fpso chapter v
TRANSCRIPT
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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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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
Qualitative: reasoning
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.
Qualitative: reasoning
through viewpoints
Low
Phase III: SOLVE
Establish Scenarios Subjective, i.e., many correct
answers
Qualitative: reasoning
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.
Qualitative: reasoning
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 [% ]
T a x o n o m i c L e v e l s ( T L )
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]
T a x o n o m i c L e v e l s ( T L )
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]
T a x o n o m i c L e v e l s ( T L )
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 +
W_flow · d F + W_weight · d W
Calculate Rack Fitness (AL2):
ZAL2(d - ,d +) = W_cost · d C + W_time · d T +
W_flow · d F + W_weight · d W
Calculate Rack Fitness (AL2):
ZAL2(d - ,d +) = W_cost · d C + W_time · d T +
W_flow · d F + W_weight · d W
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