Watercut WΣW History Matching @model predicts production adjustments coefficients from WΣW plot by minimizing the following goal function:

E[\alpha_W(t), \alpha_O(t)] = \sum_t \ \min D \big( P_{\rm mod}(t), P_{\rm hist}(t) \big) \rightarrow 0

where is the distance between each historical point and model curve on WΣW plot:

D \big( P_{\rm mod}}(t), P_{\rm hist}(t) \big) = \sqrt{ \big( WOR_{\rm mod} - WOR_{\rm hist} \big)^2 + \big( ΣWOR_{\rm mod} - ΣWOR_{\rm hist} \big)^2  }

where

WOR_{\rm hist} = \frac{\alpha_W(t) \cdot q_W^\uparrow}{\alpha_O(t) \cdot q_O^\uparrow}

ΣWOR_{\rm hist} = \frac{ \int\limits_0^t \alpha_W(t) \cdot q_W^\uparrow \, dt}{ \int\limits_0^t \alpha_O(t) \cdot q_O^\uparrow \, dt}

and means minimal distance between point and the model curve .

The results of the history matching are illustrated on Fig. 1 below.


Fig. 1.1 – WΣW plot before history matching	Fig. 1.2 – WΣW plot after history matching


Fig. 1.2 – The production adjustments coefficients from Watercut WΣW History Matching @model

See Also