It might be the early morning hours speaking here, but unless I'm wrong seems like you guys forgot about something
When calculating the value of the resistor that sets the current (in both posted designs), don't forget it will pass the current of the zener/431 as well as the current of the OPAmp. The TL081 for example has Icc of up to 2.8mA (1.4mA typical). That alone is capable of turning the zener off completely even from 30V supply.
Same for the design void_error has posted, the MCP6021 can have Icc as high as 1.35mA, and the CCS is set to just 1mA. So it might be best to set the CCS somewhat higher - 2mA or so will leave plenty of current for the voltage divider (~350uA) + LMV431 to operate (will have at least 300uA).
thanks for the comments, but i have built the circuit and is working fine... including the voltage drop across the zener
TL081 has a typical suppply current of 1.8mA - that's 18V drop @ 10k resistor... with a 30V supply rail and 12V zener it's just the right value, isn't it ?
why should someone burn more power than needed in a zener ? you should always burn just the bare minimum in a zener - just enough to cover the variations in input voltage and variations in the current through the load.
i haven't measurent the supply current of those TL081s i have , but i would expect it will be less than the typical 1.8mA at 12V single supply. i assume the 1.8mA is @ the higher supply voltages +-15V (that's 30V single supply).
regarding the power consumption of the tL081 - it's supposed to be pretty static, the inputs are sitting pretty much at the same potential all the time and the output is driving a small mosfet in it's linear region , and it's a mosfet with very little gate capacitance anyway.
i would rather expect that someone will raise an objection against the TL081
it's not guaranteed that the common mode of tl081 will reach the top rail... but if you have a look at the datasheet... it says: typical common mode input +15/-12 @ supply +-15V => therefore it should reach out to the top rail. btw... tested a couple of TL081s and they're all reaching the top rail.
EDIT:
btw... we can safely assume the typical supply current , because we are relying on the typical common mode range. if the TL081 in question has a higher supply current , then it's not a typical chip and has some deviations including other parameters - like the common mode input range we are relying on