Decline curve analysis, explained
The three Arps curves
J.J. Arps published these in 1945 and they still carry most of the reserves reported in the United States. They differ only by the b-factor.
| Curve | Rate equation | Where it fits | Caution |
|---|---|---|---|
| Exponential (b = 0) | q(t) = qi · e^(−D·t) | Mature, boundary-dominated conventional wells; most stripper production. | Loses a constant percentage each year. Conservative and the easiest to defend to a bank. |
| Hyperbolic (0 < b < 1) | q(t) = qi / (1 + b·Di·t)^(1/b) | Unconventional wells in the first several years; anything still in transient flow. | Decline itself decelerates. A b above ~1.2 will forecast reserves that never arrive. |
| Harmonic (b = 1) | q(t) = qi / (1 + Di·t) | Rare in practice; sometimes fits long-lived, pressure-supported wells. | The flattest Arps case. Treat a harmonic fit as a claim that needs evidence. |
qi is the initial rate at the start of the fit, Di the nominal decline at that point, t time, and b the decline exponent.
How to run the analysis
Gather clean rate history
Monthly volumes by well, at least 12–24 months. Strip out months with known downtime or you will fit the workovers instead of the reservoir.
Plot rate on a log scale
Log rate against time. Exponential decline is a straight line on that plot — if your data is straight, you are done choosing a model.
Fit qi, Di and b
Fit only the stabilized period, not the flush production after a workover or a frac. Constrain b to the range that is physically plausible for the play.
Apply the economic limit
Forecast stops when monthly revenue no longer covers LOE. Everything past that point is not reserves, it is a plugging schedule.
Integrate to EUR
Cumulative production from today to the economic limit is remaining EUR. Multiply by your NRI to get the barrels you actually get paid on.
A worked example on a stripper well
Exponential decline, because the well is long past transient flow. All figures illustrative.
EUR is barrels, not dollars. Those barrels arrive across 25 years, so they have to be discounted before they mean anything — that step is the valuation model, not the decline curve.
Why downtime corrupts a decline fit
A decline curve is supposed to describe the reservoir. If the well sat shut in for nine days waiting on a pump, that month's volume is a maintenance record, not a reservoir signal — and a fit that includes it prices in a decline the rock never had.
This is the quiet reason continuous monitoring matters to valuation as much as to operations: when every shut-in hour is timestamped and attributed, you can fit on producing time and hand a buyer, a bank or an engineer a history that means what it says.
Common questions
What is decline curve analysis?
Decline curve analysis, or DCA, fits a mathematical curve to a well's historical production rate and extends it forward to estimate future production and estimated ultimate recovery. It is the most widely used reserves method for producing wells because it needs only rate history — no reservoir model, no simulation.
What is the b-factor in the Arps equation?
The b-factor sets how fast the decline rate itself declines. At b = 0 the well loses a constant percentage every period (exponential). At b = 1 it is harmonic, the flattest standard case. Unconventional wells often fit b values between 0.8 and 1.4 early in life, which is why many forecasts switch to an exponential terminal decline after a set number of years to avoid overstating reserves.
What is the difference between nominal and effective decline?
Nominal decline (D) is the instantaneous rate used inside the equations. Effective decline is the actual year-over-year percentage drop you would observe — for an exponential curve, effective = 1 − e^(−D). A 0.22 nominal decline is roughly a 20% effective annual decline. Mixing the two is the most common arithmetic error in DCA.
How much production history do you need?
Twelve months is a workable minimum for a conventional well in stabilized flow and 24 months is much better. For unconventional wells, early history is dominated by transient flow and short fits systematically overstate reserves. If the well was recently worked over, the fit starts after the flush production settles, not at the peak.
Where does decline curve analysis go wrong?
Four places: fitting flush production after a workover, using a b-factor above what the play supports, forgetting the economic limit so the curve runs to zero rate instead of zero margin, and forecasting gross production when what you own is a royalty-burdened fractional interest.