Well Decline Curve and Remaining Reserves

Exponential says the rate falls by the same PERCENTAGE each year, which makes the cumulative a simple difference of rates over the decline constant, and the economic life a logarithm. TWO FORMS OF THE SAME NUMBER CIRCULATE AND GET CONFUSED: the nominal decline that goes in the exponent, and the effective annual decline -- one minus exp of minus the nominal -- that people actually quote as 'a 25% decline'. For shallow declines the two are close; for steep ones they diverge badly, and mixing them up moves reserves directly. Both are reported here, and so is what the reserves would be if the entered figure were read the other way, because which of the two a quoted decline is meant to be is exactly what nobody writes down. THE PRACTICAL OUTPUT IS THE DATE RATHER THAN THE BARRELS. A well is abandoned when its rate no longer covers lease operating expense, and solving the curve for that rate gives a year -- which is what plugging liability, equipment redeployment and the decision to work a well over are scheduled from. AND EXPONENTIAL IS THE WRONG MODEL FOR AN UNCONVENTIONAL WELL. Shale wells decline hyperbolically, very steeply at first and then flattening, so forcing an exponential fit on early data dramatically understates reserves while forcing a hyperbolic fit with a high b factor far into the future overstates them. This fits exponential and says so. It does not fit hyperbolic or harmonic decline, choose a b factor or a terminal decline, fit a curve to production data or judge whether a fit is valid, account for interference, artificial lift changes, workovers, shut-ins or curtailment, evaluate reserves under any classification standard, or produce an economic evaluation. SPE and PRMS reserve definitions, the operator's engineering standards, and a qualified reservoir engineer govern.

exponential decline q(t) = q_i exp(-Dt); cumulative N = (q_i - q)/D; economic life t = ln(q_i/q_econ)/D; effective annual decline = 1 - exp(-D).

Exponential decline only. Unconventional wells decline hyperbolically and this says so rather than fitting them.

Two exponentials and a logarithm.

Estimate. AHJ and licensed professional govern.

Field names used by the API: initial_rate_bpd, decline_rate, rate_is_effective, economic_limit_bpd, years_ahead, nominal_decline, effective_decline, economic_life_years, remaining_reserves_bbl, rate_at_years_bpd, cumulative_to_years_bbl, misread_reserves_bbl, misread_life_years

• Exponential decline only unconventional wells are hyperbolic and need a b factor and a terminal declinethe reservoir engineer
• Constant economic limit the limit moves with price and with operating costthe operator's economics
• Not a reserves estimate no classification standard is appliedSPE and PRMS definitions