  It is well known that photospheric flux emergence is an important process for
stressing coronal fields and storing magnetic free energy, which may then be
released during a flare. The \emph{Helioseismic and Magnetic Imager} (HMI)
onboard the \emph{Solar Dynamics Observatory} (SDO) captured the entire
emergence of NOAA AR 11158. This region emerged as two distinct bipoles,
possibly connected underneath the photosphere, yet characterized by different
photospheric field evolutions and fluxes. The combined active region complex
produced 15 GOES C--class, 2 M--class, and the X2.2 Valentine's Day Flare
during the four days after initial emergence on February 12th, 2011. The M and
X class flares are of particular interest because they are nonhomologous,
involving different subregions of the active region. We use a Magnetic Charge
Topology together with the Minimum Current Corona model of the coronal field to
model field evolution of the complex. Combining this with observations of flare
ribbons in the 1600\AA\ channel of the \emph{Atmospheric Imaging Assembly}
(AIA) onboard SDO, we propose a minimization algorithm for estimating the
amount of reconnected flux and resulting drop in magnetic free energy during a
flare. For the M6.6, M2.2, and X2.2 flares, we find a flux exchange of
$4.2\times 10^{20}\unit{Mx},\ 2.0 \times 10^{20}\unit{Mx}, \hbox{and} 21.0
\times 10^{20}\unit{Mx}$, respectively, resulting in free energy drops of
$3.89\times 10^{30}\unit{ergs}, 2.62\times 10^{30}\unit{ergs}, \hbox{and}
1.68\times 10^{32}\unit{ergs}$.
