Application of Supervised Learning for Automatic History Match Quality Assessment
Authors: Kayode B. O. , Zahrani T. 
Published: February 2025

Abstract
History matching is the process of updating a geological model until its simulated outputs like pressure, and water-cut matches with historical measured data. During a history matching study, it is usual to evaluate how closely the simulated results of the wells match with measured data, this is known as history match quality assessment (HMQA), and through such assessment be able to evaluate the quality of the dynamic model. In this work, we developed a machine learning approach for automatic HMQA.
Traditionally, the three most popular approaches used for HMQA are Root Mean Square Error (RMSE), Multi-Objective Functions (mObjFunc), and Visual inspection (also known as eyeballing). RMSE and mObjFunc are purely statistical approaches, while eyeballing is based on human judgement. The challenges with RMSE and mObjFunc includes (i) susceptibility to data outliers, leading sometimes to inaccurate HMQA, (ii) the value or score they calculate don't necessarily convey a qualitative judgement of history match quality and (iii) the value or score they calculate depends on the data-types involved. For example, the calculated RMSE score for an equivalent history match quality would be different if the data being assessed is a Water-cut (WCT) than if it was a pressure match. The Visual inspection of the history match to decide whether it is excellent, acceptable or poor is based on human judgement. The challenges with visual inspection include (i) it could be subjective when applied by different users, (ii) it could be tiring when conducted on several hundreds of wells for various data-types and (iii) eyeballing rules are not standardized, therefore the HMQA decisions on every well may not follow a consistent rule. Other approaches for HMQA include the use of match factor and the use of history matching index with moving linear regression analysis etc.
In this work, we developed a Human Mind Model (HMM) for automatic HMQA of pressure and water-cut history match using supervised learning. In this approach, the user provides labeled training examples of excellent, acceptable and poor matches. The HMM model trains itself on the learning examples to determine the data density distribution (D3) that characterize each of the labeled training examples. The D3 of a training dataset is the fraction of historical data for which simulation result is within a given deviation. Using the learned D3 parameters of labeled examples, HMM predicts the HMQA of other wells using a consistent set of rules learnt from the training dataset. The approach ensures that each wells’ history match is evaluated against a consistent set of guidelines learnt by the algorithm.
In an example application involving history matching of water-cut and pressure for several wells on a hypothetical simulation model, which usually takes time for HMQA by visual inspection, the HMM conducted the HMQA within a significantly less time, generated a report and created a spatial map of history match quality which helped to identify which areas of the simulation model requires additional modifications to improve history match.
The novel aspect of this work is its ability to mimic the nuances of human judgement rather than just statistics in assessing history match quality. This work can be incorporated into commercial simulation or visualization applications, for expeditious and unbiased history match quality assessment.