I dunno what your batch size is, and I'm not sure how things go for beer as usua;lly it's talked about with wine, but the ratio of exposure might over or under oak the batch, maybe taste it every week or so depending on contact area to see how it's progressing.
Is it a new barrel or a used barrel? The infusion of oak character fades over time/use. I bought a new barrel and got a great oak flavor out of just 4 weeks aging. However the second batch through the barrel went 8 weeks and I got the same level of oak flavor.