  A model for strongly writhing confined solar eruptions suggests an origin in
the helical kink instability of a coronal flux rope which remains stable
against the torus instability. This model is tested against the well observed
filament eruption on 2002 May 27 in a parametric MHD simulation study which
comprises all phases of the event. Good agreement with the essential observed
properties is obtained. These include the confinement, terminal height,
writhing, distortion, and dissolution of the filament, and the flare loops. The
agreement is robust against variations in a representative range of parameter
space. Careful comparisons with the observation data constrain the ratio of the
external toroidal and poloidal field components to
$B_\mathrm{et}/B_\mathrm{ep}\approx1$ and the initial flux rope twist to
$\Phi\approx4\pi$. Different from ejective eruptions, two distinct phases of
strong magnetic reconnection can occur. First, the erupting flux is cut by
reconnection with overlying flux in the helical current sheet formed by the
instability. If the resulting flux bundles are linked as a consequence of the
erupting rope's strong writhing, they subsequently reconnect in the vertical
current sheet between them. This reforms the overlying flux and a far less
twisted flux rope, offering a pathway to homologous eruptions.
