Place ginger, half of orange, and half of grapefruit in a food processor; pulse 4 times or until finely chopped. Place orange mixture in a Dutch oven. Repeat procedure with remaining orange and grapefruit. Add water to pan; bring mixture to a boil. Cover, reduce heat, and simmer until mixture is reduced to 6 cups (about 50 minutes), stirring occasionally.
Add 6 cups sugar; uncover and cook until sugar is dissolved. Increase heat to medium-high, and bring mixture to a boil. Cook until the mixture is thick and reduced to 5 cups (about 35 minutes), stirring occasionally. Remove from heat, and cool.