Look up the heat transfer coefficient to determine the material used to construct the heat exchanger. Most plate heat exchangers are constructed of steel or aluminum, both of which have a coefficient of 25 Wm^2 K.
Calculate the rate of heat transfer by dividing the total amount of energy you want to remov (in BTUs) by the time frame (in hours) you want to remove the energy.
Determine the difference between the input and output temperature of the refrigerant by subtracting the output temperature from the input temperature.
Divide the heat transfer rate by the temperature difference times the heat transfer coefficient to get the contact surface area of the heat exchanger. The path within the plate will determine the contact surface area per heat exchanger size. Dividing the contact surface area by the ratio will give you the overall size of the heat exchanger you need.