A bag assembly for use with a heat exchanger includes a flexible bag having of one or more sheets of polymeric material, the bag having a first end that bounds a first compartment and an opposing second end that bounds a second compartment, a support structure being disposed between the first compartment and the second compartment so that the first compartment is separated and isolated from the second compartment. A first inlet port, a first outlet port, and a first drain port are coupled with the flexible bag so as to communicate with the first compartment. A second inlet port, a second outlet port, and a second drain port are coupled with the flexible bag so as to communicate with the second compartment.