electrostatics - Realistic vs Idealistic capacitance

I am doing an investigation into the differences of calculating capacitance using the well know formula for an idealistic parallel plate capacitor, based on the assumption of a uniformly distributed electric field:$C=\epsilon_0 \frac{A}{d}$ vs using numerical methods for calculating the capacitance of a realistic model i.e. with fringe fields (see here for a more detailed explanation of my methods).

I am investigating how the capacitance changes as i move the plates further away from each other, and what i have found is that, based on the results I'm getting, as the plates are moved further away from each other the ratio of realistic/idealistic increases, implying that the realistic electric field can store more energy.

My question is, is this correct and if not why?

Thanks

[Edit] I originally thought that this may be because the realistic formula is only valid for small d, however the ratio seems to increase linearly, rather than converging to a value and then dropping off leading me to think that this is not the problem?

[Info for comments]

$$C=\frac{\epsilon_0 L}{V} \sum_{bound} |\phi_{outer}-\phi_{plate}|$$

$$C_{\infty}=\frac{\epsilon_0 A}{d}$$

Dividing them, where $A=lL$ i.e the area of the plate, gives:

$$\frac{C}{C_{\infty}}=\frac{d}{V l} \sum_{bound} |\phi_{outer}-\phi_{plate}|$$