Coolant going to reservoir thereby depleting coolant capacity in the radiator

Took car for a drive and after about eighteen minutes of driving, the "add coolant" indicator illuminated on the dash. When I pulled over to inspect under the hood, the reservoir was full of coolant. The normal level of coolant in the reservoir is about 1/4 to 1/3 of the reservoir's capacity. After I let engine cool down, I opened the radiator cap, and added coolant to the radiator. I drove another fifteen minutes or less, and the symptoms repeated themselves. I could not detect any leaks other than the exit tube of the reservoir. I pressure tested the radiator cap and the cap appeared to hold pressure. I checked the color of the coolant in the reservoir and I did not detect oil in it. I checked the oil dipstick and the oil was not contaminated. I would appreciate it if you can lead me in the right direction in finding the defect.