I'll take a stab here since it looks like the forum has been quiet for awhile...
Fuel consumption per km will be a function of many parameters (weather, sea-state, hull form, windage, prop efficiency...). Fuel consumption per hour is a little more manageable as it's a bit less sensitive to many of these parameters. My experience has been that the published Beta Technical Data Sheets provide a reasonable rough estimate for fuel consumption per hour (https://betamarineusa.com/usa-resources/Data_Sheets/Engines/B38/#page=2). The data sheet for Beta 38 indicates 2 liters/hour (~.53 gal/hr) at 2200 rpm (based on the theoretical loading of a properly matched propeller).
For what it's worth, my fuel consumption per hour over the first 200 hrs of operation (Beta 25 on a 10,000 lb 38' sailboat) has been slightly lower than what is shown in the Beta technical data sheet. My boat is light with a very efficient (low drag) hull form (primarily a racing sailboat).