# GULF MARGINAL PRODUCTION—2: Model identifies marginal structures, future output

All producing properties are unique and have costs and benefits specific to each stage of its life cycle.

As fields mature and operations transition into the later stages of their production cycle, decreasing revenue streams, higher operating costs, and fewer upside opportunities lead to declining profitability. Eventually, properties are abandoned when marginal cost exceeds the marginal revenue of production.

In Part 2 of this three-part series, we categorize the inventory of committed assets in the shallow water Gulf of Mexico and introduce the model framework used to identify marginal structures and the level of their future production.

__Asset classification__

**Committed assets**

In January 2007, the Gulf of Mexico had 3,847 structures.

About 40% of the structures were not in production, either because they were held by lease production or preparing for decommissioning. In water less than 1,000 ft deep, 2,364 structures were producing.

A structure is said to be producing if it produces any amount of oil or gas in the year of observation, while an idle structure once produced hydrocarbons but has not been productive for at least 1 year prior to 2006. A few hundred auxiliary structures have never produced and are also included in the total of nonproducers.

Committed assets refer to those structures that were producing in the gulf at the time the study was initiated (January 2007) and do not involve planned or anticipated installations from future development plans or projects installed after the study date.

**Production type**

Producing structures are classified by primary output and structure type in Table 1.

A structure is labeled an oil structure if its producing gas-oil ratio is <5,000 cu ft/bbl and a gas structure if its GOR is >5,000 cu ft/bbl. Over two thirds of the committed asset inventory are gas producers.

Fixed platform is the most common structure type, followed by caissons and well protectors. The unknown category in Table 1 represents structures with missing identifiers on structure type or water depth.

**Production class**

To facilitate an automated approach to production forecasting, each producing structure is classified by age and profile type into five subcategories, denoted as: (I) Young, (II) Normal, (III) Chaotic, (IV) Latecomer, and (V) Unknown.

A young structure is defined to be any structure with less than 7 years' production history. For young structures, a production forecast is achieved through a history match, using the statistical characteristics of structures that have been previously removed as the matching set.

Normal and chaotic structures have produced to a condition of pseudosteady-state flow and allow curve fitting with standard regression techniques. Normal structures have production profiles that are best-fit by a decline curve with R^{2} ≥0.75, while chaotic structures have a best-fit decline curve with 0.50 ≤R^{2} <0.75.

Latecomer structures exhibit unusual profiles, usually multiple peaks, that do not conform to standard curve fitting techniques. For latecomer structures, various heuristic techniques are applied to generate the forecast curves.

The number of active structures classified by production class and type is shown in Table 2. Production modeling of the shallow water structures yielded 525 young structures, 1,280 normal structures, 90 chaotic structures, 427 latecomers, and 42 unknown structures.

Most of the structures were modeled with standard decline curves, but a significant number of young structures, as well as structures with latecomer attributes, also exist. Production forecasting associated with young and latecomer structures are expected to be subject to a larger degree of uncertainty than normal assets.

**Economic status**

Producing structures are classified as either economic or marginal depending on the level of its revenue relative to a structure-specific threshold at the time of observation (Fig. 1).

If the revenue of structure s at time t is denoted as r(s, t), and the value of the marginal and economic thresholds are denoted as τ_{m}(s) and τ_{a}(s), τ_{m}(s) >τ_{a}(s), then a structure is said to be economic at time t if r(s, t) ≥ τ_{m}(s).

A structure is said to be marginal at time t when the revenue of the structure falls below the marginal threshold but remains above the abandonment threshold; i.e., τ_{a}(s) < r(s, t) < τ_{m}(s). At r(s, t) = τ_{a}(s), the economic limit of the structure has been reached, where the operating cost equals the revenue generated from production, and whereupon a rational decision maker would stop production.

The time a structure turns marginal and uneconomic is denoted as T_{m}(s) and T_{a}(s), respectively. Production during the time a structure is classified as economic or marginal is called economic and marginal production.

__Model framework__

The number of committed shallow water structures classified as economic or marginal and the quantity and value of their production is forecast as follows:

•

Initialization.Determine the production class of each structure, select the model input variables, and quantify the manner in which the input parameters are expected to vary.•

Production forecast.Forecast future production based on model parameters assuming stable reservoir and investment conditions.•

Revenue forecast.Forecast future revenue for assumed hydrocarbon prices and marginal and abandonment thresholds.•

Structure classification.Classify a structure as economic and its production as economic when generated revenue falls above the marginal threshold, and a structure as marginal and its production as marginal when its gross revenue falls above its abandonment threshold but below its marginal threshold.•

Categorization.Categorize and count the structure count, annual production, and discounted future revenue from the collection of economic and marginal structures.

__Initialization__

**Variable selection**

The user selects the input set depending upon the objectives of the problem. The variables employed in this analysis include: the price of oil and gas (P^{o}, P^{g}), the marginal and abandonment threshold multipliers (m, a), and the discount rate (D).

An exponential model with decline parameter d is associated with those structures that do not have a sufficient production history to perform regression analysis. The input parameters of the model are denoted by the vector (d, P^{o}, P^{g}, m, a, D).

**Parameter distribution**

Each system parameter is governed by a distribution function f_{i}, i = 1, …, 6. The specification of each function is determined by empirical analysis or user preference.

For example, if the historic price of oil is determined to follow a Lognormal distribution according to the parameters μ and σ^{2}, P^{o} ~ LN(μ, σ^{2}), the user may model future prices according to this specification or may prefer to assume another distribution type, such as the uniform distribution U(a, b) with end points (a, b). Model variables are held fixed for all structures across time for each iteration of the simulation.

**Design space**

The distribution functions of the model variables that are employed in the simulation are shown in Table 3. We refer to the collection of input variables and the intervals of their distributions as the design space ∑ shown by Equation 1.

The design space serves to represent reasonable bounds on the model parameters to help ensure that we encompass user beliefs in future scenarios. If the distribution type or any parameter interval of the design space changes, output values and the coefficients of the regression model will also change.

Fortunately, small perturbations in ∑ along one or more directions do not change the output significantly, because the parameters are already defined through reasonably large intervals and perturbations near the endpoints of the interval in either direction (e.g., changing d ~ U(0.05, 0.30) to d ~ U(0.08, 0.25)) will only make an incremental change in the design volume.

Changes in the dimensionality of the design space, however, which would occur by adding or deleting one or more variables, will have a significant impact since in this case the structural aspects of the model have been modified.

__Methodology__

**Production forecast**

For each structure, the best-fit production curve is used to forecast future oil and gas production under the assumption that production will not be altered in the future due to reservoir-production problems or additional investment.

Extrapolating the results of an empirically derived equation to the future assumes that all the factors affecting performance in the past have exactly the same cumulative effect in the future. This is a strong assumption, referred to as "stable reservoir and investment conditions," and the ability of our model to accurately reflect future production is highly dependent on this assumption.

The production forecast for each structure for each hydrocarbon stream i (i = oil, gas, boe) is initialized in the year 2006 (t = 1) and given by q^{i}(s) as shown by Equation 2.

**Revenue forecast**

Revenue is estimated by multiplying the oil and gas production forecast by the average market hub prices in the year received.

Hydrocarbon quality (API gravity, sulfur content, etc.) and transportation expense (netback cost) to deliver production to market are not considered. Oil and gas prices are assumed constant throughout the life cycle of the structure. Revenue for structure s in year t is computed by Equation 3 yielding the revenue forecast vector r(s) shown in Equation 4.

**Structure classification**

Production transitions from commercial to marginal status at the marginal limit τ_{m}(s). At the economic limit, the structure will be abandoned (Fig. 1).

The time at which a structure becomes marginal is determined by comparing the revenue of the structure in year t, r(s, t), to the marginal threshold of the structure,τ_{m}(s), as shown by Equation 5.

The time at which a structure is no longer profitable is determined by comparing the revenue r(s, t) to the economic limit of the structure, τ_{a}(s), shown by Equation 6.

The values of m and a are selected from user-defined distributions to capture the sensitivity of the model output to variations in threshold levels (Fig. 2). Multiplying the thresholds by factors m and a will shift the levels up or down relative to their baseline position, inducing either an earlier or later transition.

The values of τ_{a}(s) are determined using historic data for structures categorized according to structure type, primary production, and water depth. The value of τ_{m}(s) is fixed at a multiple of the economic limit, selected as 2τ_{a}(s). Since a ~ U(0.5, 3) and m ~ U(a, 6), the maximum spread between thresholds will range between 4 to 24. Note that the interval defining the marginal threshold multiplier is bound below by the abandonment multiplier to ensure that for each iteration of the simulation the marginal threshold is always greater than the abandonment threshold.

T_{m}(s) denotes the time when structure production transitions from economic to marginal status. T_{a}(s) denotes the time when production is no longer profitable and cash flow terminates. The cash flow vector given by Equation 4 terminates at T_{a}(s) as shown in Equation 7.

We assume that once a structure reaches its economic limit it will be removed from the gulf. According to federal regulations, structures only need to be removed from a lease once lease production stops. We did not incorporate this aspect of leasing regulations into the model since it does not affect the production forecast.

**Categorization **

An asset will transition from economic to marginal status at some point during its life cycle, and continue to produce marginally until it becomes unprofitable. The production profile qi(s) of each structure is decomposed into its economic and marginal components, qie(s) and Q^{i}_{m}(s), based upon the values of T_{m}(s) and T_{a}(s), shown in Equation 8.

"Economic" production is defined by q(s,t) for t = 1, …, Tm–1, and "marginal" production is defined for t = T_{m}, …, T_{a}, given by Equations 9 and 10. At any point in time, a structure is either "economic" or "marginal."

The production and revenue levels at which a structure transitions between the economic and marginal states is used to delineate commercial and marginal production. From an operator's perspective, this classification would not be considered a production milestone, but for modeling purposes, it is useful to categorize production and structures in this manner.

The revenue stream is similarly segmented into economic and marginal components corresponding to its economic and marginal production terms given by Equation 11. r_{e}(s) corresponds to the economic revenue stream and r_{m}(s) corresponds to the marginal revenue stream, shown in Equations 12 and 13.

**Decomposition**

The cumulative production, Q(s), and discounted revenue, V(s), associated with structure s is decomposed into economic and marginal components for oil, gas, and boe output streams, beginning from 2006 (t = 1) through the time the structure reaches marginal status (t < T_{m}(s)), and thereafter, until the structure is no longer economic (T_{m}(s) ≤ t < T_{a}(s)). The values of Q^{i}_{e}, Q^{i}_{m}, and Q^{i}_{T} (s), are given by Equations 14-16. See Fig. 3 for the cumulative production and operational milestones.

The discounted revenue of the economic and marginal production streams are computed utilizing an industry-wide discount rate D. The values of the economic, marginal, and combined valuations—ve(s), V_{m}(s), and V_{T}(s)—are given by Equations 17-19.

**Simulation-regression analysis**

The input parameters for each loop of the simulation include (d, P^{o}, P^{g}, m, a, D) and the output include {σ_{e}(Γ), σ_{m}(Γ), Q^{o}_{T}(Γ), Q^{g}_{T}(Γ), ve(Γ), V_{m}(Γ), V_{T}(Γ)}, where Γ represents the aggregate of the five production classes described previously (young, normal, chaotic, latecomer, unknown).

The model curves used to forecast production is fixed, with the exception of structures in the latecomer class where a subset of profiles is modeled with an assumed decline parameter. The values of (d, P^{o}, P^{g}, m, a, D) are sampled from their respective distribution functions for each loop of the simulation, the output metrics are computed, and after a sufficient number of computations, the model outputs are regressed against the input parameters.

__Model structure__

**Model specification**

A linear model is specified in Equation 20 that relates the output measures to the input parameters. The value of the output functions f are selected from the set {Q^{i}_{e}, Q^{i}_{m}, Q^{i}_{T}, ve, V_{m}, V_{T}} while the input parameters (X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}) = (d, P^{o}, P^{g}, m, a, D).

A linear model is specified for ease in interpretation; if model results turn out to be unacceptable, or if significant interaction effects are expected, it is straightforward to apply a nonlinear specification. The model coefficients αi, i = 0, …, 6 are unique to f and will vary with the size, shape, and dimension of the design space.

**Expected signs**

The signs of the model coefficients are expected to follow certain values.

The coefficient α_{0} represents the fixed term (intercept) of the functional and its sign is indeterminate. The inclusion/exclusion of the fixed term coefficient in the formulation is user dependent.

The coefficient α_{1} is associated with d, which as discussed previously, defines the rate of decline for a subset of latecomer structures (those structures that did not yield best-fit curves or have enough data to perform a forecast). The magnitude of the coefficient α_{1} relative to the other model coefficients depends upon the proportion of total production controlled by this subset of assets.

If d increases, and all other model parameters are held fixed, structure production will decline faster and reach its economic limit sooner, and so the quantity of reserves and its value will decline. We would thus expect α_{1} < 0 for the functionals Q^{i}_{e}, Q^{i}_{m}, Q^{i}_{T}, as well as V_{m}, ve, V_{T}, since increasing d will lead to declining cumulative production and value.

The coefficients α_{2} and α_{3} are associated with the price of oil and gas, respectively. As Po and Pg increase, revenue streams for all assets will increase, delaying the onset of the economic limit. This will allow the production of additional reserves, which at elevated prices, will lead to a greater discounted cash flow. Thus, increases (decreases) in P^{o} and P^{g} will lead to increases (decreases) of α_{2} and α_{3}, and so we would expect α_{2}, α_{3} > 0 across all the functional outputs Q^{i}_{j} and V^{i}_{j} (i = oil, gas; j = m, e, T).

We expect differences to exist in the relative magnitude of oil and gas price for a particular asset (depending, say, if it is primarily an oil or gas producer) and on the stage of its life cycle; e.g., if it is economic or marginal. Because the value of economic production is expected to be at least an order-of-magnitude larger than a marginal producer, oil and gas prices are expected to play a more significant role for economic production.

The coefficient α_{4} is associated with the multiplier m, and the coefficient α_{5} is associated with the multiplier a. Recall that m and a are used to vary the marginal and economic thresholds τ_{m} and τ_{a}. The impact of the variation in the multipliers varies depending upon the functional under consideration.

The value of m ranges over a positive interval bounded below by a and above by twice the upper limit of the economic threshold interval. As m increases, m·τ_{m}(s) will increase, and production will become marginal at an earlier time, decreasing the amount of economic production (Q_{e}) and its value (ve). Since marginal production occurs at an earlier time and at a higher rate, the amount of production that is classified as marginal (Q_{m}) will subsequently increase along with its value (V_{m}).

The value of the coefficient α_{4} is thus expected to be negative for the functionals Q_{e} and V_{e}, and positive for Q_{m} and V_{m}. For the composite functionals Q_{T} and V_{T}, coefficient α_{4} will not enter into the model formulation because there is no need to segment the production and revenue streams.

The variable a ranges over a positive interval, and as a increases, a·τ_{a}(s) will increase, forcing production out of profitability at an earlier time. This should not have a measurable impact on Q_{e} and V_{e}, but the change will reduce marginal production (Q_{m}) and its value (V_{m}). Thus, the coefficient α_{5} will not enter into the economic production model but is expected to be negative for the functionals Q_{m} and V_{m}. By linearity, Q_{T} and V_{T} should also be negative. Coefficient α_{5} will not enter into the Q_{e} and V_{e} functional since the amount and value of economic production is not influenced by what happens at the end of the life of the structure.

The coefficient α_{6} is associated with the discount rate D used to compute present value, and thus, will only influence the valuation estimates V_{m}, ve, and V_{T}. The manner in which discount rate varies with present value is well known: as D increases, the value of future revenue declines, and so we expect the sign of coefficient α_{6} to be negative for all three valuation functionals.

Further, since changes in discount rate have a greater impact on early cash flows, we would expect that the magnitude of α_{6} would be greater for V_{e} than V_{m} since it is defined earlier in the life of cycle of the asset. Coefficient α_{6} is not included in the model specification for cumulative production since it is only relevant in the valuation estimate.

Next: The author models the number of committed assets in the Gulf of Mexico that are expected to be marginal over a 60-year horizon.

__Brazil__Petroleo Brasileiro SA has towed out the platform jacket for Mexilhao gas field for setup in the northern Santos basin off Brazil.

The 182 m tall jacket left a fabrication yard in the Niteroi borough of Rio de Janeiro on the morning of Nov. 19 for the 140-km tow to the field location off Sao Paulo state. Mexilhao is expected to go on production in 2010.

Mexilhao is Brazil's largest fixed gas platform. Production capacity is 530 MMcfd of gas through a pipeline with landfall at Caraguatatuba, where the Monteiro Lobato gas treatment plant is under construction. The plant will also handle gas from Urugua and Tambau fields off Rio de Janeiro and from the Tupi field pilot in the Santos basin.

__New Zealand__

Global Resource Holdings LLLP, Littleton, Colo., is seeking farmout partners to explore the 8.1-million-acre PEP 38451 in the deepwater Taranaki basin off New Zealand.

GNS Science and Australian Worldwide Exploration have completed seismic interpretation reports based on 3,400 line-km of proprietary 2D seismic shot in December 2008 and January 2009. The reports confirm that all of the essential elements of the petroleum system are present.

A thick sedimentary section includes a large untested Late Cretaceous delta that contains significant volumes of source rocks, excellent reservoir facies, and good seals.

Global's newly processed seismic data images potential source rocks in the extensive Rakopi Formation coal measures that are confidently tied to well data. The Rakopi formation, the proven source rock for oil in Maui, Maari, and Tui fields, is up to 1 km thick and covers an area of nearly 20,000 sq km in PEP 38451.

__Gulf of Mexico__

Helix Energy Solutions Group Inc., Houston, said its Energy Resource Technology GOM subsidiary made a deepwater Gulf of Mexico oil discovery in Green Canyon Block 490 and made a shelf discovery at South Timbalier 145 field.

The Green Canyon discovery on the Jake prospect went to 13,504 ft in 3,740 ft of water and cut 134 ft of net oil and gas pay in a single interval. The well was conventionally wireline logged and fluid samples were recovered. It was cased and temporarily abandoned for a future subsea completion.

Following the discovery, Helix's estimate for the prospect is 50-75 bcfe gross proved, probable, and possible recoverable. Development options are under study, and production is estimated to start in mid-2011. ERT's working interest is 25%.

Another new well that ERT drilled in South Timbalier 145 field, where it is operator with 75% working interest, went to 14,193 true vertical depth and logged 20 ft of oil and gas pay. The well is being completed and expected to go on production in December 2009.

__Alabama__

venture Oil & Gas Inc., Laurel, Miss., gauged an exploratory well off the southeast flank of Huxford (Smackover) field in Escambia County, Ala.

The 1 Mason 36-14, in 36-2n-6e, 22 miles west of Brewton, flowed at the rate of 457 b/d of 43° gravity oil and 538 Mcfd of gas on a 10⁄64-in. choke with 2,627 psi flowing tubing pressure from Smackover perforations at 14,902-936 ft. Gas is 1,500 ppm hydrogen sulfide.

__Oklahoma__

Red Fork Energy Ltd., Perth, said a well east of Vinita, Okla., logged 52 ft of Devonian Woodford shale above TD of 485 ft with excellent log characteristics and gas shows across the entire section.

The well is the Wattenbarger 1-22, in 22-25n-21e, Craig County, 5 miles east of Vinita. Top of Woodford shale is at 385 ft.

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