This is a challenging question, but very valid. It is aimed at the heart of the question of the value of knowledge management, and is an industry-specific way of asking "what can Knowledge Management do for my business".
This is how I answered him - first some preamble, then the serious answer.
To answer the question, you first need to look at the link between knowledge and performance. The more a team or department of company knows, the better they perform, and if they can learn from performance, they can build up a store of knowledge and perform even better. If knowledge and performance are linked, then knowledge management drives performance improvement.
This is how the link would work in the oil sector.
Imagine a drilling team in an unfamiliar area. Using KM techniques, they learn with each well how to drill more effectively, more safely and more cheaply. KM can help them learn faster, and accelerate the learning curve and the improved drilling performance.
Lets take the issue of construction projects in the oil sector. KM can transfer lessons from one project to another and so can eliminate repeat mistakes, wastage of time and exploring blind alleys, so allowing you to deliver projects faster, cheaper, safer and more effectively, and so bring production on stream faster.
Or if we look at producing oil platforms, by sharing and reusing best practices from other platforms they can improve their own efficiency and learn how to work better.
The answer is to the question " How many more barrels can KM deliver?" is - it depends how may barrels you are currently wasting through projects delayed by repeat mistakes, production limited by second-best practices, and drilling teams learning far too slowly. All of these are the result of staff not having access to the best knowledge, not having access to the best practice, and not being able to learn effectively. This is the production you are currently losing through not having Knowledge Management.