I'd be somewhat surprised if you can generate useful surface area info. Traditional surface area measurements that scientists use will not be especially useful if you want to know how much bacterial surface attachment area you have, for example.
Not only will you have to decide how small of a pore you'd count below which you would not, you also need to decide how much contact it needs to have with the outside water to count it. Then of course, you'd need a method that fit that set of criteria.
For example, water may be able to penetrate pores much smaller than the size of a bacteria. Do you want to count those? There may also be pockets where the exchange of chemicals between the pore interior and the bulk water takes days or weeks. Would you count that?