for heat exchanger sizing there are two predominant methods
1. LMTD
2. Effectiveness-NTU
LMTD is closest to what you've done, so let's go with that.
Q=U A F deltaTlm
U is the overall heat transfer coefficient
A is the area
F is a correction factor for flow arrangment (usually 0.6 to 0.85) which is read from a graph
deltaTlm is the log-mean temperature difference which is defined different ways for different flow arrangments...essentially it calculated the average difference in temperature between the two working fluids
now to complicate things more, because phase change is occuring, the heat exchanger has to be discretized into three segments (liq-liq, liq-2phase, liq-vapor)
each of these segments will have vastly different U-values which should be obtained through a nussult correlation. In the case of the 2-phase U-value, this evaluation is very complicated and hard to get accurate without some experimental data.
That being said, and since you don't appear to be familliar with HEXs, you should consult a HEX manufacturer which will be able to provide performance characteristics of their particular models. Care should still be taken as most OEMs overstate the performance by as much as 10 percent.
Still another worry is that the performance will degrade over time as fouling occurs. The heat transfer coefficients will decrease requiring the R-22 flow rate to be increased. Be sure to get the performance results in both new and fouled conditions.