By Saad Iqbal
The Well That Was Running Out of Time
Three weeks ago I was staring at eighteen months of monthly production data from a marginal oil well, trying to answer a question that had real money attached to it: was this well worth a workover, or was it time to let it decline into plug-and-abandon territory. The field superintendent wanted an answer by Friday. The spreadsheet I’d inherited had gaps, a few obviously bad meter readings, and a decline trend that didn’t fit neatly onto a straight line on semi-log paper the way the textbook examples always do.
This is the moment every reservoir and production engineer knows well. Decline curve analysis, or DCA, is one of the oldest tools in the industry’s kit, first formalized by J.J. Arps in 1945, and it’s still the fastest way to turn a messy production history into a forecast a manager can act on. What’s changed in the last couple of years isn’t the math. It’s how quickly you can get from raw numbers to a defensible curve, because you can now hand the messy part to an AI system with a code execution tool and get a fitted model back in the time it takes to make a coffee.
I want to walk through exactly how I did it on this well, step by step, so you can run the same process on your own data.
What Decline Curve Analysis Actually Is
Think of a producing well the way you’d think of a battery draining under load. Early on, the pressure differential driving fluid to the wellbore is high, so the rate is high. As the reservoir depletes, that differential shrinks, and the rate falls. The question DCA answers is simply: given the shape of the drop-off so far, what shape will the rest of the curve take, and how much oil or gas is left to recover before the well hits its economic limit.
Arps described three possible shapes, and this is the part worth understanding before you ever touch a keyboard. If the fractional decline rate stays constant over time, you get an exponential curve, the steepest of the three. If the decline rate itself slows down over time, you get a hyperbolic curve, described by a parameter called b that sits between 0 and 1. At the extreme end, when b equals 1, you get a harmonic curve, the gentlest long-term decline of the family. Most unconventional wells behave hyperbolically early on and are often constrained to exponential decline later in life, because an unconstrained hyperbolic curve will overestimate reserves if you let it run forever, a mistake regulators and reserve auditors watch for closely.
None of that is new. Arps’ equations have been in every petroleum engineering textbook for eighty years, and dedicated forecasting platforms like ComboCurve have built entire businesses around automating this workflow at scale across thousands of wells. What’s new is that a solo engineer, or a small operator without a six-figure software budget, can now do a rigorous version of the same fit in a plain-language conversation with an AI tool that can actually execute code, not just describe it.
Step-by-Step: Running the Analysis With AI
Here’s the actual sequence I used, using Claude’s code execution tool, though the same steps apply with any AI assistant that can run Python.
Step 1: Get the data into a clean, structured format
I exported the well’s monthly oil volumes from our production accounting system into a CSV with two columns: month and barrels per day. Before doing anything clever, I pasted the raw data in and asked the AI to flag anything statistically odd, missing months, zero-production entries from downtime, obvious double-counted rows. It caught two months where a meter recalibration had produced a rate that was roughly triple the surrounding months, which I then excluded as a mechanical artifact rather than a true reservoir signal.
This step matters more than people give it credit for. Arps decline curves are sensitive to which data points you feed them. Fit a hyperbolic curve to a decline history that includes an artificial spike, and you’ll get a b-factor that flatters the well’s future far more than the reservoir will actually deliver.
Step 2: Ask for all three fits, not just one
Rather than asking the AI to pick a curve shape for me, I asked it to fit exponential, hyperbolic, and harmonic models to the cleaned data using nonlinear least squares, and report the fitted parameters (initial rate qi, initial decline Di, and b-factor where applicable) alongside the R-squared for each. This took under a minute of actual compute time. Having all three side by side is the point: it turns “trust the software” into “compare the evidence,” which is exactly what a reserves auditor will ask you to do anyway.
Step 3: Sanity-check the b-factor against physical reality
The hyperbolic fit came back with a b-factor of 1.4, statistically the best fit to the historical points, and industry-implausible. A b-factor above 1 implies a decline rate that decelerates faster than physics generally allows for this kind of reservoir drive, and left unconstrained it will forecast a “long tail” of production that rarely materializes. I asked the AI to re-run the fit with b constrained to the 0 to 1 range, standard practice per SPE guidance, and to switch to exponential decline once the effective annual decline rate dropped below a threshold I specified. This single constraint changed the estimated ultimate recovery by close to 20 percent versus the unconstrained fit, which is the difference between a workover that pays out and one that doesn’t.
Step 4: Visualize the comparison before trusting a number
I had the AI plot the cleaned production history against all three fitted curves on both linear and semi-log axes, since a curve that looks convincing on a linear plot can reveal a poor fit once you switch to log scale, where true exponential decline shows up as a straight line. Seeing the actual data points scatter around the constrained hyperbolic curve, rather than just reading an R-squared value, is what actually convinced me the fit was reasonable rather than merely mathematically optimal.
Step 5: Turn the curve into a decision
The final step converts the fitted curve into an economic answer: integrate the forecast rate out to the well’s economic limit, apply current pricing and lease operating costs, and compare the resulting present value against the cost of the proposed workover. I asked the AI to build this cash flow model directly from the fitted decline parameters so that if the field superintendent asked “what if oil is $58 instead of $65,” I could re-run the answer in seconds rather than rebuilding a spreadsheet.
Where AI Genuinely Helps, and Where It Doesn’t
AI code execution collapses the mechanical part of this workflow, cleaning data, fitting three curve families simultaneously, constraining parameters, building a sensitivity table, from an afternoon of spreadsheet wrangling into a focused fifteen-minute session. That’s real and it’s valuable, especially for smaller operators managing a handful of wells who can’t justify a full field-wide platform.
What it doesn’t replace is judgment about which decline model actually fits the drive mechanism, how to handle wells with commingled zones, or when a curve break indicates a genuine change in reservoir behavior versus an operational hiccup like a choke change or an artificial lift conversion. Purpose-built platforms such as ComboCurve exist precisely because full-field forecasting across thousands of wells, tied into type curves and reserve booking workflows, is a different scale of problem than the single-well fit I ran here. The AI is a very fast, very literal-minded junior analyst. You still have to be the reservoir engineer.
The Bigger Lesson
The math behind decline curve analysis hasn’t changed since 1945. What’s changed is the distance between “I have messy production data” and “I have a defensible forecast,” and that distance has gone from days to minutes for anyone willing to describe the workflow clearly to an AI tool that can actually run the numbers. The well I opened with got its answer by Thursday afternoon, a workover recommendation backed by a constrained hyperbolic fit and a cash flow sensitivity table, not a gut call. That’s the quiet, unglamorous way AI is actually changing energy engineering: not by replacing the eighty-year-old equations, but by making sure engineers spend their time on the judgment calls those equations still require, instead of the spreadsheet mechanics around them.
