How E&P companies forecast future production from unconventional gas wells—an issue usually confined to the petroleum engineering realm—is now in the limelight. Recently, U.S. regulators began investigating whether some publicly owned shale-gas producers have overestimated their reported reserves in previous filings.

As part of the probe, the U.S. Securities and Exchange Commission has subpoenaed company records, including those from early 2008. The documents reportedly include material related to the analyses of production-decline curves, historical performance of shale-gas wells vs. production forecasts, and the appropriateness of various decline-curve-analysis (DCA) methods.

The SEC rules allow E&P companies to book reserves based on the use of “reliable technology,” including computational methods such as reservoir simulation. By definition, reliable technology has a repeatable, consistent track record and is in widespread use in a given area.

In the past, companies have not been asked to justify reserves bookings by demonstrating that classic DCA meets SEC criteria for reliability. After all, this engineering technique has a successful, established, 60-year track record. Now, however, requirements may be changing.

the three forecasts under a time-limit cutoff of 4,000 days were fairly close in predicting EURs.

Analyzing well performance

Petroleum engineers estimate proved developed producing (PDP) reserves in various regions worldwide using DCA techniques. In the hands of a skilled evaluator, DCA yields repeatable, consistent results.

DCA is a simple, fast technique for estimating petroleum reserves for large populations of wells. Those conducting DCA use classical rate-time equations empirically developed by J. J. Arps and others, before 1945, to calculate production declines of three observable types: exponential, hyperbolic and harmonic. The current discussion focuses on when and how quickly production from a shale-gas well transitions from hyperbolic to exponential decline during flow-regime changes.

A well begins producing in early-time transient flow (producing from new fractures) with possibly high bottomhole pressures (BHP), followed by boundary-dominated flow (as the well draws production from the boundaries of the drainage area), and low, constant BHP.

The original Arps exponential model was based on boundary-dominated flow, which is reached in months in conventional reservoirs.

A transient-flow regime, however, can last for years as tight gas is produced through a network of fractures, tight zones or horizontal sections. So, shale-gas evaluators have resorted to using a hyperbolic b exponent in the Arps equation, which generates the curved portion of the production decline before it straight lines into long-tailed exponential decline.

Two schools of thought clash on how high the b factor or exponent can be. Some evaluators force a 0

The assumption that b is less than one, however, does not mesh with what industry is seeing in actual shale wells. Hyperbolic b values approaching two, in some cases, have been shown to theoretically (and in practice) model early shale-gas production. To limit higher b values, evaluators plug in a trailing exponential segment to generate rate-time plots.

DCA, type curves and analogs

Typically, a petroleum engineer begins a DCA exercise by plotting stable initial production rates in detail, over one month’s time, for instance. At the beginning of the well’s production decline trend, extrapolating forward involves a high degree of technical uncertainty.

Historical trends are frequently not sufficient to define early-time declines in subject wells, so evaluators look at decline curves from other producing wells (analogs) in the same field or reservoir, if available. Evaluators generate a type curve from analogous wells to get an average production profile, which can guide forecasts for the subject “immature” well.

Type curves are generated first by normalizing historical production from analog wells on a rate-time plot. Normalizing involves starting the plot of each of those wells at the same point in time for the sake of comparison.

Then the rates of each well are totaled at incremental points in time and divided by the number of wells to plot an average production curve. It is difficult in most cases to find true analog wells with long histories and frac lengths, sand concentrations, lateral lengths and orientations similar to subject wells.

Classic DCA method

Evaluators use type curves and apply the b Arps hyperbolic parameter that best matches the shale-gas well to forecast initial production decline. Relatively high b factors generate good curve fits. However, b values decrease as the well transitions to boundary-dominated flow and exponential decline, so evaluators have used a minimum decline (Dmin) final segment for at least 25 years to account for the onset of reservoir depletion in the well’s production tail.

Higher Dmins, for instance 10% or higher, can under-predict estimated ultimate recoveries (EURs) when used with high hyperbolic b factors. Conversely, if a Dmin is too low, then the forecast will overstate reserves.

“The minimum decline rate is a ‘bolt-on’ improvement to a method that cannot simultaneously match early- and late-time behavior without using at least two segments,” says Scott Wilson, a senior vice president at Ryder Scott Petroleum Consultants.

“It’s not technically elegant, but this combination of two segments—hyperbolic b factors and using Dmins during exponential decline—crudely honors the curvature from transient to boundary-dominated flow.” Wilson evaluates oil and gas shale plays across North America.

using a production-rate cutoff of 35 Mcf of gas per day, the three techniques show more divergence.

New DCA methods

Petroleum engineers are developing new DCA techniques to mathematically model early-time, fracture-dominated transient flow in horizontal, fraced shale-gas wells. Dr. John Lee, a professor at the University of Houston, introduced an empirical method—the stretched-exponential production decline (SEPD) model—at the Society of Petroleum Engineers annual meeting a year ago.

The stretched exponential function was first introduced by physicist Rudolf Kohlrausch in 1854 to describe the discharge of a capacitor. More than 150 years later, the oil and gas industry is using the SE function to model fluid flow rather than electron flow.

Lee was an engineering fellow at the SEC during the rules-change process for reserves reporting in 2008. He is also a member of the National Academy of Engineering.

Texas A&M University professor Peter P. Valko developed the SEPD model, which has proved successful in a test case involving some 2,800 horizontal, fractured Barnett shale wells.

“The SEPD trend seems to be quite consistent at least in a completion type—most importantly for horizontal wells intersected by several propped fractures with an overall amount of sand reaching millions of pounds,” says Lee.

The technique models fracture-dominated flow by considering the reservoir to be heterogeneous and comprising “a great number of contributing volumes (from possibly thousands of fractures) individually in exponential decay.”

Other models

The SEPD model is not the only one considered to be an earnest attempt to solve problems in analyzing prolonged transient flow in shale gas. This year, Anh N. Duong, of ConocoPhillips, introduced his own empirically derived decline model that is based on long-term linear flow in a large number of wells in tight-and shale-gas reservoirs.

“Arps curves give more optimistic forecasts compared to the new approach,” stated Duong in his SPE paper, “Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs (Paper No. SPE 137748). Like Lee, Duong used Bar-nett shale wells to test the forecasting method.

“The method that looks best to me is not the SEPD model, but the method proposed by Duong,” says Lee. “We have not found a single case with decent data in which the method failed, and it works in the Bakken oil shales, Barnett gas shales and elsewhere.”

Lee and others agree that all performance analysis methods used to evaluate shale gas can be reliable if done properly. Referring to Duong’s method, he notes, “The EURs this method predicts have been quite close to the SEPD model and Arps with a realistic Dmin.”

None of the methods are as reliable during early well life. “There’s nothing magical about the SEPD method. It’s often very wrong, high or low, with the first year’s data, but settles down and forecasts only slightly changing EURs after the first year or two,” Lee says.

He doesn’t support the use of Arps in evaluating shale-gas reserves because EUR estimates tend to be too high at early stages of production. “I can’t in good conscience recommend Arps to anyone,” he says. “It is technically in- correct because its use in ultra-tight reservoirs violates assumptions made in the derivation of the model. Secondly, in almost all cases, b decreases with time, meaning that the EUR estimates tend to decrease with time.”

Is the Arps hyperbolic functional form even appropriate in the modern age? Ryder Scott’s Wilson says that a more important question should focus on the competence of the evaluator to use classic DCA or other newer tools to get the best answers.

“A hammer in the hands of a master carpenter can do a wonderful job. It may not do such a good job while in the hands of a two-year-old trying to wake up his father,” he says.

As promising as they are, the new DCA approaches are relatively experimental. Production forecasts based on any widespread use of those techniques may be questioned by regulators, bankers and others for now.

Lee does not claim that repeating the analysis in another play will lead to similar consistency, but believes that with some variations, the main concepts will be applicable. His research group is continuing to test the new DCA methods on significant groups of wells in unconventional resource plays other than the Barnett, including the Bakken and Fayetteville.

“One concern is whether the new methods will continue to be valid for both long-duration transient flow and long-duration stabilized (boundary-dominated) flow in the same production history,” Lee says. ”Limited testing indicates they are, but we have a lot more research to do in many different resource plays to be ‘reasonably certain’ of the answer.”

The research group also is testing SEPD and Duong long-term predictions in wet-gas and oil windows, as well as looking at the validity of the models in handling the complications of multi-phase flow in oil shale plays.

Despite these unanswered questions, Halliburton has built scripts and incorporated the SEPD algorithms into its optional modeler module, now available in its Aries economic evaluation software. The company said in October that it had received inquiries but no clients were using the SEPD-programmed option yet.

However, as momentum picks up with sales to early adopters, the future may be bright for DCA techniques that model linear, fracture-dominated flow when gas production and cash flow from unconventional wells reach a peak.

Ahead of the curve

Ryder Scott recently compared classic DCA with the SEPD and Duong techniques on a field in the Haynesville shale play. A well in this field is included (see chart). The classic equation was a modified Arps hyperbolic with a b of 0.9 and reasonable Dmin of 6%.

The three forecasts under a time-limit cutoff of 4,000 days were fairly close in predicting EURs. The Duong method projected an EUR of 1.88 billion cubic feet (Bcf), which was very similar to the Arps method, which projected 1.95 Bcf. The SEPD method predicted a 1.65-Bcf EUR.

Using a production-rate cutoff of 35 Mcf of gas per day, the three techniques show more divergence (see chart).

Total field life using the Duong method is 19 years with a 2.01-Bcf EUR. The modified Arps method yields a life of 24 years and EUR of 2.19 Bcf. Field life using the SEPD method is eight years with a 1.62-Bcf EUR. The Duong method results in a projection very close to the Arps DCA forecast.

“This well is very typical of the behavior we have seen throughout the field for all three methods,” notes Lucas Smith, petroleum engineer at Ryder Scott. “The graph with a production-rate cutoff shows how each of the projection methods behaves in the long term for a particular fit. The end of the life of the wells is what differentiates the ultimate recoveries, but also is where we have the least amount of history to compare.”

This limited test case will have to be combined with other cases to provide meaningful results before any conclusions can be made. Ryder Scott will continue to test and evaluate the newer DCA methods and other performance-based analyses as they are developed, Smith says.

SEC compliance

The SEC concept of “reasonable certainty” implies that as more technical data becomes available over time, proved reserves are much more likely to increase rather than decrease. U of H’s Lee argues that because the b exponent tends to decrease with time in classic DCA, the method is susceptible to criticism under the “reasonable certainty” criterion.

Wilson says, “Hyperbolic declines over long periods of time can result in overstated reserves, but it is also true that evaluators use a modified equation with a Dmin value that limits EURs to a proved-reserves basis.”

Lee uses what some would call a “fudge factor” of 0.8 to incorporate conservatism in his SEPD predictions, which are optimistic in 50% of the cases. “The requirement for a P90 demands a procedure for which 90% of the predictions are conservative, so we apply a safety factor of less than one,” he explains.

Ultimately, the focus of regulatory reviews may be whether a company uses a Dmin or safety factor to rein in optimistic shale-gas reserves estimates.

“Companies have publicly stated that they use Arps with no Dmin,” says Lee. “I believe that Arps, with or without a Dmin, is subject to abuse and is, in fact, abused regularly.”

This article is adapted and updated from an article in the September 2011 Ryder Scott Reservoir Solutions newsletter, by Mike Wysatta.