Modeling oil production with new empirics

ABSTRACT

This article first provides an overview of some stylized features of upstream oil production in light of recent developments in the US shale industry. Empirical observations motivate the formulation of a dynamic optimization model for oil extraction, in which an oil producer determines the optimal “intensity” of drilling wells. Given the intensity, oil production is a state variable where oil flow is characterized by a hyperbolic decline curve that captures the effects of geological constraints. Numerical simulations of the model highlight the importance of both output prices and cost efficiencies in understanding historical dynamics of shale oil production.

KEYWORDS:

• Drilling intensity
• dynamic optimization
• fracking technologies
• Hotelling model
• hyperbolic decline curve
• oil extraction

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ In this study, horizontal wells also include directional wells. For summaries of developments in the recent rise and fall of the US shale oil industry, see Fitzgerald (2013, 2015), Melek (2015), Decker, Flaaen, and Tito (2016), and Energy Information Administration (2016).

² The data are compiled according to well startup date instead of calendar date. Wells completed after 2014 had a productive life less than 36 months by 2016. For these wells, Rystad Energy used the Arps model described in Section III to generate production forecasts.

³ A hyperbolic decline curve becomes a straight line after a double-log transformation. As those decline curves in Figure 6 indeed display this property after log transformations, a hyperbolic decline curve seems to be a reasonable specification for modeling shale oil production in Section III.

⁴ The transversality or terminal condition specifies a fixed duration (T) that represents the time when the oil producer expects a given well to cease production. This condition is an economic limit that occurs when the revenue of producing an additional barrel of oil equals the additional cost of producing it, which means that the profitable capacity has been exhausted. Continued production at or below this limit generates no economic gain.

⁵ Numerical simulations were carried out in MATLAB. We have simulated the model with different lengths of well lifespans up to 20 years. Holding all parameters constant, an increase in the length of the horizon (a larger value of T) leads to a larger value of Q₀, and hence a higher decline curve. The reasoning is that, all else being equal, the longer a well is expected to yield a viable production flow, the greater the total discounted return. As a result, the greater the drilling intensity will be.

⁶ Although both the parameters c and ω can be adjusted, the value of ω was held constant for consistency in the reported simulations and for simplicity of illustration.