Testing whether production changed because of a neighbor

The claim

The claim usually arrives in one of a few forms. Our well's oil production fell after the operator next door began injecting. Our water cut rose after they fractured the offset well. Their disposal well pressured up our formation and our wells stopped producing. Each of these says that a measured quantity changed, that it changed at a particular time, and that the change was caused by a particular thing someone else did.

The first two parts are statistical questions before they're anything else. Did the quantity change, by how much, and when? Production data are noisy, they drift, and they have their own trends from depletion, workovers, and price-driven operating decisions, so a change that looks obvious on a chart may be within the ordinary variation of the well, and a change that's real may be hidden in it. The third part, cause, is where statistics stops and the subsurface analysis begins, and it's important to be clear about the handoff.

The data

The raw material is the monthly production record for the well or wells in question, usually oil, gas, and water volumes and the days produced, reported to the state and available in the file. From it come the derived quantities the claim is about: rate per producing day, water cut, gas-oil ratio. Alongside it go the dates of the alleged cause, from permits, completion reports, and injection records, and the same production records for comparable wells nearby that weren't exposed to the alleged cause, which serve as controls.

The data have to be cleaned before they're tested, and the cleaning is part of the record. Months with zero days produced, reporting corrections, and operator changes all leave marks in the series that can look like effects, and each one is identified and handled in a way the deliverable states.

Why ordinary methods overstate the case

The first thing a careful analysis does is refuse to treat monthly production as independent observations. A well's production this month is close to its production last month; the series is autocorrelated, and that has a specific consequence. Standard regression assumes each data point carries fresh information, so it counts sixty months of data as sixty independent pieces of evidence. When the months are correlated, they carry far less than that, and the standard method reports a confidence that the data don't support. Small effects look significant that aren't.

The remedy is to estimate the uncertainty with methods built for correlated data: regression with autocorrelation-robust standard errors, which adjust the confidence to the amount of independent information actually present, and the resampling approach described below. A production analysis that reports a tight confidence interval without saying how it handled autocorrelation should be read with that in mind.

Before and after, with controls

The core design is an interrupted time series. The production record is modeled as a trend before the alleged cause, and the model asks whether the level or the slope changed at that date by more than the pre-existing trend and noise would predict. On its own that's a before-and-after comparison with the trend accounted for, which is already better than comparing two averages, but it can't distinguish an effect of the neighbor from something that happened to every well in the area at the same time: a price drop, a weather event, a field-wide operating change.

The controls do that. The same model is fit to comparable wells that weren't exposed to the alleged cause, and the question becomes whether the exposed well changed relative to them. If the whole field fell in the same month, the exposed well's fall isn't evidence of the neighbor. If the exposed well fell and the controls didn't, it is. Choosing the controls, and stating why they're comparable, is one of the judgments the deliverable has to defend.

Letting the data find the break

The interrupted time series takes the date of the alleged cause as given and tests for a change there. Changepoint detection turns that around: it searches the series for the date at which a change in level or slope is best supported, without being told where to look. If the date it finds matches the alleged cause, that's independent support. If the data's own break is a year earlier, or coincides with a workover in the well's file, the story about the neighbor has a problem the claimant needs to answer.

Placebo dates

The next question is how unusual the observed change is for this well. Placebo testing answers it by pretending the alleged cause happened on other dates, many of them, across the well's history where nothing is claimed to have happened, and running the same test each time. The result is a distribution of the changes the method finds on ordinary dates. If a change the size of the one at the alleged date turns up on a quarter of the placebo dates, it's the kind of thing this well does, and the evidence is weak. If it turns up on almost none, the change at the alleged date is unusual for this well, and the evidence is strong. The placebo distribution is often the single most persuasive exhibit, because it needs no statistical training to read.

Honest uncertainty

Every estimate carries uncertainty, and for correlated data the usual formulas understate it. The moving-block bootstrap estimates it by resampling the series in blocks of consecutive months, which preserves the correlation within each block, and refitting the model many times to see how much the estimate moves. The interval it produces is wider than a textbook interval, and it's the honest one. Where the estimators used have closed-form results in the textbooks, they're checked against those results so a reviewer can confirm the implementation before arguing with the conclusion.

What the result looks like

The deliverable states, in plain language, whether a change in the quantity is supported at the alleged date, its estimated size with an interval, whether the data's own changepoint agrees with the alleged date, how often a change that size appears on placebo dates, and how the exposed well moved relative to its controls. The methods are named, the constants are declared, and the calculations are delivered in a native workbook with coefficients derived in the sheet rather than pasted in, so the other side can rerun the analysis without asking for code. The technical detail goes in appendices; the findings go in sentences a judge can read.

What it can't establish

A statistical result establishes whether a change occurred, when, and whether its timing supports the story told about it. It doesn't establish mechanism. A production decline that begins the month a neighbor starts injecting, is unusual for the well, and doesn't appear in the controls is strong evidence that something happened to that well at that time and not to the others. Whether the something was the neighbor's injection, and how the pressure or fluid got from there to here, is a subsurface question answered with the well files, the pressure record, and the geology, as described in the practice's pressure record review and the explainer on injection pressure.

The two analyses belong together, and either one alone can mislead. A plausible mechanism with no statistical change in the data is a theory looking for an effect. A statistical change with no mechanism is a coincidence looking for a cause. The practice's statistical testing of cause and effect is designed to be read next to the subsurface analysis, and to say plainly which of the two is carrying the argument.

This page describes a method. It isn't engineering certification, a regulatory determination, or legal advice, and it doesn't describe any engagement.