ESTIMATING DRILLING COSTS-Conclusion: Systems approach combines hybrid drilling cost functions
Drilling costs can be estimated with a combination of established, analytic techniques. This article, concluding a three-part series, presents a general framework to estimate costs with a formalized systems perspective.
This framework combines regression-based techniques, as employed in the joint association survey, with the multidimensional attributes of drilling, as incorporated in the mechanical risk index (MRI), directional difficulty (DDI), and difficulty index (DI) models (OGJ, Aug. 6, 2007, p. 39; Aug. 13, 2007, p. 46). A generalized methodology to frame the drilling cost estimation problem is presented and illustrated with an example from the Gulf of Mexico.
Drilling objectives
The objective in drilling a hydrocarbon well is to make hole as quickly as possible subject to the technological, operational, quality, and safety constraints associated with the process. These objectives are frequently conflicting and depend on factors that interrelate; vary with respect to time, location, and personnel; and are subject to significant private and market uncertainty.
Drill rates are often constrained by factors that the driller does not control and in ways that cannot be documented. In many situations, the causes of dysfunction are complex, occurring simultaneously, where effective solutions have not been developed.
Evaluation of drilling performance commands a high degree of visibility across oil and gas companies, and over the past few decades, various methods have been proposed to evaluate drilling cost and complexity. Understanding the drilling process requires isolating the factors of drilling and quantifying their interaction.1-4 There is no way to identify all of the characteristics of drilling that might be important, but we can observe many characteristics, and in practice it is usually sufficient to consider a set of factors that adequately represent the technical aspects of drilling conditions.
Well characteristics are measured directly, while operator experience and wellbore quality frequently need to be represented by other variables. Many unobservable factors also affect drilling performance, such as well planning and preparation, project management skills, communication and training,5-10 but these variables are usually outside the scope of analysis.
The premise of a systems approach to cost estimation is that process characteristics from several wells will allow the factors that influence drilling cost to be discovered. We first outline the drilling performance benchmarks and estimation techniques common in industry. Main factors that characterize the drilling process are then defined. The generalized functional approach is specified and calibrated, and an example is used to illustrate the procedure.
Performance benchmarks
Two methods are commonly used to benchmark drilling performance.
The first method is based on experimental design and controlled field studies. Typically, one or more parameters of the drilling process are varied and the impact of the variable(s) on output measures such as the rate of penetration (ROP) or cost/ft (CPF) examined.
The second method to study factor effects is based on an aggregate assessment of well data. In this method, data that characterize a set of wells are collected, and relationships are established between the variables based on empirical modeling techniques.
The aggregate approach to analysis uses a set of drilling data and seeks to discover relationships between various factors of drilling and the cost and complexity of the well bore. In this approach, wells drilled under a wide variety of conditions provide the raw data to explore the manner in which factors contribute to drilling cost.
In the Gulf of Mexico, the joint association survey (JAS) and the mechanical risk index (MRI) are popular methods used to evaluate drilling cost and complexity. The JAS estimates drilling cost using survey data and quadratic regression models constructed from four descriptor variables. The MRI is a risk index that employs six primary variables and 14 qualitative indicators to characterize wellbore complexity. For additional details on these metrics, see the first two parts of this series (OGJ, Aug. 6, 2007, p. 39; Aug. 13, 2007, p. 46).
Factors
There are many factors and events that affect the time and cost to drill a well. Measurable factors include the physical characteristics of the well, geology, and drill parameters; indirect characteristics, such as operator experience and wellbore quality, are represented through other variables.
Factors such as well planning and execution, team communication, leadership, and project management skills will also affect drilling performance but are often considered beyond the scope of analysis.
Associated with every well w is a vector of dependent variables, φ(w), and a matrix of observations of independent variables, X(w). The matrix of observations is used to explain the dependent variables and is selected based on the underlying engineering and mechanical processes associated with drilling, the choice of dependent variable, data availability, and the level of classification.
There is no way to identify all the relevant characteristics of drilling, but we can identify many factors, and in practice it is only necessary to identify the set of factors that describe the primary elements of the process.
Well characteristics
A wellbore is a three-dimensional tubular structure that is described in geometric terms with respect to the length, diameter, and curvature of the hole’s trajectory. The drilled interval (DI) is the difference between the total depth (TD) and the spud depth (SD), DI = TD - SD, while the vertical interval (VI) is the difference between the vertical depth (VD) and spud depth, VI = VD - SD. The spud depth is the distance from the rotary table to the seabed.
A well consists of segments of casing string Si oriented at the angle A(Si) relative to a reference coordinate system. The maximum angle of the wellbore is computed as MA = maxi A(Si). If MA ≥ 85°, the well is categorized as a horizontal well under the indicator variable HW: HW = {1, MA ≥ 85°; 0, otherwise}. If L(Si) denotes the length of well section Si, then the total length of the horizontal section of a well is denoted as HL, Equation 1.
Each casing section has a diameter Di = D(Si) and radius Ri = R(Si), and length Li = L(Si) measured from the rotary table. If k = NS represents the number of strings associated with the well, then a well is characterized by the vectors D = (D1, D2, ..., Dk) and L = (L1, L2, ..., Lk). The incremental well casing length is denoted by L* = (L1*, L2*, ..., Lk*), where Li* = Li - Li-1, for i = 1, ..., k, and L0* = 0.
Operators generally prefer the production casing to be as large as possible to maximize production, but large production casing requires a large wellbore, which is typically more complicated and expensive to drill. Average hole size and volume removed characterize the geometry of the final drilled well. The average hole size (HS) of the wellbore is determined by the weighted average diameter of the casing string, Equation 2, while the volume of rock removed (VR) without washout is defined by Equation 3.
Well complexity
Complex wells arise from diverse factors, including the nature of the geologic formation, depth of the target, size of the reservoir sands, trajectory of the wellbore, experience of the contractor, and technology applied. Well complexity is difficult to quantify and frequently ambiguous because practices, opinions, and experiences among drilling contractors vary so dramatically.
High-pressure/high-temperature (HP/ HT) wells must be planned and drilled with significantly less formation data than shallower and cooler wells. If the formation pressure (FP) exceeds 10,000 psi or temperature (T) exceeds 300° F. anywhere along the wellbore, then a binary indicator will classify the well as complex (Equation 4).
The ratio of the horizontal length to the total footage drilled describes the percentage of the well’s footage drilled under horizontal conditions, Equation 5. The aspect ratio, AR (Equation 6), measures the aggregate curvature of the well trajectory, and the extended reach ratio, ER, is the ratio of total depth to total vertical depth, Equation 7. All of these metrics provide, with some degree of correlation, alternate measures of well complexity.
Site characteristics
Primary wellsite characteristics include geographic location and, for offshore environments, distance to the nearest onshore service station and water depth at the site. Water depth and environmental conditions expected to be encountered is a primary determinant in selection of the rig required for drilling.
As the water depth increases and environmental conditions become harsher, larger and more robust rigs are required with extra hoisting capacity, mud-circulation systems, mooring systems, etc. The region and country in which a well is located is an important consideration in obtaining government regulations and permits, customs, port handling, and transportation.
The maturity of the infrastructure support services and the knowledge and experience of the operator will also play a role in determining drilling cost.
Operator preference
The operator decides not only where to drill, but also how to drill, and how to let the contract. The contract type (day rate, turnkey, combination) and duration, job specification (one well, multiple wells), supply and demand conditions at the time and negotiating strategies are important factors in determining drilling time and cost.
Many different rigs can be used to drill an offshore well; rig selection depends upon such technical factors as type of well being drilled, water depth and environmental criteria, vessel availability, type and density of seabed, expected drilling depth, and load capacity. Equipment selection involves tradeoffs that balance weather risk and the potential cost of delay.
Drilling program
Different types and sizes of bits are used according to the hardness of formations, pressure regime, and drilling plan. The final bit size is denoted FBS.
Mud weights vary over each well section. The average mud weight is defined by Equation 8, where MW(Li*) represents the mud weight applied to the well section L*i, i = 1, ..., k. The maximum mud weight employed in the drilling program is the maximum weight over the entire well as shown in Equation 9. To the extent that high-pressure wells are more complex to drill, MWA and MWMX represent well complexity.
Formation evaluation
Formation evaluation is a critical step in exploration because it is the stage in which information about the presence or absence of hydrocarbon-bearing reservoirs is acquired. Time spent coring, logging, reaming, and testing is “flat” time, however. Therefore, for all other things equal, if a well requires more extensive formation evaluation, then its drilling performance metrics will not look as favorable if time is not adjusted for this activity.
A common decision in offshore operations involves the use of logging while drilling (LWD) vs. wireline (WL) techniques. Adding LWD to a directional well can add a few hours to each hole section for rig up and servicing, while drill pipe-conveyed WL logging may take days leaving the rig idle. Total formation evaluation cost may be less with LWD in cases where the well is deep and highly deviated, rig day rates and penetration rates are high.
Exogenous events
Offshore drilling may be subject to significant delays caused by weather; weather downtime can play an important factor in the total cost of the operation.
It can affect offshore drilling operations in various ways: Weather too severe for operations involving supply boats may lead to delay if stock levels on the rig decline to a critical level; weather may slow anchoring up and moving time; weather may be too severe for drilling to occur; extreme weather may result in damaged or lost drill strings and risers; etc.
If operating limits are exceeded because wave heights, ocean currents, or eddies are too strong, drilling operations will be temporarily abandoned and resumed when conditions fall within the operating capabilities of the equipment. Waiting on weather (WOW) needs to be considered separate from the drilling performance metrics to normalize for conditions beyond the control of the operator.
Many problems during drilling may require suspension of the activity. Most contracts specify a certain amount of “free” downtime (24 hr/month is typical), but outside this allowance, the contractor does not receive payment for the time the rig is inactive. Delays that are not directly accountable to the driller are usually charged at a reduced rate.
One of the most common problems in drilling a hole is that something breaks inside the well, such as a piece of bit or drill string, or something falls down the wellbore, such as a wrench or other tool. If fishing is unsuccessful, the hole will either be sidetracked or the driller will set a whipstock, and in the worst case, a new hole may need to be spudded.
Other drilling problems include stuck pipe, sloughing shale, lost mud circulation, formation damage, embrittlement, and abnormal pressure. Rig equipment failure, lost circulation, weather, and stuck pipe are the main causes of trouble time in the Gulf of Mexico.
Dependent variables
The time to drill a well is described by the number of the dry-hole days, DHD, defined as the number of days from the spud date to final well depth, plus any time spent batch setting, pre-installing or pre-setting casings. Dry-hole days normally includes time for all operations essential to well construction, such as tripping, running casing, and cementing (known as “flat time”), as well as interrupt and weather time and time spent on sidetracking. Time spent coring, logging, or other evaluation techniques are excluded.
Total number of days from the rig arrival on location until the rig is released is the total site days, TWD. This time includes the time for mooring and demooring, where applicable, completion and testing, suspension and plug and abandonment activities. Normal dry-hole days is DHD excluding all nonproductive time such as freeing stuck pipe, repairing equipment, and WOW.
The cost of operations during the dry-hole day period plus the casing batch set, preset period is denoted DHC. The definition of DHC will vary with each operator but will normally include the cost of operations, plus overhead, base operations, incentive payments, logging, transport, materials supply, marine vessel support, marine supply base, port facility, and warehousing. The cost of wellheads and technical and mechanical sidetracks are also normally included.
The costs for completion and well test operations, production strings and liners, trees, completion equipment, long-term daily rental of completions equipment, well design, site survey and preparation, rig mobilization and demobilization, well suspension and reentry, and plug and abandonment are not included in DHC. The total well cost TWC is the dry-hole costs plus all the cost that were specifically excluded.
Primary drilling performance metrics include the rate of penetration ROP and the cost per ft CPF drilled, shown in Equations 10 and 11.
Unobservable variables
Many variables known to influence drilling performance, such as well planning and preparation, project management, and technology are difficult but not impossible to quantify. The significance of these factors cannot be overstated, but because the manner in which these variables influence the drilling program are difficult to ascertain, such factors are not usually incorporated in analysis.
Functional model
The generalized functional model is best viewed as a generalization and synthesis of the benchmark indices used in industry. We combine the regression methodology used in the JAS with the multidimensional attributes of drilling incorporated in the MRI, DDI, DI, and related metrics.
Methodology
Regression analysis provides a standard and transparent analytic framework to establish relationships between performance and cost metrics and drilling variables. The functional approach to drilling cost estimation follows four basic steps, shown in Box 1 on this page.
Design space
Drilling data need to be categorized before assessment. Selecting the “appropriate” level of categorization depends upon the problem requirements, the amount and quality of information available, and the nature of the question under consideration.
Various levels of categorization may be defined, such as “deepwater wells” or “shallow water deep gas wells” or more specifically, through specification of constraint sets, such as 13 ppg ≤ MXMW ≤ 16 ppg, TD ≥ 15,000 ft, 500 ft ≤ WD ≤ 1,000 ft, etc. This is formalized through the design space Ω and the set of descriptor variables Xi shown in Equation 12.
Selection of the values of Ai and Bi, i = 1, ..., p, is specified by the user. If all available wellbore data are used to generate the design space, then the volume would be unconstrained (i.e., Ai = 0, Bi = ∞), and the model results would likely exhibit significant variability because the sample data are highly heterogeneous. A trade-off exists between capturing the right amount of data variability within the design space vs. the ability to generalize the model results from the constructed functions.
The manner in which drilling factors influence performance is frequently incorporated through a weight term associated with the occurrence of the event. The weight is a numerical measure, either a constant or a functional expression, and often subjective in nature.
A more general approach is simply to note the presence or absence of the drilling factor, or its magnitude, and to infer the appropriate weight through the model structure. This not only eliminates the subjective element introduced by the user, but also allows the significance of individual factors to be determined in relation to other factors and wellbores.
The procedure to incorporate drilling factors in the model is to let variable Xi indicate the presence of the term: (1, ith condition/factor present; 0, otherwise), and then to analyze the regression model to determine the impact of the factor. Any factor believed to affect drilling performance can be considered, and the only restriction is that the factors should not be redundant or strongly correlated with other variables, in accord with standard regression protocol.
Specification
A preliminary assessment of well data determines the factors that serve as useful descriptor variables. Typically, 10-20 variables will suffice to characterize the drilling process.
The initial model φ(Ω) shown in Equation 13 is constructed for the design space Ω for each of the reported output variables DHD(Ω), DHC(Ω), and TWC(Ω), and the coefficients (α0’, α1’, ..., α’q) are estimated for each output measure. After the initial model is computed and the statistical significance of the variables determined, the variable set is refined and the model reestimated. Usually, only variables with p-values <0.05 are maintained, but other criteria may also be applied. The final reestimated model is specified with all the regression coefficients reported.
Calibration
The database employed in the model calibration consists of 50 wells drilled in the Gulf of Mexico, 2000-03. The sample set is meant to be illustrative, rather than representative, and given a more comprehensive database, more general models are readily established. The quality and completeness of well data varied widely, and, where possible, the data was checked for consistency with public sources.
The restricted time window minimizes the impact of inflation, technological improvements, and volatility in the market rates of rigs, but if these factors were considered relevant, they could be examined separately. Only project data representing actual cost were processed, and to minimize the influence of scale effects, batch and campaign drilling operations were excluded from consideration.
Further, only “new” wells were considered; sidetracks, slot recovery or enhancement, and multilateral wells were excluded. All the wells in the sample set were drilled with day rate contracts with water and synthetic fluids, and none of the wells was horizontal or drilled underbalanced. The hole’s size, volume removed, well status, and average mud weight were not available for analysis.
Construction
Functional relations for DHD and DHC were computed based on the sample set described.
The initial factor set included 13 variables: {WT, WD, DI, HD, VD, AR, CR, HL, MA, FBS, NS, MXMW, SALT}. The design space was unconstrained and defined by Ai = 0, Bi = ∞, i = 1, ..., 13. All the variables are numeric, except well type and salt section, which are categorical: WT = 1, exploratory well; WT = 0, development well; SALT = 1, salt section encountered while drilling; SALT = 0, no salt section encountered.
The quantitative factors include water depth (WD, in 100 m), drilled interval (DI, in 100 m), horizontal displacement (HD, in 100 m), vertical depth (VD, in 100 m), aspect ratio (AR, unitless), complexity ratio (CR, unitless), horizontal length (HL, in 100 m), maximum angle (MA, º), final bit size (FBS, in.), number of casing strings (NS, integer valued), and maximum mud weight (MXMW, in specific gravity).
Expected signs
The expected signs of the coefficients are easy to ascertain in most instances and provide a first check on the veracity of the model results. If the signs of the coefficients do not follow the expected pattern and the variables are statistically significant, then additional structural issues may need to be investigated.
Exploratory wells are expected to take more time to drill because of the potential risk involved, and because greater water depth means additional complexity, technical and environmental complications, the water-depth coefficient is expected to be positive.
The drilled interval is the length of the wellbore, and all things being equal, it is clear that the greater the drilled interval the longer the time (and the greater the cost) of drilling. The drilled interval is expected to be a primary explanatory variable across all model types.
The vertical interval is expected to be correlated to the drilled interval for exploratory wells, but for horizontal wells, the correspondence is expected to be weaker.
The sign of the horizontal displacement, aspect ratio, and extended reach ratio is uncertain. The aspect ratio and extended-reach ratio describe the geometry of the wellbore trajectory, and because they are strongly correlated, only one of the variables needs to be included in the regression model.
The coefficient of the final bit size is expected to be positive because a large wellbore should take more time to drill and cost more than a small wellbore. The number of casing strings directly indicates the complexity of the well; and the maximum mud weight positively correlates with the pressure profile. Increasing the number of casing strings or applying greater mud weight is expected to be associated with slower drilling time and greater costs.
Statistical analysis
Table 1 depicts the average dry-hole days, dry-hole cost, and total well cost for the sample set. Derived measures such as the rate of penetration (ROP), dry-hole cost/day (CPD), and dry-hole and total cost/meter (DHCPM, TWCPM) also appear.
The average dry-hole days/well was 35; the average dry-hole cost was $11.2 million/well. The average rate of penetration over the drilling cycle was nearly 100 m/day. Observe that the standard deviation of the performance statistics is in most cases only slightly less than the average values, indicating that the data spread is significant. Total well cost is nearly $1,000/m more than the dry-hole drilling cost. The dry-hole and total well cost data are strongly correlated, ρ(DHC, TWC) = 0.94, with weaker but still significant correlations between dry-hole days and cost: ρ(DHD, DHC) = 0.72, ρ(DHD, TWC) = 0.76.
Table 2 presents drilling factor statistics. The factors exhibit significant variability and a low level of correlation, with one notable exception-the extended reach and aspect ratio-indicating that the two measures provide roughly the same information about the well geometry and do not both need to be incorporated in the model.
Model results
Table 3 shows functional relations for DHD, DHC, and TWC. The average dry-hole days and dry-hole cost are estimated as shown in Box 2.
Most of the variables are statistically significant and of the expected sign, and the most significant variables for DHD include drilled interval and number of strings, for DHC and TWC, water depth, drilled interval, and number of strings. The statistical significance of the variables and model fits appears reasonable considering the modest sample size. Box 3 provides an example of the use of the model.
References
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The authors
Editor’s note: The biography for Mark J. Kaiser appeared with Part 1 of this series, OGJ, Aug. 6, 2007, p. 39.
Allan G. Pulsipher (agpul@ lsu.edu) is executive director and Marathon Oil Co. professor at the Center for Energy Studies at Louisiana State University. Before joining LSU in 1980, he served as chief economist for the Congressional Monitored Retrievable Storage Review Commission, chief economist at the Tennessee Valley Authority, a program officer with the Ford Foundation’s division of resources and the environment, and on the faculties of Southern Illinois University and Texas A&M University. He has a PhD in economics (1971) from Tulane University.
