An analysis of history matching errors
We use a simple 2D model of a layered reservoir with three unknown parameters: the throw of a fault, and high and low permeabilities. Then consider three different cases where in each case two parameters are kept fixed and the third one is varied within a specific range. Using a weighted sum of squares of the difference in production for the objective function, we plot it against the varying parameter for each case. It mainly shows a complex function with multiple minima. We see that geological 'symmetry' and also vertical spreading are some sources of non-monotonicity in the production and transmissibility curves. These result in a multi-modal objective function and consequently non-unique history matches. The behaviour of the system in the forecast period is also studied, which shows that a good history matched model could give a bad forecast.
history matching sum of squares inverse problems uncertainty error analysis likelihood