Formula , what sized plate heat exchanger to use

149,940 btu's/ hr. But assuming 70k @80%, 56k, you can only flow about 3.75 gpm.

Again, do not build anything off that drawing until an expert like @EdTheHeaterMan or @hot_rod looks at it and tells you what's wrong with it. I think the general idea is correct, but they may have some comments on the HX or circulator sizing. Or they may tell you it's totally wrong! So wait until tomorrow when they come take a look…

Meanwhile, as an improvement for flow control, you would probably want a globe valve on each loop to fine tune the flow rate/delta T. That along with a 3-speed circ should give a full range of temp and flow adjustment.

Also note that the 170 supply temp and 150 return temps I put on the drawing would represent conditions when the boiler loop had heated up enough for the bypass to open fully. But depending on when you start the secondary circulator, it might never get that hot. If you started both loops simultaneously, the oversized HX might keep the primary loop from ever getting that hot. But the bypass would still protect the boiler return temp.

the very best way is to use one of the free online sizing software programs

You need flow data and some temperatures Im guessing a 5x10 20 plate would move all that boiler can offer

Shell and tube are commonly used for pool and spa as they have 2” connections for high flow

Your limitation will be the boiler output

If the pool size is 600 gallons and your cold fill water is 55°F, and you want to heat it to 85°F, the simple math is that you need about 150,000 BTU to do that.

600 gal × 8.34 lb/gal = 5,004 lb × 30°F = 150,120 BTU total

If you have a 40,000 BTU output heater, then you will complete the process in less than 4 hours. However, that does not account for heat loss once the pool water temperature rises above the ambient temperature. Assuming the pool is indoors and the ambient temperature does not drop below 60°F, then during the second hour you will need to account for some loss based on: the surface area of the pool, the temperature of the air surrounding the piping, and finally evaporation. You may need to add roughly 15,000 BTU per hour for part of the second hour and through the third and fourth hours.

As far as the heat exchanger is concerned, I believe @hot_rod indicated that a 5 × 10 × 20 plate exchanger with 1" ports will handle anything the boiler will put out. I actually used a Weil‑McLain WMPH-125 for a job like this once. (Yours could be smaller) Unfortunately they no longer offer that product, and the Triangle Tube company they sourced it from is also no longer in business. Bell and Gossett has a BP410-20LP that should work for you.

For the pump you might use a Taco 007 circulator pump or a Grundfos UPS15‑58 circulator pump on low speed on the closed-system boiler side. On the open system side, you may want something that will provide a higher flow rate for the best heat-transfer performance. A stainless steel hydronic pump such as the Taco 006‑ST4 stainless steel circulator could work, or the Grundfos UPS15‑58 circulator pump on medium speed, although you may find that the cast-iron pump will need replacement more often in that application.

Any cast-iron boiler with about 45,000 BTU DOE output or 38,000 BTU AHRI Net output should work, since the Net rating already includes the 15% piping and pickup factor.

If the 600 gallons is correct then you can do this with:

• Crown AWR070B by Velocity Boiler Works (or the AWR038B with a 6 hour heating time)
• Taco 007 (or equal) comes with the boiler
• Bell and Gossett BP410-20LP
• Taco 006-ST4 for the pool side of the HX
• You may also want to look at plastic pumps that are common in the Pool and Spa industry to see if there are lower cost options there.

I selected a dependable, low cost boiler since you are not operating it year round for space heating or domestic hot water. These parts should do the job for you. But perhaps @hot_rod may have some better ideas. He has more experience with more projects under his belt.