ends. Into this vessel highly pressurized well-stream (mixture of gas, oil, water, and sand) enters, and goes

into the cyclone to reduce its momentum. From this point on, the well-stream flows toward the outlets

located in the other end of the tank, and while it flows, gas bubbles and oil droplets in the oil / water will

rise, while oil and water droplets in gas / oil will sink. The rising / sinking properties of the gas bubbles

and oil droplets gives the separator length and diameter, and are determined based on hydrodynamics and

thermodynamics. The internals however, are designed from a more mechanical point of view. The mission

of the WEIR plate is to trap the water and prevent it from entering the oil outlet, and its height is designed

according to the anticipated rates of gas, oil and water. The separated oil is flowing over the WEIR plate

and is tapped through a VORTEX BREAKER in order to prevent gas from being sucked into the oil


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outlet. Similarly, water is also tapped through a VORTEX BREAKER in order to prevent oil from being

sucked into the water outlet.


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Separator Diameter

BAFFLE plate

(frontal view)

Cyclone

WEIR plate

(frontal view)

VANE DEMISTER

(top view)

Hole diameter

Weir Height

Separation Length

Vane Demister LocationQ well-stream•

Q water•

Q oil•

Q ga s•

Maximum Baffle Spacing

Gas / Sand /

Water / Oil

Normal

Interface

Level

Normal

Liquid

Level

Water Jetting

System

Pre ssuriz ed

water

Vortex

Breakers

(top view)

GA S

OI L

WATER

Figure 5-1

Typical Gravitational Inlet Separator, with Internals.

M A R K E T S E G M E N T S

I N L E T S E P A R A T I O N

( F I R S T S T A G E )

H I G H P R E S S U R E S E P A R A T I O N

( S E C O N D S T A G E )

L O W P R E S S U R E S E P A R A T I O N

( T H I R D S T A G E )

H O R I Z O N T A L S T A N D A R I Z A T I O N : L E V E R A G E A C R O S S D I F F E R E N T M A R K E T A P P L I C A T I O N S

V E R T I C A L S T A N D A R I Z A T I O N :

S C A L I N G F O R D I F F E R E N T P E R F O R M A N C E L E V E L S

Figure 5-2

Scaling and Leveraging of Gravitational Separators


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Since the well-stream may contain sand / silt a WATER JETTING system is designed to help

keep the sand / silt floating in the water long enough for it to be tapped out with the water. The mission of

the BAFFLE plates is to damp the movements of the liquids in case of ship-induced motions and to

prevent oil from entering the VANE DEMISTER (or gas outlet) at any pitch angles. Motion damping is

achieved by perforating the plate with holes big enough to allow adequate flow but small enough to trap

the oil between two BAFFLE plates for the duration of a wave period. Preventing oil from entering the gas

outlet is achieved by having the proper spacing between plates. Hence, the pitch angle determines the

plate spacing whereas the oil viscosity determines the size and number of holes. The mission of the VANE

DEMISTER is to ‘catch’ the smaller oil droplets on their way out, by utilizing the fact that oil, being

heavier than gas, will move ‘straight’ ahead and hit the demister walls when the flow changes direction.

However, changing the flow direction increases flow velocities / turbulence, which again increases the

possibilities of the oil droplets being re-entrained into the gas.

5.1.2 Flexibility: Scaling and Leveraging

As indicated earlier, economic feasibility for marginal fields can be achieved by multi-field

solutions, which again requires flexible solutions able to handle a variety of production profiles and oil

compositions. In the context of this research flexibility is achieved through standardization of products

(whole or in part). Standardization in this context is to deliver discontinuous products that sacrifice

operational performance for better delivery schedule and / or cost. Two major standardization schemes are

product scaling and product leveraging, see Figure 5-2.

The scaling of gravitational separators involves determining the best length and diameter and

is very much based on thermodynamics. These issues are very complex and are dealt with in a separate

research study, see (Grødal 1998; Grødal, Realff et al. 1998). In this research, on the other hand, we deal

with leverage and assume the length and diameter to be fixed. Hence, our focus becomes finding the right

internals for a given range of flow-rates and oil properties. The identified applications for this example

problem are inlet separation (very high pressure), high pressure separation, and low pressure (atmospheric

pressure) separation. The low pressure separation in the separator train discharges stable crude oil to

storage and / or transportation, and requires normally longer separator lengths due to higher oil viscosity.

However, this is assumed to only affect the assembly of internals and not the design of the internals per se.


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5.1.3 The Appropriateness of This Example Problem

As indicated in Section 1.6.2, evaluating appropriateness of example problems / case studies

deals with a method’s Empirical Structural Validity. However, the purpose of any example problem / case

study is to support a method’s Empirical Performance Validity. According Section 1.6.2 this is done by

demonstrating that the outcome (i.e., the product) of the method performs satisfactorily, and that the

elements of the method contribute positively to achieving this satisfactory outcome, i.e., that both the

method and its outcome are ‘useful’. Hence, the appropriateness of any example problem / case study lies

in their ability to demonstrate this ‘usefulness’. In order for an example problem to support a

demonstration of usefulness it must first of all be representative of the general problem intended to be

addressed by the method. Secondly, the quality of the data associated with the example problem must

support conclusions with statistical certainty. Firstly, are separator trains representative of the general problems intended addressed by the

HPPRM? The general problem intended addressed by the HPPRM is developing HPPs for large, complex,

expensive, Made-To-Order systems that are produced in small numbers, and that are designed for

different applications yet share much of the same technology. Separator trains are Made-To-Order in

small numbers; they are relatively expensive (compared to weight for example); they are designed for

different applications (inlet, high pressure, low pressure) yet they share much of the same technology; and

they have low complexity. All the characteristics except being large and complex are covered. However,

since the purpose is to illustrate the HPPRM, having low complexity may be the most important feature,

ensuring focus on method rather than complexity related uncertainties. Consequently, it is asserted that

gravitational separator trains are indeed representative for the general problem intended addressed by the

HPPRM.

Secondly, are the available separator data suited to support conclusions with statistical

certainty? This matter deals with the quality of the available data, and what impact the data-quality will

have on demonstrating the HPPRM usefulness. What impact will for example dummy data have on a

usefulness demonstration? This is evaluated in Table 5-1 where the only information that really affects a

demonstration of usefulness is the correctness of the clustering, the selection of the TLs, and the solving of

the model. To ensure that ‘wrong’ TL selection does not impact the demonstration, all possible TLs are

evaluated. To verify correct clustering, the structure must be known. To verify correct solving, the correct

answer must be known. The chosen strategy to obtain a known data structure, is to tailor the input data.

Tailoring data in this context means generating data where the clustering structure is known. This can be

done by using a known distribution in an automated data-generation procedure (e.g., MS-Excel’s random


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number generator with a distribution) to fix mean and variance. Further, the chosen strategy to obtain the

correct answer when solving is enumeration.


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Table 5-1

The Example Correctness’ Impact on the METHOD Verification

Phases / Steps What Constitutes

Correctness

Verification Strategy

Impact on

Usefulness

Demo.

Phase I: DEFINE

Select OTUs, Char.,

AL and Samples

Subjective, i.e., many correct

answers

Qualitative: reasoning

through viewpoints

Low

Record Data Recorded data correspond to

real data

Quantitative: manual

checking

Low

Cluster Data Ability to reveal the actual

present structure of therecorded data

Quantitative: use sets of data

with known structures tochoose best similarity coeff.

and clustering algorithm

High

Phase II: MODEL

Select Taxonomic

Levels

Subjective, i.e., many correct

answers.

Quantitative: checking all

possible levels.

High

Partition Realization

Processes

Partitioning is realistic. Qualitative: reasoning

through viewpoints

Low

Determine Designs

Rules

No violation of physical laws

and being realistic


through viewpoints

Low

Model Relationships Subjective; complex problemsrequire assumptions and

‘guesstimates’.

Qualitative: reasoningthrough viewpoints

Low

c-DSP for deviations

to base-case

Subjective; choice of base case

has many correct answers.


through viewpoints

Low

Phase III: SOLVE

Establish Scenarios Subjective, i.e., many correct

answers


through viewpoints

Low

Solve the Problem Ability to find the ‘correct’

solution for a given input

Quantitative: enumeration to

find the correct answer, then

find / modify solvers to copewith this discrete problem.

High

Decide on HPP Subjective; i.e., many correct

answers.


through viewpoints.

Low


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5.2 EXEMPLIFICATION OF PHASE I: DEFINE

The objective in this section is to exemplify Phase I of the HPPRM by taking the separator

example problem through it step by step. Anchored in the general problem of designing gravitational

separators outlined in Section 5.1, the gravitational separator is partitioned in Section 5.2.1 into its

Operational Taxonomic Units (OTUs), its Characters, and its Assembly Levels. In Section 5.2.2

representative samples are tailored for the purpose of illustrating the method and its usefulness. In Section

5.2.3 the tailored data is coded and recorded before being clustered and visualized in Section 5.2.4. In

Section 5.2.5, the clustering is evaluated in terms of its ‘correctness’, i.e., we evaluate the ‘usefulness’ of

Numerical Taxonomy in revealing the potential(s) for standardization that is inherent in an existing

product portfolio. The computer code is given in Appendix B, see Figure B-2.

5.2.1 Step I.1 – Select OTUs, Characters, and Assembly Levels

The selection of Operational Taxonomic Units (OTUs) and characters is very much guided by

the purpose of the clustering, which is to illustrate Phase I, and demonstrating the usefulness of using

Numerical Taxonomy for defining what to include in a Hierarchical Product Platform.

In order to illustrate the methodology, the problem is simplified to reduce complexity-related

uncertainties that could confuse this purpose. The simplification, again, is anchored in the objective of the

HPPRM, which is standardization of products (whole or in parts) across different applications. In this

particular case, the objective is standardization of separators (whole or in parts) designed for very high

pressures (inlet separation), high pressures, and low pressures, for a given range of oil composition, and

flow-rates of gas, oil and water.

As already indicated, the major separator design problem is to determine the main dimensions

of the separators (length and diameter). Since the scope in this research is standardization, these variables

are assumed fixed according to results presented in (Grødal 1998; Grødal, Realff et al. 1998)that are based

on performance levels corresponding to typical marginal fields (Pedersen, Grødal et al. 1997). This

reduces the problem to standardizing internals for INLET, HIGH PRESSURE, and LOW PRESSURE

separation.

The very act of standardization presupposes the existence of design proliferation due to varying

design requirements. The sub-systems / design variables unaffected by varying input, are obvious

standardization targets and are not dealt with here. The WATER JETTING system and the VORTEX

BREAKER are typically such sub-systems. Further, sub-systems which heavily rely on heuristics and


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require a lot of experience, are not included here. The VANE DEMISTER and the CYCLONE are

typically such sub-systems.

Developing a Hierarchical Product Platform is to find at which level of assembly the best

compromise of cost, schedule, and performance occurs. This is based on the assumption that standardizing

at higher levels of assembly will improve schedule and decrease time related cost, while increasing

material related and lost-performance related cost. Having a hierarchical structure of assemblies implies

further a nesting of design characteristics. Each part / sub-assembly being assembled is characterized by a

set of variables, and assembling them adds a new set of variables characterizing the configuration of the

assembled parts.

Which of the remaining separator internals (the BAFFLE plates and / or the WEIR plate) are

best suited to demonstrate this nesting effect? The WEIR plate is only characterized by its height, which

is not related to any assembly. The BAFFLE plates, on the other hand, are characterized by their

perforation and their spacing. The perforations are not related to any assembly, whereas the spacing is a

result of the BAFFLE plates being assembled. Hence, the problem is simplified to standardize the

BAFFLE plates (single or in racks) for a family of separator trains consisting of an inlet separator, a high

pressure separator and a low pressure separator. As indicated earlier, determining the separator main

dimensions is not considered the scope of this research.

Since the problem has been reduced to standardization of BAFFLE plates, the only separator

main dimension that needs to be fixed is the separator diameter. Hence, the separator length is considered

a minimum value (i.e., the shortest separator in the separation train). The simplified separator and its

variables are illustrated in Figure 5-3. When viewed separately the BAFFLE plates are characterized by

the diameter of their holes and the relative area of the perforation. When viewed as an assembly, the

BAFFLE plate racks are characterized by their maximum spacing and the number of plates in each rack.

Based on this the OTUs to be grouped and their descriptive characters are summarized in Table 5-2.

Table 5-2

OTUs and Characters for the BAFFLE Plate Standardization Example

Assembly

Level

OTUs

(what to group)

Characters

(criteria for grouping)

1 The individual baffle plates for separation trains

consisting of a inlet, a high pressure, and a low

pressure separator.

1.1: The diameters of holes [mm]

1.2: The perforated area [%]

2 The baffle plate racks for separation trains

consisting of a inlet, a high pressure, and a low

2.1: The spacing of baffle plates [mm]


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pressure separator. 2.2: The number of plates in rack [#]


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Maximum Baffle Plate Spacing

(free variable)

S.ASS [mm]

Hole diameter

(free variable)

D.BFL [mm]

Separator Diameter D.SEP

(f i xed var iab le)

BAFFL E plate

(fr ontal view)

Separation Length, L .SEP (min imum value)

Vane Demister Location: H .DM T (f i xed var iab le)

H.NLL

(maximum

value)

Perforated Area

(free variable)

A.BFL [%]

Number of Baffle Plates

(free variable)

N.ASS [#]

Figure 5-3

The Simplified Gravitational Separator and its Variables.


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5.2.2 Step I.2 – Obtain and Select Samples

According to assertions made in Section 5.1.3, the method’s usefulness depends on its ability

to reveal the structure that is present in the data recorded from the actual samples, hence, evaluating this

ability becomes a crucial task. The chosen approach to evaluate this ability is to use data where the

structure is known and compare this structure with the structure obtained from clustering the data, hence,

the data is tailored to fit this purpose.

The tailoring is based on the fact that as gas is separated from the oil, its viscosity increases.

This requires longer separation lengths, bigger holes in the baffle plates and / or longer spacing. The last

separation stage is typically where most of the gas is removed, resulting in a viscosity significantly above

the preceding stages5-1. Based on the given reasoning, a typical separator train designed for large

production rates (Grødal 1998) is scaled down to fit marginal field production rates, and its characteristicsis given in Table 5-3.

Table 5-3

Typical Separation Train for Production Capacities below 50.000 bbl/day

based on (Grødal 1998)

Design Variables

FIRST STAGE

(inlet)

SECOND STAGE

(high pressure)

THIRD STAGE

(low pressure)

Diameter (fixed) 2000 [mm] 2000 [mm] 2000 [mm]

Baffle plate: hole diameter 12.5 [mm] 15.0 [mm] 17.5 [mm]

Baffle plate: perforated area 17.5 [%] 20.0 [%] 22.5 [%]

Baffle rack: plate spacing 450 [mm] 525 [mm] 1100 [mm]

Baffle rack: separator length 6500 [mm] 6500 [mm] 14500 [mm]

Baffle rack: number of plates 14 [#] 12 [#] 13 [#]

Ten separator trains (i.e., 30 separators) will be used as the ‘population’, and design parameter

values will be assigned randomly within a range around the values given in Table 5-3. The extension of

the ranges is chosen to overlap in a way that is anticipated to produce a certain structure in the numerical

data. This anticipated structure is then compared to the structure given by the clustering to see whether

there is correspondence or not. The ranges are given in numerically in Table 5-4 and the overlaps are

5-1 Oil viscosity in typical separator train (Grødal 1998): first stage 0.0002464 [Pas], second stage 0.0005153 [Pas],

and third stage 0.003734 [Pas].


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illustrated in Figure 5-4. Numbers where generated within these ranges using a uniform distribution to

create a ensure complete randomness.

The intended structure for Assembly Level 1 (the plates individually) is no mixing between

baffle plates from IN and LP mix. Further, the plates from HP should mix fairly evenly with plates from

IN and LP. The intended structure for Assembly Level 2 is racks for LP should clearly stand out while

racks for IN and HP should mix nicely.

Table 5-4

The Ranges of the Parameters

Baffle Plate:

Hole diameter

[mm]

Baffle Plate:

Perforated area

[%]

Baffle Rack:

Plate Spacing

[mm]

Baffle Rack:

Lengths (i.e., no.

of plates [mm]

Inlet (IN) [10 – 15] [15 – 20] [400 – 500] [6000 – 7000]

High Pressure (HP) [12 – 18] [18 – 22] [450 – 600] [6000 – 7000]

Low Pressure (LP) [15 – 20] [20 – 25] [1000 – 1200] [14000 – 15000]

5.2.3 Step I.3 – Record Data

In order to process the data in an efficient way, it has to be stored in a way that it can easily be

retrieved. This leads into the discussion around coding and classification. Coding addresses how to

retrieve data whereas classification addresses what characters to use. In the following, coding for this

example problem is discussed.

First of all, each OTU should be assigned a unique code so that it is recognizable within the

clustering structure. Further, the coding structure has to enable retrieval of data that is to be compared.

Hence, for Hierarchical Product Platforms in general each item has to be coded for its level of assembly,

its product type affiliation, and a unique code within its product type. In addition, the homology5-2

aspect

of classification may require that items are coded for their location and / or their function within the

overall product. For this example problem, the homology aspect is not considered, hence, the baffle plates

and their assemblies are coded for their assembly level, their product type affiliation, and their separator

train affiliation. This gives each baffle plate and rack (i.e., each OTU) a unique ID number XYZ, where X

5-2 Generally homology refers to “corresponding or similar in position, value, structure, or function”. Specifically, in

biology homology refers to “similar in structure and evolutionary origin, though not necessarily in function, as the

flippers of a seal and the hands of a human being”.


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is the associated separator train number, Y is the associated assembly level, and Z is the associated

product type. This coding scheme is summarized in Table 5-5.

LP

HPIN

Hole Diameter

[mm]

15 20 25

Perforated Area

[%]

Plate Spacing

[mm]

5.000 10.000 15.000

Separator Lengths

[mm]

10 15 20

400 500 1000

LP

HPIN

LP

HPIN

LP

HPIN

Figure 5-4

Visualization of Parameter Ranges


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To achieve the required ‘retrievability’, it is recommended to use a database in some way,

shape, or form. For this example problem, the database features in MS-Excel is used with record-labeling

as outlined in Table 5-6. The actual numbers are given in Table 5-7.

Table 5-5

The Coding Scheme for Baffle Plates and Racks

OTU ID # X Y Z

Description Train number affiliation Assembly level Product Type affiliation

Allowable

Values

1 through 10 1 = single baffle plates

2 = baffle plate racks

1 = IN = Inlet separator

2 = HP = High pressure sep.

3 = LP = Low pressure sep.

Worth noting is the last entry in Table 5-6; “Subassemblies”. Products in general are

hierarchical in nature in the sense that any assembly is made up of items from a lower assembly level.

Hence, starting the comparison at level 1 enables information of one assembly level to be used at

subsequent assembly levels, and hence, time consuming re-computation can be avoided.

Table 5-6

The Entries of the Baffle Plate / Rack Database

OTU name OTU ID # Character 1 Character 2 Subassembly

Baffle plate X 1 Z Diameter of hole [mm] Perforation area [%] Not applicable

Baffle rack X 2 Z Plate spacing [mm] Number of plates [#] X1Z


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Table 5-7

Baffle Plate Input Parameters for Separator Example Problem

OTU

AL1

Hole-

Diameter

Perforated

Area

OTU

AL2

Plate

Spacing

Separator

Lengths

AL1

Plates

111 13.45 15.39 121 416 6771 111

112 17.12 18.66 122 493 6910 112

113 17.82 22.29 123 1173 14730 113

211 10.76 15.25 221 408 6726 211

212 14.10 19.74 222 491 6939 212

213 15.79 21.32 223 1078 14534 213

311 13.32 17.62 321 465 6323 311

312 15.49 19.13 322 499 6783 312

313 17.08 20.06 323 1056 14767 313

411 12.19 19.55 421 444 6655 411

412 15.71 19.64 422 486 6447 412

413 17.70 22.24 423 1007 14996 413

511 11.01 18.58 521 496 6420 511

512 15.73 19.79 522 507 6979 512

513 15.30 24.39 523 1104 14191 513

611 10.39 19.98 621 462 6516 611

612 14.08 18.88 622 470 6444 612

613 17.62 23.43 623 1148 14151 613

711 10.79 15.42 721 447 6107 711

712 17.40 21.05 722 590 6072 712

713 18.85 20.90 723 1142 14964 713

811 13.00 18.00 821 434 6655 811

812 15.64 20.67 822 511 6521 812

813 16.24 22.00 823 1031 14043 813

911 13.05 19.20 921 405 6584 911

912 16.90 20.66 922 549 6532 912

913 19.78 22.34 923 1155 14089 913

1011 10.23 18.94 1021 447 6833 1011

1012 16.27 18.28 1022 469 6915 1012

1013 19.10 23.91 1023 1046 14371 1013

[mm] [%] [mm] [mm]


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5.2.4 Step I.4 – Cluster Data

The clustering results for Assembly Level (AL) 1 and Assembly Level (AL) 2 are given in

Figure 5-5 and Figure 5-6 respectively.

5.2.5 Step I.5 – Evaluate Clustering

When evaluating the clustering, the main question is whether it represents the structure that is

present in the input data or not. Note that dissimilarity is a relative metric, hence, is not associated with

any physical meaning except ‘distance’ in a space spanned by the characters. We start by looking at

Assembly Level (AL) 1; the structure of the plates individually. This structure is given in Figure 5-5, and

first we look at Taxonomic Level (TL) 19 where OTU 213 through 712 are clustered. In this cluster, there

are 3 LP plates and 3 HP plates which is the ‘equal’ mix we were expecting due to the overlap. The next

significant cluster appears at TL 24 where OTU 113 through 713 are clustered. In this cluster, we see that

the clusters of LP plates are more similar to the HP / LP mixed cluster than to the IN / HP mixed clusters,

which is exactly as expected; we anticipated no mixed IN / LP clusters. The next significant cluster

appears at TL 26 where the IN / HP plates are mixed together as predicted. The next significant cluster

appears at TL 27 where the mixed IN / HP cluster goes together with the mixed HP / LP cluster. The next

two clusterings appear at TL 28 and 29, which appears to add an ‘outlier’ to other clusters. There seem to

be ‘many’ outliers for such a small population, however, due to the uniform distribution this is not

considered strange. Then we look at Assembly Level (AL) 2; the structure of the plate racks. This

structure is given in Figure 5-6, and we start at TL 26. At this level, the LP racks comes together (except

one), and we see that in the two preceding clusterings the IN and the HP racks comes together as well.

Hence, we have a situation where the racks cluster according to their type, which is not unexpected. LP

racks are definitively different from the other two. For IN / HP racks, the skewed spacing-overlap together

with the AL 1 clustering gives a complete distinction between these two rack types. However, the

distinction is not sharp; the separate clusters are created at about dissimilarity 0.12 whereas they are

joined at TL 27 at a slightly higher dissimilarity of 0.14. All this information taken together, we assert

that the clustering performs as expected. The next question is whether this clustering is useful, which is

dealt with in the next section.


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1 1 1

2 1 1

7 1 1

5 1 1

1 0 1 1

6 1 1

1 1 2

1 0 1 2

2 1 2

6 1 2

4 1 1

9 1 1

3 1 2

4 1 2

5 1 2

3 1 1

8 1 1

1 1 3

4 1 3

6 1 3

9 1 3

1 0 1 3

2 1 3

8 1 2

8 1 3

3 1 3

9 1 2

7 1 2

7 1 3

5 1 3

OTUs

0 5 10 15 20 25 30-0.1

0

0. 1

0. 2

0. 3

0. 4

0. 5

Number of Designs [#]

D i s s i m i l a r i t y [ - ]

DESIGN CLUSTER DENDROGRAM

ASSEMBLY LEVEL 1

TL 29

TL 28

TL 27TL 26

TL 24

TL 30

TL 19 …

…

Figure 5-5

Baffle Plate Clusters @ AL 1

TL 26

TL 27TL 28TL 29

TL 30

0 5 1 0 1 5 20 25 3 0-0 .1

0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

1 2 1

2 2 1

7 2 1

1 2 2

1 0 2 2

2 2 2

6 2 2

3 2 2

4 2 2

5 2 2

7 2 2

8 2 2

9 2 2

3 2 1

8 2 1

4 2 1

9 2 1

5 2 1

6 2 1

1 0 2 1

1 2 3

6 2 3

4 2 3

7 2 3

9 2 3

1 0 2 3

2 2 3

8 2 3

3 2 3

5 2 3

O T U s

Number o f Des igns [# ]

D i s s i m i l a r i t y [ - ]

D E S I G N C L U S T E R D E N D R O G R A M

A S S E M B L Y L E V E L 2

Figure 5-6

Baffle Rack Clusters @ AL 2


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5.3 EXEMPLIFICATION OF PHASE II: MODEL

In this section, Phase II of the HPPRM is exemplified based on the clustering of the separator

example problem from Phase I. First of all, the Taxonomic Levels (TL) to be considered are selected in

Section 5.3.1 based on analyzing the data to find the most promising clusters. Then the realization

processes are partitioned in Section 5.3.2 along Assembly Level (AL) lines. Knowing the TLs and the

processes, the design rules for each TL / AL is established in Section 5.3.3. Then the relationships are

modeled in Section 5.3.4 before compromise DSPs are formulated in Section 5.3.5 to integrate product

and processes. The computer code is given in Appendix B, see Figure B-2.

5.3.1 Step II.1 – Select Taxonomic Levels (TL)

Having established that the chosen clustering produces meaningful clusters (see Section 5.2.5),

the question remains; are the clusters useful? This question has to be answered in context of what the

clustering is intended for. As already stated the clustering is intended for identifying the “potential for

standardization at different assembly levels”. This is based on the assumption that similarity in the chosen

characters is an indicator of standardization potential. Since the characters are chosen for this purpose,

one would expect this assumption to be true. However, being a relative measure, the dissimilarity does not

interpret into physical meaningful units, which is a drawback in engineering where tolerances have to be

met. Clusters based on relative measures, however, point to promising areas for further investigation

For the individual plates (AL1) the clusters that get attention are at TL26, 27, 28, 29 and 30.

The design parameter values are randomly generated between ranges as given in Figure 5-4, and the result

at TL26 is given in Table 5-8. For space conservation, the result for all the other TLs are visualized in

Figure 5-7 and Figure 5-8 for hole-diameter and perforation area respectively.

Table 5-8

Baffle Plate Clustering Analysis @ AL 1 / TL 26

TL

26 dia. perc. dia. perc. dia. perc. dia. perc. dia. perc.max N/A N/A 19.78 23.91 17.12 19.79 11.01 19.98 13.45 15.42

min N/A N/A 15.64 20.06 12.19 17.62 10.23 18.58 10.76 15.25

range N/A N/A 4.14 3.85 4.93 2.17 0.78 1.40 2.69 0.17

mean 15.3 24.39 17.49 21.74 14.55 18.95 10.54 19.17 11.67 15.35

stddev N/A N/A 1.29 1.17 1.59 0.74 0.41 0.73 1.54 0.09

mean+std N/A N/A 18.78 22.91 16.14 19.69 10.96 19.89 13.21 15.44

mean-std N/A N/A 16.21 20.57 12.96 18.21 10.13 18.44 10.12 15.26

Cluster 5Cluster 1 Cluster 2 Cluster 3 Cluster 4

[mm] [%] [mm] [%] [mm] [%] [mm] [%] [mm] [%]


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The information looked at is the cluster extensions (max / min), the mean, and the standard

deviation. In the figures the legends are diamonds for cluster extensions, vertical lines for standard

deviation extensions, and squares for cluster means. From Figure 5-7 and Figure 5-8 it can be seen how

the clusters go together, and how the mean and standard deviations shift clustering takes place.

Starting with the hole-diameters, we see from Figure 5-7 that at TL26 there is one single OTU

and four clusters where the largest cluster extends from 12.19 to 17.12 mm, a span of about 5 mm or

about 40% (relative). The very largest cluster appearing at TL30 extends from 10.23 to 19.78 mm, a span

of about 9.75 mm or 95% (relative). Following with the perforation area percentage (still AL1), we see

from Figure 5-8 that the very largest cluster appearing at TL30 (of course) extends from 15.25 to 23.91%,

a span of 8.7% (absolute) or about 57% (relative). The parameter variation tolerances (if any) provides the

limit for how far up on the TL scale one can go when looking for a standardization potential. The

deviation in perforation area influences the fluid dynamic properties the most, since this affects the

deviation in fluid velocities through the holes which may lead to unwanted jetting (oil may for example be

re-entrained into the gas). The deviation in hole-diameters on the other hand, affects mainly the

fabrication by deciding the number of holes needed to give the wanted perforated area. Hence, no strong

tolerance constraints on these parameters.

Moving on to the racks (AL2) the clusters that get attention are also at TL26, 27, 28, 29 and

30. The design parameter values are randomly generated between ranges as given in Figure 5-4, and the

result for TL26 is given in Table 5-9. For space conservation, the result for all the other TLs are

visualized in Figure 5-9 and Figure 5-10 for the plate spacing and separator lengths respectively. The

clustered separator lengths per se are not standardized, but gives input to standardizing the rack lengths,

see Section 5.3.3.

Table 5-9

Baffle Rack Clustering Analysis @ AL 2 / TL 26

TL

26 space length space length space length space length space length

max 447 6771 590 6979 496 6833 1173 14996 N/A N/A

min 408 6107 469 6072 405 6323 1007 14043 N/A N/Arange 39 664 121 907 91 510 166 953 N/A N/A

mean 424 6535 507 6654 450 6569 1093 14516 1104 14191

stddev 21 371 37 297 28 168 62 371 N/A N/A

mean+std 444 6906 544 6951 479 6738 1155 14887 N/A N/A

mean-std 403 6164 469 6357 422 6401 1031 14145 N/A N/A

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5

[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm]


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Hole D iameter and C lus te r ing

25

26

27

28

29

30

9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00

Ho le D iameter [mm]

T a x o n o m i c L e v e l s ( T L )

Figure 5-7

The Hole Diameter Values as a Function of Clustering

Per fo r a t ion Ar ea and C lus te r ing

25

26

27

28

29

30

14.00 16.00 18.00 20.00 22.00 24.00 26.00

Perforat ion Area [% ]


Figure 5-8

The Perforation Area as a Function of Clustering


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Plate Spacing and C luster ing

25

26

27

28

29

30

350.00 450.00 550.00 650.00 750.00 850.00 950.00 1050.00 1150.00

Plate Spacing [mm]


Figure 5-9

The Plate Spacing as a Function of Clustering

Separator Lenghts and C l uster ing

25

26

27

28

29

30

5000 7000 9000 11000 13000 15000

Separator Lengths [mm]


Figure 5-10

The Separator Lengths as a Function of Clustering


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As anticipated from the split in the input data given in Figure 5-4, Figure 5-9 and Figure 5-10

shows that the LP separator racks stands out whereas the IN and HP racks are close. Evaluating the

impact of standardization for these two parameters, however, requires knowledge of what the adversary

impacts may be. Standardizing plate spacing for an entire cluster is straight forward, since spacing is a

maximum value. Hence standardization imposes too narrow spacing for some of the separators in the

cluster resulting in more plates than necessary and hence excessive cost, time and weight.

Evaluation of rack-standardization on the other hand is based on the following assumptions. 1)

Installation of racks is preferred to installation of single plates. 2) For each rack-installation there is a

setup time required, hence, installing one ‘long’ rack takes less time than installing many small racks (for

the same amount of plates). Standardizing racks for an entire cluster reduces the rack-size (number of

plates per rack) so it can fit in whole-multiples into all the separators for that particular cluster. Hence, for

clusters where separator lengths differs beyond a certain value, the rack-size goes down and consequently

the number of racks goes up resulting in excessive installation time. This is not a feasibility issue, but a

cost and time issue, thus, there is no need to impose TL constraints for plate spacing and rack lengths.

So, which TLs should we focus on? We have shown 1) that variation in hole-diameters mainly

affects the fabrication (cost and time issue) thus imposes no feasibility constraints. 2) That variation in

perforated area percentage mainly affects the fluid velocities through the holes, an effect that is difficult to

assess. 3) That variation in both spacing and rack lengths represent cost and time issues thus imposes no

feasibility constraints. Based on this we conclude that there are no reasons for imposing any TL

constraints. After all, the purpose of this exercise is to illustrate the HPPRM and to demonstrate its

usefulness, hence, investigating all TLs makes sense, especially since it is asserted in Table 5 that the

correctness of the TL selection impacts the usefulness demonstration.

5.3.2 Step II.2 – Partition Realization Processes5-3

Knowing the assembly levels we can now associate the corresponding sub-processes. Assembly

Level 1 (AL1) deals with realizing one unit plate. This implies designing it (i.e., hole-diameter, perforated

area percentage, plate spacing and rack-size), retooling manufacturing cell for this particular series

(assuming production of more than one plate), and fabricating the plate (i.e., cutting it circular to the

correct diameter and cutting / drilling all the holes). This is illustrated at the top in Figure 5-11 where the

patterned Unit Fabrication indicates an aggregated time, and where the fading gray-shading indicates that

5-3 Note that in this example problem , no alternative processes are proposed.


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design and retooling is influenced by the degree of standardization. This is further elaborated in Section

5.3.4.

Assembly Level 2 (AL2) deals with fabricating plate-series, assembling them into racks and

installing the racks into the respective separators. This is illustrated at the bottom in Figure 5-11 where we

assume double fabrication and assembly lines, where the plates are assembled onto their respective racks.

In the cases where the plates are to be put into more than one rack, there is a setup time between each rack

which makes more racks unfavorable from a time and cost perspective. As for AL1 more standardization

is assumed to decrease re-tooling time for both assembly and installation. In addition, as the number of

racks goes up for more standardization we assume that the time to install each rack goes down (being

smaller and more ‘maneuverable’). However, these effects are modeled and elaborated in Section 5.3.4.

5.3.3 Step II.3 – Determine Design Rules for each TL

In general, knowing which TLs to standardize for allows the establishment of design rules. For

this example problem we have decided to investigate all TLs for both Assembly Levels. Starting with

Assembly Level 1 (AL1) the hole-diameters and the perforated area are to be standardized within each

cluster for increasing TL. As indicated in Section 5.3.1, we impose no feasibility constraints for variations

in hole-diameters nor for variations in perforated area percentage. As the percentage of perforated area

increases the fluid velocities through the holes decreases and vice versa, however, the actual fluid dynamic

and thermodynamic effects are difficult to assess and considered outside the scope of this research.

Therefore we have decided to standardize the hole-diameters and the perforated area percentages from a

pure process perspective, i.e., choosing the alternatives that improve fabrication cost and time.

This implies choosing the combination of hole-diameter and perforated area percentage that

gives the minimum number of holes to be drilled. Hence, for each cluster the maximum hole-diameter and

the minimum perforated area percentage appearing within the cluster is chosen for all the plates in the

cluster.

For Assembly Level 2 (AL2) the actual plate to use, the plate spacing and the rack-size are to

be standardized within each cluster for increasing TL. As indicated in Section 5.3.1, we impose no

feasibility constraints for variations in plate spacing nor for rack sizes, hence we are to standardize for all

TL. Starting with the selection of plates for the racks, this in not a trivial selection. The general question

is “which parts to choose for the subassemblies”? For this particular example problem we choose the

plate in the cluster with the smallest objective function value by using a procedure elaborated in Section

5.3.4.


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The plate spacing standardization is in a way trivial, since it is a maximum value. Hence, the

narrowest spacing in the cluster becomes the spacing for the entire cluster. The rack-size standardization

on the other hand is not trivial. For the purpose of demonstrating the HPPRM and its usefulness, we assert

that standardizing the racks is something we want to do. Hence, for each cluster we are looking for a rack

that alone or in a series can fit into all the separators in the cluster.


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Design

Plate Fabr. tooling

Unit Fabrication

Cut circular

Cut holes

Plate Fabr. Line 1

Plate Fabr. Line 2

Asmb. Line tooling

Rack Asmb. Line 1

Rack Asmb. Line 2

Tooling Installation

Installing Racks

Rack Fabrication

Rack Setup

Rack Installation

AL 2 Time

AL 1 Time

System Time

A s s e m b l y

L e v e l 1

A s s e m b l y L e v e l 1

Figure 5-11

The Partitioned Baffle Plate / Rack Realization Process

End Space

Rack Length

Separation Length

Figure 5-12

The Plate Rack Standardization Concept


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This concept is illustrated in Figure 5-12 where we assume that the end space has to be positive and less

than 2.5 times the plate spacing. Hence, we are looking for the rack length that satisfies the end space

requirement for all the separators in each cluster.

5.3.4 Step II.4 – Model Relationships

Knowing the processes and the design rules, the relationships between the design parameter

settings and the operational performance, cost and time are established. First of all, the values for fixed

design variables and relevant process variables are given in Table 5-10, calibrated to give a unit cost of

USD 12 500 per plate which is the nominal industrial standard. This is based on the assumption that all

cost incurred during Assembly Level 1 is charged to the first plate.

Table 5-10The Nominal Values for Fixed Design and Process Parameters

Variable Name Value Dimension and description

D_sep 2 [m] separator inner diameter

Th_bfl 4 [mm] baffle plate thickness

Rho_steel 7850 [kg/m 3̂] specific weight of steel

T_dsign 40 [mh/pl] nominal design time charged to each plate

T_tool_plte 8 [mh/pl] nominal retooling time charged to each plate - hole cutting

T_tool_rack 8 [mh/dsgn] nominal retooling for each assembly (rigging etc.)

T_tool_inst 8 [mh/dsgn] nominal retooling for each installation

dT_fabr_disc 1 [mh/pl] nominal cutting time charged to each plate -

dT_fabr_hole 8 [sec/hole]nominal drilling time – based on 14 hr to drill 6111 holes

dT_asmb 8 [mh/pl] nominal time to assemble each plate onto rack

dT_rack_setup 4 [mh/rack] nominal time to setup for new rack assembly

T_rack_inst 8 [mh/rack] nominal time to install one rack with all plates

R_dsign 125 [UDS/mh] nominal rate for design resources

R_fabr 200 [USD/mh] nominal rate for fabrication resources

R_steel 10 [USD/kg] nominal rate for high grade steel (purchase)

I_waste 0.2 [-] index of waste; area exceeding a square plate minus a cut-out circle

I_work 8 [hr/day] workday index

N_sep 3 [#] number of separators for each train


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N_cust 10 [#] number of customers in study

For AL1 the operational performance is given in terms of the flow velocity through the plate

perforations and the weight of each plate. The flow velocity through the plate perforations ( F_bfl ) is

measured relative to the velocity between the plates and given as times the between-plate-velocity. The

weight of each plate (W_bfl ) is given in kilograms. The design and retooling time is discounted according

to Equation [5-3] to reflect that more standardization requires less design and retooling per plate for a

given production series. The size of the series used for this example problem is 30 designs, corresponding

to the 30 different plate designs that have been analyzed. The discount behavior is illustrated in Figure 5-

13.

Standardization Discounting(d i s c o u n t )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80 1.00#clusters / #designs [-]

D i s c o u n t i n g F a c t o r [ - ]

Figure 5-13

Design Time and Retooling Discounting Profile

This particular discounting profile is based on the assumption that the benefits of

standardization increase progressively with the degree of standardization. However, the maximum

discount is assumed to be no more than about a third of nominal – standardization will not reduce the

time to zero. Based on this the following relations for AL1 are established.

Steel expenditure per plate:

) _ 1( _ _ 1000

_ _

2

waste I steel Rhobfl Th sep D

steel E +⋅⋅= [kg] [5-1]

Number of baffle plate designs:

cust N sep N dsign N _ _ _ ⋅= [#] [5-2]

Standardization discounting:


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5.11 _

_

4sin5.2 −

+⋅=

dsign N

clstrs N discount

π [-] [5-3]

Number of holes to be drilled:

2

2

)1000/ _ (

_

100

_ _

hole D

sep D perf Aholes N = [#] [5-4]

The discounted design time:

discount dsignT dsigndT ⋅= _ _ [mh] [5-5]

The discounted plate tooling time:

discount pltetooll T pltetool dT ⋅= _ _ _ _ [mh] [5-6]

The unit plate fabrication time:

3600

_ _ _ _ _ _ _

holes N hole fabr dT disc fabr dT plte fablr dT ⋅+= [mh] [5-7]

The weight of the baffle plate:

100

_ 100 _

1000

_

4

_ _

2 perf A steel Rho

bfl Th sep Dbfl W

−= π [kg] [5-8]

The flow velocity increase through plate perforation:

perf Abfl F

_

100 _ = [times the velocity between plates] [5-9]

The Assembly Level 1 time:

work I plte fabr dT pltetool dT dsigndT bfl T _ /) _ _ _ _ _ ( _ ++= [days] [5-10]

The Assembly Level 1 cost: steel R steel E fabr R plte fabr dT pltetool dT dsign RdsigndT bfl C _ _ _ ) _ _ _ _ ( _ _ _ ⋅+⋅++⋅=

[USD/plate][5-11]

For AL2 the operational performance is still given in terms of the flow velocity through the

plate perforations and the weight of each rack. The flow velocity through the plate perforations ( F_bfl ) is

unchanged from AL1, while the weight of each rack plate (W_rack ) is given in kilograms. The Rack

Tooling and the Installation Tooling times are also discounted according to Equation [5-12] to reflect that

more standardization requires less retooling per plate / rack for a given production series. In addition, the

installation time per rack is discounted according to Equation [5-12] to reflect that smaller racks are more

maneuverable and easier to handle. He behavior of Equation [5-12] is illustrated in Figure 5-14.

The particular discounting profile shown in Figure 5-14 is based on 20 baffle plates for a

separator. In the base case situation (one rack with twenty plates) there is no discounting. In the extreme

case where there is twenty racks with one plate each, the time of installing one of these racks is assumed

to be 10% of the base case twenty plate rack. Based on this, the following relations for AL2 are

established.


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Standardization Discounting

(discount_rack)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

0 5 10 15 20

#racks [-]

D i s c o u n t i n g F a c t o r [ - ]

Figure 5-14

Rack Installation Discounting Profile

The discounting factor for rack installation time:

1.0) _ _ (1 _

9.0 _ +−

−= rack N plate N

plate N rack discount [-] [5-12]

The discounted rack tooling time:

discount rack tool T rack tool dT ⋅= _ _ _ _ [mh] [5-13]

The discounted installation tooling time:

discount inst tooll T inst tool dT ⋅= _ _ _ _ [mh] [5-14]

The discounted rack installation time:

rack discount inst rack T inst rack dT _ _ _ _ _ ⋅= [mh] [5-15]The total number of plates in a separator:

1 _ _ _ _ _ +⋅= rack N rack pr plate N plate N [#] [5-16]

The weight of each rack

bfl W plate N rack W _ _ _ ⋅= [kg/rack] [5-17]

The fabrication time of all plates (circular and holes): fabr dT

N plteT _ _

2

_ _ _ = [5-18

The rack assembly time

)1( _ _ _ _

_ _ _ ⋅++= N setupdT rack asmbdT N

rack dT rack T

[mh]

19]


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The rack installation time:

rack inst rack inst tool inst rack _ _ _ _ _ _ _ ⋅+ [mh] 20]

:work I inst rack T rack fabr T rack T _ /) _ _ _ _ ( _ += [days] [5-21]

The Assembly Level 2 cost:

C_rack = (dT_tool_rack + N_plate*(dT_fabr_plte + dT_asmb) +

dT_rack_setup*(N_rack-1) + T_inst)*R_fabr +

N_plate*E_steel*R_steel [USD]

[5-22]

The Total System Time:

work I plte fabr dT rack T bfl T syst T _ / _ _ _ _ _ −+= [days] [5-23]

The Total System Cost:

C_rack = C_bfl + C_rack - (dT_fabr_plte*R_fabr + E_steel*R_steel) [USD] [5-24]

The relations establish in Equation [5-1] through [5-24] all contributes to calculate the

operational performance in terms of flow velocities and weight, and the time and cost for each TL. Hence,

even if TL does not take part as an ‘active’ parameter in the calculations, it is still the parameter we are

seeking to find.

5.3.5 Step II.5 – Formulate c-DSP

Knowing the relationships between the input parameters and the parameters used to evaluate

the overall performance of the system, an integrated model is established. It is hypothesized that

formulating a set of compromise DSPs enables multi-objective solving of the model, and hence, facilitates

a systematic and sound search for robust and flexible solutions. This is initiated by establishing the system

goals.

We have already defined the operational performance as flow-velocity increase and weight.

Assuming that each made-to-order separator is optimized with respect to operational performances rather

than with respect to cost and time, we assert that no deviations from the base case operational

performance are wanted. Similarly, we have already stated that the whole purpose of introducing product

platforms is to reduce time and cost without compromising operational performance too much. However,

the question “How much reduction are we aiming for?” remains. Since we are solving for minimum

deviation from all goals, this becomes a somewhat tricky choice. Some goals are purposely set to be

impossible to achieve in order to let the system stretch towards it, e.g., zero cost and / or time. However,

too ambitious goals gives deviations that are not balanced compared to other deviations, and a situation of


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dominance in the objective function may occur. Hence, it is important to choose goals consciously. For

this example study, we have chosen to aim for a 100% reduction in both cost and time in order to be on

the safe side not to actually reach the goals – after all we don’t know how the system behaves up-front.

Based on this the goal formulations, the deviation functions, and the objective functions are

and MINIMIZE.

GIVEN

percentage of perforated area, plate spacing, and separating lengths (see Figure 5- ):

7

The nominal values of the fixed design and process variables:

– See Table 5-10

Relationships between input parameters and operational performance, time and cost

– See Equation [5-1] through [5-24]

FIND

– TL for Assembly Level 1

– TL for Assembly Level 2

Deviations from goals for individual plates (AL1)

Flow velocity deviations

) _ 1()1( _

)( _ 1 Goal FlowTLvelocity Flow

TLvelocity Flowd AL

F −−

== [ – ] [5-25]

Plate weight deviations:

) _ 1()1( _

)( _ 1 Goal Weight TLweight Plate

TLweight Plated AL

W −−== [ – ] [5-26]

Plate time deviations:

) _ 1()1( _

)( _ 1 Goal TimeTLTime Plate

TLTime Plated ALT −−=

= [ – ] [5-27]

Plate cost deviations:

) _ 1()1( _

)( _ 1 Goal Cost TLCost Plate

TLCost Plated AL

C −−

== [ – ] [5-28]


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Deviations from goals for the system, i.e., for the plate racks (AL2)

Flow velocity deviations:

(see Equation [5-25])

System weight deviations:

) _ 1()1( _

)( _ 2 Goal Weight TLweight System

TLweight Systemd AL

W −−

== [ – ] [5-29]

System time deviations:

) _ 1()1( _

)( _ 2 Goal TimeTLTimeSystem

TLTimeSystemd ALT −−=

= [ – ][5-30]

System cost deviations:

) _ 1()1( _

)( _ 1

Goal Cost TLCost System

TLCost System

d

AL

C −−==[ – ]

[5-31]

SATISFY

Design Goals:

– Keep flow velocities as is Flow_Goal = 0.00 [ – ]

– Keep weight as is Weight_Goal = 0.00 [ – ]

– Cut delivery time by 70% Time_Goal = 1.00 [ – ]

– Cut delivery cost by 70% Cost_Goal = 1.00 [ – ]

MINIMIZE

Minimize deviations from goals by the Archimedean formulation

ZAL1

(d - ,d

+) = W_cost · d

AL1C + W_time · d

AL1T + W_flow · d

AL1 F + W_weight · d

AL1W [ – ]

ZAL2(d - ,d +) = W_cost · d AL2C + W_time · d AL2

T + W_flow · d AL2

F + W_weight · d AL2

W [ – ]

This concludes the modeling, and we proceed to the next phase where this model is solved by

enumeration. For further reference, the computerized model is given in Appendix B. In order to find a

specific part of the model, please see Figure B-2.


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5.4 EXEMPLIFICATION OF PHASE III: SOLVE

In this section, Phase III of the HPPRM is exemplified based on the model established in Phase

II. First of all, the scenarios to be considered are established in Section 5.4.1. Then each of these scenarios

is solved and the results are given in Section 5.4.2. Based on the obtained solutions, a decision is made in

Section 5.4.3 regarding a Hierarchical Product Platform for the separator example problem. Finally, the

solution is critically evaluated in Section 5.4.4 in terms of its usefulness. The computer code is given in

Appendix B, see Figure B-2.

5.4.1 Step III.1 – Establish Scenarios

A scenario is a particular variant of the problem that corresponds to a specific type of

customers, represented by a set of relative importance’s attributed to each goal. Examples on customer

types could be those who are very concerned about weight for various reasons and hence, would

emphasize having a solution that is as light as possible. Another customer type are those who are very

concerned about delivery time, and so forth. The intention of solving for several scenarios is to get the

right kind of insight that will support a decision regarding standardization. Hence, the purpose of

standardization is guiding us when establishing scenarios. The chosen scenarios for this example problem

are given in Table 5-11.

Table 5-11

Scenarios Representing Various Customer Types

Scenario Descr iption W_flow W_weight W_time W_cost

1 Base-Case Scenario 0.25 0.25 0.25 0.25

2 Critical Thermodynamics Scenario 1.00 0.00 0.00 0.00

3 Critical Stability Scenario 0.00 1.00 0.00 0.00

4 Critical Path Scenario 0.00 0.00 1.00 0.00

5 Critical Economy Scenario 0.00 0.00 0.00 1.00

6 Marginal Field I 0.00 0.00 0.50 0.50

7 Marginal Field II 0.00 0.00 0.67 0.33

8 Marginal Field III 0.00 0.00 0.33 0.67

Scenario 1, the “Base-Case” Scenario, is solved to get a reference solution. This reference

solution can be used to evaluate how the goals impact the solution and to get a feel for what direction each


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goal is pulling the solution in. Based on the information about these directions, the reference solution

gives a good indicator of which goals are dominating and which are being dominated.

Scenarios 2 through 4 are solved to get a feel for what solutions are preferred in order to satisfy

each goal completely. As indicated, this is valuable information since it reveals whether some goals are

being dominated in the objective function. Further, by giving the extremes in each goal-direction it spans

and bounds the solutions space.

Scenarios 6 through 8 are solved assuming the deviations in operational performance are

acceptable, hence, focusing only on reducing cost and time. This is done by varying the relative

importance of cost and time in a systematic fashion to get a feel for each of the goal’s power to dominate

the solution.

The information that is obtained from running all these scenarios is used to gain appreciation

about the standardization problem. As indicated earlier, we are looking for robust and flexible solutions,

hence, we try to evaluate which solutions are least affected by varying weighting schemes since we cannot

be sure what the future will bring. This is elaborated in Section 5.4.3 upon making a decision.

5.4.2 Step III.2 – Solve for each Scenario

As already indicated the solution is found by enumeration, i.e., we are solving for all 900

(30x30) combinations of TL as is illustrated in Figure 5-15. For each new combination of TL(AL1) and

TL(AL2) there is exactly one new cluster being formed at each AL. For the particular AL1 cluster, the

plates are standardized according to the rules given in Section 5.3.3, and the ‘fitness’ is calculated

according to the current scenario. For the particular AL2 cluster, the racks are standardized by selecting

the fittest plate and by standardizing the spacing and rack-size according to the design rules given in

Section 5.3.3. Then the rack fitness is calculated according to the current scenario before the fitness of the

entire population (all OTUs) is calculated for this particular TL combination. This closes the loop; pick a

new TL combination.


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Set TL for Plates (AL1)Set TL for Plates (AL1)

Standardize Plate Variables (AL1):

Hole-diameter and Perforation Area

Standardize Plate Variables (AL1):

Hole-diameter and Perforation Area

Calculate Plate Fitness (AL1):ZAL1(d - ,d +) = W_cost · d

C + W_time · d

T +

W_flow · d F + W_weight · d W

Calculate Plate Fitness (AL1):ZAL1(d - ,d +) = W_cost · d C + W_time · d T +


Calculate Rack Fitness (AL2):

ZAL2(d - ,d +) = W_cost · d C + W_time · d T +


Calculate Rack Fitness (AL2):

ZAL2(d - ,d +) = W_cost · d C + W_time · d T +


Set TL for Racks (AL2)Set TL for Racks (AL2)

Standardize Racks (AL2): Standardize Racks (AL2):

Select most fit plate (AL1)Select most fit plate (AL1)

Standardize Rack Variables (AL2):

Plate-spacing and Rack-sizes

Standardize Rack Variables (AL2):

Plate-spacing and Rack-sizes

Set Scenario:

W_cost , W_time , W_flow , W_weight

Set Scenario:

W_cost , W_time , W_flow , W_weight

Calculate Population Fitness (AL2):

ZPOP = ΣΣ ZAL2 / #OTUs

Calculate Population Fitness (AL2):

ZPOP = ΣΣ ZAL2 / #OTUs

Figure 5-15

Solution Algorithm


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Now let’s take a look at some results beginning with illustrating how the clustering affects the

AL1 design parameters.

(a) (b)

Figure 5-16Standardization of Baffle Plate Design

X-axis = Different Plates, Y-axis = Taxonomic Level

Z-axes: (a) Hole-Diameters [mm], (b) Perforated Area [%]

As can be seen from Figure 5-16 the hole-diameters are being maximized as TL(AL1) increases (i.e., for

increasing degree of standardization). Likewise we can see that the perforated area percentages are being

minimized. Together with the maximized hole-diameters, this minimizes the number of holes to be drilled

and hence, minimizes the fabrication time of a unit plate. This is reflected in the reduction in time, cost

and objective function values as standardization increases. This is illustrated in Figure 5-17 where we see

the smooth decrease that corresponds well with the discounting function given in Figure 5-13.

(a) (b) (c)

Figure 5-17Performance of Baffle Plates

X-axis = Different Plates, Y-axis = Taxonomic Level

Z-axes: (a) Time [days], (b) Cost [USD], and (c) Objective Function [–]


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As for standardizing plate racks, the clustering effects are illustrated in Figure 5-18. The

parameters shown are the spacing which is minimized within each cluster, and the number of racks per

separator which is ‘tailor-made’. As the spacing decreases across the cluster, some separators end up with

more plates than they strictly need, hence, increase their production time. As the rack numbers increases,

the installation time is significantly affected, hence, this is a good indicator for predicting where the

clustering starts to be less beneficial. From Figure 5-18 (a) we see that the spacing does not really

compromise until the very last clustering at TL29, where the LP separator plate-racks are joined with the

IN / HP separator-plate-racks. Further from Figure 5-18 (b) we see that the racks are not starting to split

up until TL(AL2) = 14. Hence, we would expect beneficial rack standardization up till then.

(a) (b)

Figure 5-18

Standardization of Plate Rack Design

X-axis = Different Racks, Y-axis = Taxonomic Level

Z-axes: (a) Plate Spacing [mm], (b) Number of Racks per Separator [#]

The effect that rack standardization has on system performance is illustrated in Figure 5-19 in

terms of time, cost and objective function. The system performance is the combination of unit plate

performances and rack performances, where the rack performances cannot be calculated unless a plate has

been specified. Hence, the performance at AL2 for each TL is a function of TL(AL1).

The fact that the rack performance for each TL is a function of plate performance at a given

TL, is illustrated by showing two particular ‘snap-shots’ – one for TL(plate) = 15 and one for TL(plate) =

30 – where the performances varies. This is clearly seen in Figure 5-19 (a) and (b) where the starting

times for design 16 through 20 decreases from around 20 days to 15 days. Further, the clear dependency

between time and cost indicates that time related costs totally dominate material related costs for this

separator example. Hence, focusing on improving the process specified in Figure 5-11 may become very

beneficial. This is to be addressed in research concerning Hypothesis 2; how to evaluate alternative

processes.


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(a) TL(plate) = 15 (b) TL(plate) = 30

(c) TL(plate) = 15 (d) TL(plate) = 30

(e) TL(plate) = 15 (f) TL(plate) = 30

Figure 5-19

The System Performance

X-axis = Different Racks, Y-axis = Taxonomic Level

Z-axes: (a+b) Time [days], (c+d) Cost [105 USD], (e+f) Objective Function [–]


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By looking at the objective function in Figure 5-19 (e) and (f) a question emerges: how to

aggregate this information to make it suitable for supporting a standardization decision? This becomes

even more of a question since the surface varies with TL(AL1). Hence, for each unique combination of

TL(AL1) and TL(AL2) there is a unique objective function value for each standardized design, and we

want to capture the combination of TL(AL1) and TL(AL2) that makes the entire ‘population’ most fit,

i.e., more competitive. So what is best from a company perspective? It is asserted that it is better to offer

many customers new products that are slightly better than the old products, than offering a few customers

new products that are much better than the old ones.

How can we find this combination? One strategy is to average the system objective function

values across all standardized designs for a certain TL(AL1) and TL(AL2) combination. This is referred

to as the mean population fitness, and the danger of using this mean population fitness is that it may be

misleading since a few customers may get very fit products pulling the average up, whereas the majo

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