Full wave rectification by opamp
Your circuit (with proper resistor values) should work just fine. Try the below simulation. 







simulate this circuit &ndash; Schematic created using CircuitLab

The way it works, for those who are questioning it, is that the lower amplifier OA2 maintains the non-inverting input of OA1 at 0V when the input goes negative, which means that you're getting Vout = -Vin (it's an inverting amplifier and R1/R2 are in play). 

When the input is positive the positive input is at the input potential and the output drives then inverting input to the same potential, so the gain is +1. 

Here's a simulation of the output with a 300mV peak input at 50Hz. It won't work very well at higher frequencies because the amplifier OA2 is driven into saturation and will have sluggish recovery, but for mains frequency it's more than okay (and it operates from a single supply with a dirt-cheap op-amp). 



As an extra bonus, since it's powered from a single supply there is no need to protect the ADC input from possible negative transients.