Cost Modelling Deepwater Production Units

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Cost modelling of deepwater oil and gas facilities: A case study of spars andtension leg platformsC. Jablonowski a; A. Strachan b

a Department of Petroleum and Geosystems Engineering, the University of Texas at Austin, Austin, USA b

Wood Mackenzie Canada Ltd, Calgary, Canada

First Published:March2009

To cite this Article Jablonowski, C. and Strachan, A.(2009)'Cost modelling of deepwater oil and gas facilities: A case study of sparsand tension leg platforms',Ships and Offshore Structures,4:1,69 — 76

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Ships and Offshore StructuresVol. 4, No. 1, 2009, 69–76

Cost modelling of deepwater oil and gas facilities: A case study of spars and tension leg platforms

C. Jablonowskia∗ and A. Strachanb

aDepartment of Petroleum and Geosystems Engineering, the University of Texas at Austin, Austin, USA;bWood Mackenzie Canada Ltd, Calgary, Canada

(Received 15 February 2008; final version received 23 July 2008)

Cost models for deepwater oil and gas facilities can be valuable tools for concept comparison and selection, field developmentplanning and optimisation, and benchmarking performance. This study estimates simple cost models for spar and tension legplatform projects using public and private data on 24 major projects. In addition to providing an analysis of the variables thataffect cost, the study investigates the complexity of model specification. We evaluate sensitivity to modelling assumptions,sample selection bias and other model specification issues which can lead to improper conclusions.

Keywords: cost models; regression analysis; sample selection; spars; tension leg platforms

1. Introduction

Cost models for deepwater oil and gas facilities have a vari-ety of uses. Cost models can be employed early in prospectdevelopment to estimate expected lease values, to preparebidding strategies and to select prospects and manage theportfolio. As exploration prospects mature into defined de-velopment projects, cost models can be used to inform con-cept comparison and selection, to aid in field developmentplanning and optimisation and to benchmark projected andactual costs.

Given these virtues, it is surprising to find so little inthe offshore production facility literature on empirical costmodels or on cost-modelling methods.1 We believe that theprimary causes of this gap are (i) the proprietary natureof cost and technical data that greatly increases the effortrequired to collect the data for detailed models and (ii) theunderlying nature of the facility selection decision processthat results in a non-trivial sample selection problem.2 Weaddress both of these issues in this study. Firstly, we useprivate cost data carefully organised by industry expertsbased on public information and interviews with operatingcompanies. The specifications are parsimonious, allowingus to use publicly available technical data, but without asacrifice in model explanatory power. Secondly, we definea constrained facility choice model that facilitates diagnosisand treatment for sample selection.

∗Corresponding author. Email: [email protected] that examine design optimisation and cost estimating for specific technologies and/or projects are abundant (see for exampleBrooks and Carroll (1994), Zimmer (1994), and Stokes et al. (1996)). The gap we are referring to is in the area of aggregated analysisacross projects; the most recent published study known to the authors is Karlik (1991).2Sample selection problems in statistics and regression analysis occur when the sampling is not random. In this case study, the samples ofspars and TLPs are the result of a selection process assumed to be based on profit maximisation. Therefore, the observations cannot beconstrued as a random sample and additional computations are required to correct for this feature of the data.

This case study estimates cost functions for spars andtension leg platforms (TLPs) using data from 24 completedprojects. A two-stage regression model is specified thataccounts for the underlying facility selection process. Theremainder of this study is organised as follows. Section2 provides a brief overview of oil and gas projects andproduction facility selection, Section 3 specifies a completeregression model of facility choice and cost that accountsfor sample selection bias, Section 4 defines the independentvariables and describes the data set and Section 5 providesa conclusion.

2. Offshore oil and gas projects and productionfacility selection

The general progression of an offshore oil and gas projectbegins when an oil company acquires exploration andproduction rights from the host government. The oilcompany drills exploration and appraisal wells based ongeological data and analysis. If economic quantities of hy-drocarbons are discovered, the prospect is developed withadditional production wells and associated surface- andsubsea-production facilities. A recent overview of theproject development and stage-gate project managementsystems as applied in the oil and gas industry is availablein Walkup and Ligon (2006).

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70 C. Jablonowski and A. Strachan

In deepwater settings, the selection and configurationof production facilities is critical because of high costs andthe quasi-irreversible nature of the initial capital investment.The analysis of competing options, or concept selection, isoften complicated because several different production fa-cility types and configurations are feasible for a specificproject, and there is often considerable uncertainty regard-ing subsurface and other project attributes. The conceptselection process typically consists of numerous scenarioand sensitivity analyses of the competing options. Under-standing the concept selection process is relevant to costmodelling. At first, this link may not be obvious, but therelationship and implications will be made clear in the spec-ification of the cost models in Section 4.

In this study, we examine 24 deepwater projects whereeither a spar or a TLP was ultimately selected as the primaryproduction facility. As shown in Figure 1, these projectsspan a wide range of water depths and reserves (as measuredin million barrels of oil equivalent), and there is a substantialoverlap in the feasibility of the two production technologies.While in very deep water, spars appear to hold an advantage,and in the largest reserve cases, TLPs appear to dominate;this observation does not exclude the possibility that thealternate concept is technically feasible if not economicallycompetitive. Similar overlap is observed when the data isplotted using other project attributes. For these reasons,we assume that for all of these projects, both spar- andTLP-production facilities were considered during conceptselection.

3. Model specificationA model of the decision to employ a spar or a TLP thataccounts for the underlying cost functions of each optionis specified. A latent (unobservable) variable y∗

i is definedwhich indicates that the propensity to employ a TLP onproject i:

y∗i = Ziγ + ui. (1)

However, y∗i is not observable; instead, one observes yi ,

which takes on values of 0 (spar) or 1 (TLP) according tothe rule:

yi ={

1, if y∗i > 0

0, otherwise, (2)

where Zi is vector of prospect attributes, γ is vector ofcoefficients for prospect attributes and ui is random errorterm, ∼ N (0, σ 2).

From here one can derive the standard binary probitmodel:

Pr (yi = 1) = Pr(y∗

i > 0)

Pr (yi = 1) = Pr (ui > −Ziγ ) (3)

Pr (yi = 1) = Pr

(ui

σ> −Zi

γ

σ

).

Dividing by σ in Equation (3) is convenient because thequantity ui/σ is distributed as standard normal (zero mean

0

500

1000

1500

2000

0 50 100 150 200 250 300 350 400 450 500

Reserves (mmboe)

Wat

er D

epth

(m

)

TLP Spar

Figure 1. Distribution of spar and TLP projects by water depth and reserves (24 projects).


Ships and Offshore Structures 71

and unit variance).3 This leads to the following result:

Pr (yi = 1) = �(Zi

γ

σ

)and therefore, Pr (yi = 0)

= 1 − �(Zi

γ

σ

), (4,5)

where � (•) is the cumulative density function of the stan-dard normal distribution. If there are n observations in total,the likelihood function L for the sample is

L = n

�i=1

[1 − �

(Zi

γ

σ

)]1−yi[�

(Zi

γ

σ

)]yi

(6a)

For purposes of optimisation, the log-likelihood func-tion ln(L) = l is often employed:4

l =n∑

i=1

{(1 − yi) ln

[1 − �

(Zi

γ

σ

)]+ yi ln

[�

(Zi

γ

σ

)]}(6b)

A complete model of the facility selection decision ispossible, based on the underlying costs of each developmentconcept. The decision maker develops expectations of thesecosts during concept selection, based on intrinsic prospectattributes and design criteria for each option. This can berepresented as follows:

Cost of spar-based project = Si = X1iβ1 + e1i (7)

Cost of TLP-based project = TLPi = X2iβ2 + e2i , (8)

where Xi is a vector of independent variables for projecti, β is a vector of coefficients and the ei’s are uncorrelatedrandom error terms, ∼ N

(0, σ 2

). All that is typically ob-

served, however, because data availability (the present caseis no exception) is the eventual choice of facility, yi :

yi ={

1, if TLPi < Si

0, otherwise.(9)

Recall the variables of the function for the unobservedlatent variable, y∗

i = Ziγ + ui . A binary choice model,such as the probit, based only on the observed organisa-tional choice is straightforward but only informs on therelative difference in the coefficients of the underlying cost

3The quantity ui

/σ is standard normal because ui has been trans-

formed by subtracting its mean and dividing by its standard devi-ation.4The log-likelihood function is globally concave and is maximisednumerically. The asymptotic covariance matrix is computed byevaluating the negative inverse of the Hessian at the maximumlikelihood estimates. Also observe that γ and σ are not individ-ually identified; therefore, it is convenient to normalise σ to beone.

equations. That is

Pr (yi = 1) = Pr (TLPi < Si)

= Pr (X2iβ2 + e2i < X1iβ1 + e1i)

= Pr (e2i − e1i < X1iβ1 − X2iβ2) . (10)

If X1 and X2 have common elements and if there is un-certainty about the effect of a specific independent variable,even a very general interpretation of this model’s results be-comes difficult. Therefore, a different approach is requiredif one is to properly estimate coefficients in Equations (7)and (8).

When one can observe costs, the cost equations canbe estimated directly. Such estimates, however, suffer fromselectivity bias because one cannot observe costs for theoption not selected. To show this, examine the expectationof the error term of Equation (7):

E (e1i |ui < −Ziγ ) = E(σe1,uui |ui < −Ziγ

)= −σe1,u

(φ (−Ziγ )

� (−Ziγ )

)= −σe1,uλ1i ,

(11)

where φ and � are the probability density function (pdf) andcumulative density function (cdf) of the standard normaldistribution, respectively. Similarly,

E (e2i |ui > −Ziγ ) = σe2,u

(φ (Ziγ )

� (Ziγ )

)= σe2,uλ2i

(12)Therefore, estimating cost models without accounting

for the selectivity bias would be inappropriate, unless it isshown that the bias is insignificant. A summary of theseresults and the underlying statistics is available in Maddala(1983).

Results from the first stage facility choice estimation(γ ) can be used to compute the expected bias for each ob-servation, λi . This new variable is added as a regressor toEquations (7) and (8), where its coefficient is an estimateof σe1,u and σe2,u. This family of two stage models is gener-ally attributed to Heckman (1979). Examples of empiricalstudies employing this general approach are Masten et al.(1991), who examine organisational choice in shipbuild-ing, and Jablonowski and Kleit (2006), who examine thedecision to execute offshore drilling projects internally orto use turnkey. In this study, the dependent variable in thecost models is the total project cost, which includes thehost facility, the subsea system and the initial developmentwells.



4. Data collection and diagnosticsThe dependent variable in the cost models is the totalproject cost. The cost data was obtained from a privatedatabase of E&P projects maintained by a global E&P con-sulting practice in project analysis and economics.5 Allspars and TLPs included in the final data set were lo-cated in the US Gulf of Mexico and were installed be-tween 1986 and 2006. Costs were adjusted to constant 2006US dollars.6 Costs were assumed to occur in equal annualamounts between the start and the end year of project de-velopment. More refined cost adjustment is possible, butit requires itemised costs, detailed information about thetiming of capital spending, and drilling schedules and rigsused. An investigation by the authors into the feasibilityof organising such a database concluded this effort to beprohibitive.

The independent variables for the model (choice andcost functions) that are believed to influence the cost and thechoice of the production facility are now defined. This listis not comprehensive of all potential independent variables(we are constrained by the availability of data), but webelieve the most important variables are captured in thisdata set.

Water depth is defined as the water depth at the site ofthe host facility measured in metres. The primary impactof water depth is on the cost of TLP tendons and the costof mooring-related components for both facility types.

Oil rate is defined as the maximum oil production de-sign rate (nameplate) of the facility measured in thousandbarrels per day (mbopd). Gas rate is defined as the maxi-mum gas production design rate of the facility measured inmillion cubic feet per day (mmcfpd). Higher design ratesresult in more piping, tanks and related production equip-ment, thus increasing the topside weight and the cost of theproduction facility.

Topside weight is primarily a function of maximum to-tal liquids design rate (oil plus produced water). But waterproduction rates tend to increase as oil production rates de-crease, and the maximum design rates for oil and producedwater are typically not occurring simultaneously. Therefore,using both maximum design rates to model cost will beinappropriate in most cases. Our approach is to use themaximum oil production rate as a proxy for maximum totalliquids design rate.7

5Cost data obtained from Wood Mackenzie, Houston, Texas.6Costs adjusted using the US Department of Commerce ProducerPrice Index for Oil and Gas Field Machinery and Equipment,Series ID: PCU333132333132.7We do not use maximum total liquids design rate directly be-cause of problems validating some of the water production ratedata. Based on validated data, we find high correlations betweentopsides weight and oil rate, typically greater than 0.85, and weconclude that oil rate is an acceptable proxy for total liquids designrate.

Slot count is defined as the number of well slots avail-able on the host platform for dry trees.8 As the slot countincreases, additional space and weight capacity are required,increasing the size and the cost of the production facility.

Rig type is a binary variable that takes on a value of1 when an integrated drilling rig is included in the facilitydesign and 0 otherwise. Deepwater production facilities canbe built with an integrated drilling or workover rig,9 or withthe capability to host a temporary drilling or workover rig,either wholly on the platform or via tender-assist. When anintegrated drilling rig is included in facility design, costsincrease relative to all other platform-based rig options.

Spar type is a binary variable that takes on a value of 1when the design is a classic spar and 0 otherwise. The choiceof the spar type influences performance characteristics andcost.

Reserves is defined as the estimated reserves that areto be produced through the host facility from the primaryreservoirs measured in million barrels oil equivalent (mm-boe). Large fields can produce at higher rates, all thingsbeing equal, and this affects the choice of facility type,production capacities and cost.

Topside weight is defined as the weight of the deck andproduction facilities measured in metric tons (mt). Topsideweight is primarily a function of the quantity of steel em-ployed. As topside weight increases, there is a direct effecton the cost of the topsides and an indirect effect on the sizeand cost of the hull.

Data on the independent variables was obtained fromNutter and Albaugh (2005, 2006) and from the operat-ing company and other industry websites. Different datasources occasionally contain conflicting data. Reasonableeffort was made to confirm all data. If a data entry couldnot be confirmed across multiple sources, the observationwas excluded from the final specifications. Summaries forthe spar and TLP data sets are reported in Tables 1 and 2.

Correlation among the independent variables increasesthe potential for collinearity-related estimation problems.In the spar data, for example topside weight is correlatedwith oil rate (0.85), rig type (0.96) and reserves (0.90). TheTLP data exhibit a similar structure. Tables 3 and 4 re-port the correlation coefficients for the spar and TLP data.Choosing which variables to retain and which to excludeis not an exact science. One must compare the theoretical

8When a wellhead is located on the host platform, it is called a drytree. Access to the well for maintenance and remedial operationsis accomplished using a drilling or workover rig located on theplatform. For reservoirs where frequent well interventions areanticipated, dry trees are generally preferred as is an integratedrig. When a wellhead is located on the seafloor, it is called awet tree. Access to the well is accomplished using a floating rig(e.g. semisubmersible rig). Because of the high cost and uncertainavailability of floating rigs, wet trees are generally preferred wheninfrequent well interventions are anticipated.9Supra.



Table 1. Summary of spar data (11 projects).

StandardVariable Units Type Mean Deviation

Total cost $2006 Continuous 694.2 280.0Water depth m Continuous 1105.2 348.9Oil rate mbopd Continuous 59.8 26.0Gas rate mmcfpd Continuous 154.1 80.3Slot count slots Continuous 11.5 5.1Rig type Binary 0.27Spar type Binary 0.27Reserves mmboe Continuous 160.0 81.8Topside weight mt Continuous 7529.1 4836.8

arguments for competing specifications and weigh the ben-efits of including additional independent variables againstthe costs of potentially degenerate results.10 This process ismore complicated when the sample size is small as it is inthis study. The final specifications reported here representa careful balancing of these issues. Because of collinear-ity problems, topside weight is excluded from all of thefinal model specifications. Reserves was considered in thechoice model but was ultimately excluded for collinearityand other reasons.

5. Analysis and results

In this section, we estimate the model as specified above,starting with the choice model and then use the results tocorrect for selectivity bias in the cost functions. The depen-dent variable in the facility choice model is binary, and ittakes on a value of 1 for projects where a TLP was installedand 0 for projects where a spar was installed. The appro-priate variables to include in the choice model are thosethat would be defined (fixed) in a design basis. An exampleof this type of variable is water depth. Variables that mayhave been different between competing concepts must beexcluded.11 This feature of the model complicates the spec-ification. We discuss a few variables in detail to demonstratethis point prior to defining the final specifications.

The number of well slots on the host facility, or slotcount, can be constrained by the spatial distribution of re-serves, that is if the reserves are dispersed across a widearea, fewer wells can be drilled from a common host.

10When highly correlated independent variables are included in aregression, the variances of the coefficient estimates tend to in-crease, resulting in low t-statistics. That is, two variables knownto positively influence the level of the dependent variable can befound to be statistically insignificant. Another awkward outcomemay assign opposite signs to the variables, canceling out theireffect. Thus, judging whether a regression result is reliable de-pends on the analyst’s knowledge of the technical relationshipsand experience.11This constraint results because we do not have data on designdetails for unselected production facility options.

Table 2. Summary of TLP data (13 projects).

StandardVariable Units Type Mean deviation

Total cost $2006 Continuous 806.5 459.4Water depth m Continuous 865.1 275.0Oil rate mbopd Continuous 75.6 53.8Gas rate mmcfpd Continuous 180.8 130.4Slot count slots Continuous 12.7 10.8Rig type Binary 0.31Reserves mmboe Continuous 161.0 164.4Topside weight mt Continuous 10,132.8 7977.7

Also, reservoir properties affect expectations regardingproduction problems and the frequency of well interven-tions, and this can constrain the slot count. While theseintrinsic prospect variables influence the slot count, theconstraints are not always binding, and in many casesthe operator can compare multiple configurations of eachtype of the production facility. In these cases, the slot countmay vary between competing concepts, and therefore itwould be inappropriate to include the actual slot count(from the selected option) in the choice model. Withoutintimate knowledge of each prospect, it is not possible toconclude definitively which condition (more or less con-strained) holds more often in practice. In the base case, weassume that the slot count is more often intrinsic to theprospect rather than a tradeoff variable, and we include itin the choice model.

Variables such as the total number of wells (dry and wettree) and production rates pose a similar problem. In manycases, the depletion plan for a field is highly constrainedby the spatial distribution of reserves and initial reservoirconditions. In such cases, there is little flexibility in thedepletion plan, and deviations result in significant losses inrecovery rates and project value. In other cases, the deple-tion plan may be more flexible, and the operator can assessvarious project scales for each concept; in these cases, itwould be inappropriate to include production rates in thechoice model for the reasons already cited. Again, it is notpossible to conclude from the data available which condi-tion holds more often. In the base case, we assume that oilrate and gas rate are more often intrinsic to the prospect,and we include both in the choice model.

Because of the high correlation between oil rate andreserves, we do not include both of these variables in thechoice model. Reserves would be the preferred variable toretain for the choice model because it clearly is intrinsic tothe project, and one would expect facility choice to dependon reserves as described in the definition of this variableabove. But in preliminary specifications, we found that thisvariable is generally not statistically significant. Our hy-pothesis for this result is twofold. One possibility is that theresult is sound, and reserves are in fact not significant. Asseen previously in Figure 1, there is a significant overlap in



Table 3. Correlation coefficient matrix for spar data (11 projects).

Water depth Oil rate Gas rate Slot count Rig type Spar type Reserves Topside weight

Water depth 1.00Oil rate 0.65 1.00Gas rate 0.43 0.36 1.00Slot count −0.21 0.21 −0.61 1.00Rig type 0.16 0.73 0.23 0.52 1.00Spar type −0.29 0.09 −0.01 0.35 0.54 1.00Reserves 0.49 0.88 0.46 0.17 0.78 0.20 1.00Topside weight 0.28 0.85 0.39 0.32 0.96 0.35 0.90 1.00

Table 4. Correlation coefficient matrix for TLP data (13 projects).

Water depth Oil rate Gas rate Slot count Rig type Reserves Topside weight

Water depth 1.00Oil rate 0.26 1.00Gas rate 0.54 0.47 1.00Slot count 0.13 0.57 0.57 1.00Rig type 0.29 0.49 0.67 0.53 1.00Reserves 0.34 0.87 0.68 0.75 0.52 1.00Topside weight 0.48 0.90 0.65 0.52 0.91 0.78 1.00

facility choice throughout the range of reserves. Even if arelationship exists, it may not be measurable in a statisticalsense. A second possibility relates to data quality. Acrossall sources, the data on oil and gas reserves is the most in-consistent of all of the variables in the study. Reserves datacan be highly proprietary and may not be reported in anunbiased manner. It is also frequently updated throughoutthe early stages of a project. For these reasons, we employedproduction rates instead of reserves.

Similar arguments, in addition to the aforementionedcollinearity issues, were evaluated for the remaining inde-pendent variables. The base case specification of the choicemodel contains four independent variables: water depth,oil rate, gas rate and slot count. We do not have theoreti-cally derived hypotheses for the signs of coefficients in thechoice model. But based on the distribution of projects inFigure 1, one might expect that the sign for water depthto be negative and the signs for oil rate and gas rate to bepositive.

The results of the choice model are reported in Table 5.Because there is a significant overlap in the technicallyfeasible range of applications, it is not surprising that theresults on individual variables are generally weak. The ex-ception is water depth, which appears to be the driver forfacility choice, all things being equal. We suspect that, givena larger data set, the significance of oil rate and gas ratewould increase. The coefficient signs also conform to theexpectations mentioned in the preceding paragraph. Whilethe likelihood ratio index (pseudo R2) is low at 0.24, themodel correctly predicts facility choice in 79% of the ob-

servations. We use this base case specification of the choicemodel to compute the expected selectivity bias.

As defined above, the dependent variable in the costmodels is the total project cost, including the host facility,the subsea system and the initial development wells. Inthe cost models, the expectation for the sign of all of the

Table 5. Regression results for choice model (binaryprobit).

Variable Coefficient t-statistic

Constant 1.8466 1.61Water depth −0.0029 −2.33Oil rate 0.0123 1.14Gas rate 0.0043 1.13Slot count −0.0383 −0.86

n = 24; Log likelihood = −12.54841; Likelihood ratio index= 0.24.

Table 6. Linear cost model (spars).


Intercept −258.8573 −1.35Oil rate 6.0876 3.40Gas rate 1.1419 1.70Slot count 30.4256 2.88Spar type 146.3163 1.78−σe1,u 33.8045 0.27

n = 11; R2 (adj) = 0.88.



Table 7. Linear cost model (TLP).


Intercept 54.8080 0.66Oil rate 3.1686 4.22Gas rate 1.2924 4.09Slot count 15.7242 4.30Rig type 121.7436 1.42−σe2,u 75.9172 1.05

n = 13; R2 (adj) = 0.95.

coefficients is positive.12 The results from the estimation ofEquation (7) for spars are reported in Table 6.

The overall fit of the model is good and yields an ad-justed R2 of 0.88. Oil rate and slot count are significantat the 95% level; gas rate and spar type are significant atthe 85% level. All coefficients have the expected sign. Theselection bias is not significant.

Water depth is excluded from the final regression be-cause it was found to be statistically insignificant acrossvarious specifications. The incremental cost of mooring indeeper water, while positive, is considerably smaller thanthe incremental cost of other project attributes and is notmeasurable in a statistical sense.

Rig type is excluded because of problems encounteredincluding it and oil rate in the same specification (the corre-lation coefficient between the two variables is 0.73). Also,the rig type and spar type variables are identical except fortwo observations, even though the correlation coefficient iscomputed to be 0.54 (this results because both variables arebinary, thus reducing the normal usefulness of the corre-lation coefficient in detecting collinearity). Given that oilrate and spar type exhibit a low correlation (0.09), rig typewas dropped. The results from the estimation of Equation(8) for TLPs are reported in Table 7.

The overall fit of the model is very good, yielding anadjusted R2 of 0.95. Oil rate, gas rate and slot count aresignificant at the 95% level; rig type is significant at the 80%level. All coefficients have the expected sign. The selectionbias is significant at the 70% level.

As it was the case in the spar regression, water depth isexcluded from the final regression because it was found tobe statistically insignificant across various specifications.This is a somewhat surprising result given the cost oftendons. Upon further inspection, however, we observe thattwo thirds of the TLP observations are clustered withina 300 metre range. This concentration of data, and thesmall number of observations, is the likely cause of thisresult.

The coefficients from each of these models can be com-pared directly. For example, the marginal cost of 1 mbopd

12There is no expectation for the sign of the selection bias coeffi-cient.

of oil capacity on a spar costs about $6 million, whereason a TLP the same capacity costs about $3 million. Themarginal cost of gas capacity is similar for each facility.Each additional well slot on a spar costs about $30 million,whereas on a TLP it costs about $16 million. Also, a classicspar design adds almost $150 million to the expected cost,and an integrated drilling rig on a TLP adds $122 million.Recall that costs are in 2006 US dollars. If the model is tobe used in a predictive mode, additional adjustment wouldbe required to account for recent increases in costs. From2006 to mid-2008, there has been a 16% increase in theindex used for adjustment in this study.

We can compare these results to cost models estimatedwithout the correction for the sample selection bias. Inthe case for spars, the differences in coefficient estimatesare insignificant. This is the expected result given thestatistical insignificance of the bias coefficient. In the casefor TLPs, the intercept term increases by 112% and thecoefficients for oil rate and rig type are reduced by 11%and 10%, respectively. The remaining coefficients areessentially unchanged. In most cases, the difference in theresiduals between the two models is small and would notbe material with respect to decision –making. But in manycases, it exceeds $20 million and the maximum differenceequals $85 million. If the sample selection bias is takento be significant, using the uncorrected model duringconcept selection could result in an incorrect decision. In abenchmarking setting, use of the uncorrected model couldlead to an incorrect assessment of the estimated or actualproject cost.

As an alternative to the base case, we also estimated achoice model using water depth as the only independentvariable. This model represents the opposing arguments tothose of the base case choice model, that is that productionrates and the number of slots are not intrinsic to the project.The results were then used to estimate the sample selectionbias and to estimate the cost functions. Notwithstanding therelatively weaker explanatory power of the variable choicemodel (71% correct predictions; likelihood ratio index =0.11), the results for the cost functions were very similarin all respects to the results based on the base case choicemodel. This suggests that in this setting, the arguments andassumptions regarding the appropriate variables to employin the choice model are not critical to the estimation ofthe cost functions. It is not clear whether this result canbe generalised, and we intend to investigate this questionformally in a future study.

6. Conclusions

This case study estimates cost functions for spars and TLPsusing data from 24 completed projects. A two-stage re-gression model is specified that corrects for the sampleselection bias by accounting for the underlying facility se-lection process. We find that the sample selection bias is



not a significant problem in cost models for spars, but itis potentially significant in cost models for TLPs. The cor-rected cost models are reported for both facility types andcan be used to value and select prospects, to inform con-cept comparison and selection, to aid in field developmentplanning and optimisation and to benchmark projected andactual costs.

The regression theory and technique employed in thisstudy are somewhat advanced, but engineers with somebackground and interest in statistics will be capable of im-plementing this approach. Also, these models are availablein most commercial regression packages. But specifyingmodels such as this is not a minor undertaking. The datarequirements are significant, and technical expertise andunderstanding of the decision being evaluated is required.Diagnostics during the preliminary regression stage are alsocritical and require some experience in applied regressionanalysis.

Acknowledgements

The authors thank Jerry Kepes, who inspired the originalformulation of the problem, and Bill Lamport for assistanceon the design aspects of spars and TLPs. John Lynaugh,Kannika Yodpetchpongsri, Cengizhan Yenerim and Chaiya-porn Wiboonkij-Arphakul provided excellent research as-sistance. The authors also thank Wood Mackenzie for pro-viding industry cost data. Partial financial support for thisproject was provided by the Cockrell School of Engineer-ing at the University of Texas at Austin. All errors andomissions remain the responsibility of the authors.

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