Mahdi1980:
Your question is a valid and practical one. Your problem is complicated by having to work with an unreliable and uncooperative screw compressor manufacturer and supplier.
Today, there are two types of screw compressors being employed: flooded and dry. You fail to tell us which one you have, so it is hard to get an idea of what the temperature of the recirculated oil (before the cooler, really is - or should be. My experience with screw compressors has been primarily with the flooded variety and reputable manufacturers like Mycom and Atlas-Copco. They always responded to spare parts, operating information, and service requests.
If you can’t obtain any information from the manufacturer and you have no operating manual that details out the operating temperatures and flow rates of your oil system, then you have a serious problem with your supplier and the best thing would be to cease doing any further business with them. It appears you are left “out on a limb”, without any backup from your manufacturer. You need more than the oil type and cooler inlet and outlet temperatures in order to design an equivalent water cooled cooler. Primarily you need the oil design flowrate. If you don’t know that, you can’t get started on any cooler design.
Why replace the air-cooled model with a water-cooled one? If you can’t obtain a water-cooled model from your manufacturer, then I would just continue with the air-cooled one.
I can tell you from field experience that your cooler outlet oil temperature should be 100 to 120 oF - depending on your oil’s viscosity ratings. But I can’t even guess what the design flow rate should be. The manufacturer is the one who determines that.