In Illinois, we commonly use the Doyle log and tree scale to determine board feet. Board feet for logs is a function of diameter inside bark (DIB) at the smallest end of the log and log length. In your example, the estimated board feet would be approximately 243 board feet.
Diameter of log = 24 inches
Approx. DIB = 22 inches
Log length (L) = 12 feet
Board Feet (Doyle) = ((DIB-4)^2 * L) / 16
Board Feet = ((22-4)^2*12) / 16
Board Feet = 243
So, how much is this black walnut log worth? Good question...it's worth whatever someone is willing to pay you! HOWEVER, the going stumpage rate for quality black walnut right now is around $0.80 - $2.00/bd ft for sawlogs (used to make lumber) and $3.00 - 10.00/bd ft for veneer logs (used to make fine face veneer for furniture, architectural paneling, etc.).
Several questions remain...is your log good quality or poor quality? Is this a yard tree that may or may not have metal or lots of defect in it? Is it worth trying to sell to a custom sawmill operator or logger? On the other hand, is it worth more as firewood? These are the kind of questions that usually require the onsite visit of a forester or someone whom you trust to provide you with an unbiased opinion.
Therefore, as I have stated in several other "Ask a Forester" questions, here are your options:
(1) Contact a custom/portable sawmill owner http://www.illinoisurbanwood.org/documents/ILCustomSawmillsDirectory2011.pdf
(2) Contact your local Department of Natural Resources (DNR) District Forester http://dnr.state.il.us/conservation/forestry/DISTFRSTMAP.pdf and have him/her recommend a local timber buyer or portable sawmill operator.
(3) Contact a local professional consulting forester http://dnr.state.il.us/conservation/forestry/CONSULTING_FORESTERS_06.pdf who may be able to assist you in finding a buyer for your walnut tree and log.
(4) Contact a timber buyer directly from the Department of Natural Resources Licensed Timber Buyers List http://dnr.state.il.us/admin/systems/Pdfs/TimberBuyers.pdf
(5) Place an advertisement in your local newspaper to see if you can solicit interest in your black walnut log.