Perhaps that's a valid way to look at the terms. I would be able to comment on that more easily if I had the paper.

From the abstract (emphasis added as it pertains to b):

This paper considers the relationship between the extraction rates and remaining reserves of oil. A simple exhaustible resources model suggests a linear extraction rule, with slope terms common to all extractors when discount rates are homogeneous. Differences in pricing behavior and costs determine the intercept. Panel data from the world oil industry exhibit a robust and stable extraction–reserves relationship across countries and through time. Common slopes characterize extraction over large ranges of reserves although there is a concave relationship across non-OPEC members, and a significantly lower estimated slope within OPEC countries. These findings may be explained by risk aversion, differences in discount rates, and measurement error in the reserves data.

There is not much to go on from that to understand how he derives b but a seems to me self-evident.