First, just to reiterate Dan's comment about 'expert' versus 'expertise'. In my organization we take this a step further and consider 'experience' as part of the same spectrum, on the basis that even a complete novice has valuable experience from which others can learn.
Regarding your key question: Not exactly the answer you wanted, but there is AI technology such as Starmind (starmind.ai) which develops a neural network of connections between 'concepts' and 'people' based on the digital content created by the people. So it's not looking at what documents they are reading, but only what they are creating - and making a broad assumption that content creation somehow equates to experience. The more a person creates content relating to a concept, the more he/she is associated with that concept, hence the greater the indicator of experience (which may be roughly equated with expertise, etc.). So in principle, you can use e.g. Starmind technology to 'find an expert'.
Jonathan / UK