ADA4807

We are using the amplifier ADA4807-2 as an integrator. The ADA4807 is powerd from 6V. As an integrator the output is saturated to the rails. In our circuit it seems that the current consumption without any load increases with a few milliammperes when the output saturates to the rails. Is this behaviour as expected for this amplifier?

An LTSpice simulation of our circuit does not show increased current consumption when the output saturates to the rails.