Chicago Paper - Application of Law and Equal Expectations to Oil Production in California

In February, 1918, the conclusion was published by Lewis and Beal "that wells of equal output on the average will produce equal amounts of oil in the future, regardless of the ages of the wells." This conclusion was based upon the study of data collected principally in Oklahoma and was not known at that time to be true for other oil fields. An abundance of statistical proof was later collected by the senior author of the present paper, which showed that the conclusion was undoubtedly well founded and that it applied to other fields as well. Accordingly, it was later restated2 as the "law of equal expectations" as follows: "If two wells under similar conditions produce equal amounts during any given year, the amounts they will produce thereafter, on the average, will be approximately equal, regardless of their relative ages." Although only scanty data from the California oil fields were available at the time this publication was prepared, sufficient information was analyzed upon which to base the insert on Fig. 80, which showed beyond a doubt that the law held at least for a part of the Midway oil field in California. Recently the authors have collected more complete data in California, and it is the purpose of this paper to explain the method used in demonstrating the truth of the law and, in addition, to give several methods by which curves constructed in accordance with this law can be used in a practical way with ease and accuracy. The Family Curve The law of equal expectations means that each individual of a group of wells producing under similar conditions will decline along approximately the same type of curve, the rapidity of decline varying with the output