Modeling the growth in gas reserves from known fields.

1. INTRODUCTION

The extent to which future domestic demand for natural gas is satisfied by imports of LNG is contingent on the adequacy and cost competitiveness of North American supplies. One of the most important sources of supply is accounted for by reserve appreciation, i.e., reserve growth, in known fields. Indicative of the importance this supply source, in 2006, the latest year for which published reserve data are available, approximately 98 percent of the dry natural gas reserve additions in the United States were accounted for by reserve changes in known fields. (1)

Based on an extensively applied methodology developed by Arrington (1960), the increase in proved ultimate recovery is presumed to increase at a diminishing rate with the age of the field. An excellent overview of the methodology is presented in Morehouse (1997). While the contribution of the economic environment to the growth process has been acknowledged by geologists, the application of the Arrington method presumes that growth is independent of the economic environment. Given the implicit assumption that growth is systematically affected only by age, the contribution of reserve growth to supply will invariably diminish as fields become more mature.

This paper challenges this view. Specifically, we estimate the growth in reserves from over 500 known gas fields in the federal offshore waters of the U.S. Gulf of Mexico (GOM). A single equation model of natural gas reserve growth in the Gulf of Mexico is developed and estimated. Specifically, the annual growth rate in a gas field's reserves is hypothesized to be a function of the age of the field as measured by the number of years since first production, the field's reserve size in the year of first production, the real price of natural gas, water depth, and a set of unobserved field-specific factors. Unlike a traditional fixed effects model that cannot account for time-invariant variables, the empirical analysis makes use of a three-stage estimation process that estimates fixed effects in the presence of time-invariant variables. The results strongly suggest that age is not the sole factor in explaining a field's annual reserve growth. In particular, we find that the annual growth rate in the reserves of a field is significantly affected by initial discovery size, prices, water depth, and unobserved field-specific effects. Hence, estimating oil and gas reserve growth using an Arrington based approach may yield a distorted assessment of future energy supplies.

2. MEASURING RESERVES GROWTH: THE CURRENT STATE OF THE LITERATURE

Ideally, one would measure reserve growth by comparing the current known oil and/or gas volumes (equal to cumulative production plus remaining reserves) of fields discovered in say, 1950, with their initial discovery sizes. Unfortunately, this is often not possible because the initial discovery sizes of fields discovered before 1975 or so are many times unknown. The standard solution to this problem is based on the work of Arrington (1960). With his method one can estimate reserve growth even when the initial discovery sizes are unknown and the number of time series observations is small. The Arrington method makes use of a ratio which has come to be known as an annual growth factor. This factor is the ratio of known oil and/or gas volumes from fields of a given age relative to the known volumes of fields in the previous age category. Mathematically, under the Arrington method one computes annual growth factors (AGF) as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where:

In equation (1), the numerator is summed over all discovery years for fields that are k years old; the denominator is the corresponding sum for fields that are k-1 years old. For example, when k = 5, the numerator would equal the sum over all discovery years of the known petroleum values for fields that are five years old; the denominator would equal the corresponding sum for fields that are four years old. Accordingly, the equation in this case would yield a weighted average of the AGF for five year old fields. In the absence of growth, the AGF would equal unity. Values of the AGF less than unity imply negative reserve revisions.

In his original paper, Arrington fitted a smooth curve between the three year weighted averages of the AGFs for a sample of reservoirs and the number of years since discovery. This curve was used to arrive at a predicted AGF for each year following discovery, [PAGF.sub.k]. The predicted cumulative growth factor for k years after discovery ([PCGF.sub.k]) is the product of the predicted annual growth factors, i.e.

[PCGF.sub.k] = [PAGF.sub.1] x [PAGF.sub.2] x [PAGF.sub.3] ... x [PAGF.sub.k] (2)

Note that this methodology implicitly assumes that the age of the field or reservoir is the only systematic determinant of reserve growth. If this is not the case, then the method will likely yield a biased measure of growth. For example, if, as we suspect, the economic environment affects reserve growth, then an Arrington-based supply analysis will underestimate the response of supplies to higher prices.

Numerous studies including Marsh (1971), Dolton et. al. (1981), Root (1981), Megill (1989a, 1989b, 1989c, 1989d), Attanasi and Root (1994), Attanasi, Mast, and Root (1999) and Root et, al. (1995) have applied variations of the basic Arrington method to project growth for fields in the U.S. onshore. Application of the method by Klett (2004) to Energy Information Administration oil and gas reserves data over the period 1977-1996 yielded AGFs that declined rapidly over the first three years following discovery and then stabilized at a value slightly more than unity until about 90 years following discovery.

Several studies have applied Arrington's methodology in examining reserves appreciation in the GOM Outer Continental Shelf (OCS). These studies make use of annual field level data from either the Energy Information Administration (EIA) Oil and Gas Integrated Field File (OGIFF) or the Field Reserve History file from the United States Minerals Management Service (MMS). These data are available from 1977 and 1975 onwards, respectively.

Using the MMS GOM OCS data, Drew and Lore (1992) find that the annual growth rate for all oil and gas fields ranges from 10% per year in their first decade of productive life to 5% per year in the second decade, and to 3% in the third decade. Lore, et.al. (1996, 1999) calculate AGF's and PCGFs using (1) and (2) respectively for 876 fields from the MMS database. Their results indicate that fields on average more than double in size within 6 years of discovery and triple within 16 years. They calculate that fields quadruple in size in about 40 years.

Attanasi (2000) examines reserve appreciation in the GOM OCS using the EIA OGIFF data. Based on the restricted least squares estimate in which AGFs are assumed to decline monotonically with the age of the field, Attanasi concludes that reserve appreciation in the GOM OCS is more robust than that reported by Lore et al. (1996, 1999). Specifically, he concludes that oil fields grow by a factor of eight within 50 years while gas fields grow by a factor of almost six.

There are two notable studies of reserve growth in the North Sea which do not rely on the Arrington method. Watkins (2002) examined reserve appreciation for 126 oil fields in the North Sea. In contrast to the GOM research noted above, Watkins analyzes reserve appreciation from the year of first production instead of the year of discovery. This is justified by noting that the time interval between discovery and first production in the offshore can be long and that the number of years since the year of first production is a better measure of field maturity than the number of years since discovery. In contrast to the Arrington based findings for the GOM, he reports substantially lower reserve appreciation factors. In an earlier working paper, Sem and Ellerman (1999) also examined oil field reserve appreciation in the North Sea. Like Watkins, appreciation is measured as of the year of first production. Using both random and fixed effects specifications, the CGFs are regressed on the age of the field, age interacted with binary variables representing field size, a binary variable representing the sector in which the field is located, and a binary variable representing the post-1985 time period. Their results indicate that with the exception of medium sized fields, oil reserves appreciate 2-3% per year regardless of sector, year, or age. For the medium sized fields, i.e. those fields with reserves between 100 and 400 million barrels in the first year of production, no significant reserve appreciation could be statistically discerned. The authors regard this outcome as a puzzle and conclude the paper by suggesting that the inclusion of "time varying factors such as the amount of development drilling, injection, prices (emphasis added) or perhaps changing tax treatment may contribute to a greater understanding of reserve appreciation in the North Sea." (Sem and Ellerman, 1999, p. 35)

3. DATA AND MEASUREMENT ISSUES

In this paper, we employ a database from the United States Minerals Management Service (MMS) to evaluate the reasonableness of the Arrington method in estimating the reserve growth of known gas fields in the federal offshore waters of the U.S. Gulf of Mexico (GOM). We focus on natural gas because of the gas prone nature of the Gulf. The database was downloaded from the MMS website (http://www.gomr.mms.gov/homepg/offshore/fldresv/resvmenu.html). This database provides a year by year reserve history for every oil and gas field in the federal offshore waters of the Gulf of Mexico over the period 1975 through 2003. In contrast to the United States Energy Information Administration's reserve estimates, this database is not based on a survey of the operators. Instead, the estimates are produced by MMS, who as leaseholder, has access to the proprietary data that are needed to estimate reserves. In theory, this provides the data series with a consistency that a survey based database cannot hope to match. This may not be a trivial consideration given that the reserve estimates can change with changes in reserve ownership when the database is based on survey. For example, the 2000 EIA survey of domestic oil and gas reserves deducted 533 Bcf. of natural gas reserves from the reserves of operators in the Texas portion of the Federal offshore Gulf of Mexico who transferred the operations of existing fields to another operator; the acquiring operators reported that the transfer increased their reserves by 767 Bcf (EIA, 2001, Table 8). Finally, given the intense interest of the investment community in the reserve replacement ratio, firms have a financial interest in the estimates that they report. One example of where financial incentives are believed to have contributed to a reserve overstatement is Royal Dutch/Shell Group's admission in 2005 that its oil and gas reserves as of 2002 had been overstated by 41 percent (New York Times, 2005).

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