Thank you for the additional information. I have a better idea what is going on. I will follow through my original points and then come back with a few other suggestions.
1. Based on your comment, I now know that this pump is hanging in a pit (or well) with a water level 7 feet above the first stage impeller. But, I still don’t know how far this water level is below the centerline of the discharge flange. This is where it can get complicated. The pump curve is based on differential head, but what is the reference? For an end suction horizontal pump, the suction pressure would be referenced to the suction flange and the discharge pressure would be referenced to the discharge flange. But, you have no suction flange. For a well pump, the differential head is calculated with both suction and discharge referenced to the center of the discharge flange. So, rather than taking discharge pressure and subtracting suction pressure, you would take discharge pressure and add suction lift. So, if the water level is 20 feet below the centerline of the discharge, the differential pressure would be discharge pressure plus 20 feet. Now, I am not sure if this is the same reference system used for all vertical turbine pumps. I am looking at a catalog for a Byron Jackson vertical well pump. You need to look at the manual for the particular pump you are working with. In any case, if I was correct and you were using the wrong reference, then the calculated differential head would be even higher and you would be plotting performance even further above the curve. So, this is not the answer.
2. Yes. I normally adjust the pump curve flow and head for the actual speed it is runing then plot the raw data on that curve. I use a spreadsheet program to adjust the curve. I will attach a link to my spreadsheet at the bottom. But, it should also work to adjust the head and flow using the affinity laws and plot it on the full-speed curve.
3. You are going beyond the intention of the affinity laws. But, once again, this cannot be your problem. If you were off the curve by 5% or 10%, this might explain it. But your data is not even in the correct pattern. It would be better if you had a family of curves for your pump for different speeds and started with the curve that was closest to the running speed. If you only have one curve for full speed, than the best you can do is exactly what you are doing.
4. This point is the key. If you are measuring the discharge pressure right at the discharge of the pump with no valve, no orifice, no strainer, between the measurement point and the discharge of the pump, then something is wrong. The incorrect pattern in your data cannot be described by an issue with the RO membrane. If there was something wrong going on downstream, the pump would still follow its curve. If the membrane plugged off, the flow would drop and the pump would be force back up on the curve and the pump discharge pressure would increase. I cannot see anyway to resolve this. I have to believe that one of the main sources of your data is wrong. You need to verify that you are getting accurate data for flow, speed and discharge pressure. Of those three, I suspect speed as the culprit. You didn’t mention the driver of this pump: engine, turbine or VSD on a motor. Why is the speed changing? Is there a control system that is varying the speed? What is the measurement used to input into the speed control system? I believe your tachometer is bad and the driver is running faster than you think and speeding up as the flow increases. If that is the case, then you really are measuring and plotting the system curve.
5. If the SG is above 1.0, then I guess this is something like brine, or dilute caustic, or amine, or some chemical. It would be better if we didn’t have to guess. But, since you told us it is going to an RO system, it must be some form of dirty water that you want to purify.
Get the information from the pump manufacture and make sure you are using their curve as intended with the correct references for the suction and discharge pressures. Recheck all of the data with the thought that your instruments could be bad. Check the speed with a strobe to verify that that tachometer is working right. Replace the pressure gauge. Calibrate the flow meter.
Johnny Pellin