The ensemble Kalman filter (EnKF) algorithm is an elegant and effective method to optimize model parameters based on differences with predictions of model and measurement data. Great progress has been accomplished using EnKF for data assimilation within reservoir modeling during the last two decades. A typical example where data assimilation is necessary is history matching—the process of adjusting the model variables to account for observations of rates, pressure, saturations, and other variables. In contrast, much less attention has been given to flow model optimization for other workflows, such as drilling, production, flow assurance, and well testing.
Providing two examples of applying the EnKF for real-time quantification of sensor-generated data is the aim of this paper. These examples include the analysis of the declining production curve and zonal pressure sensor data for evaluating matrix permeabilities and processing the multichannel optical to monitor the cleanup of hydrocarbon fluid samples during formation-tester sampling.
Additionally, how the EnKF algorithm can be successfully applied to segmented multichannel sensor field data obtained from multichannel optical density sensors exhibiting the gradual transition from oil-based mud (OBM) filtrate to native formation fluid during formation-tester sampling stations is discussed. A simple algebraic proxy model is used to predict the decline of the volumetric fraction of OBM filtrate with time during formation-tester sampling.
To implement and test the algorithm, a proof-of-concept MATLAB code was developed. Synthetic (simulated) pressure flow rate data were used for the production decline case while the actual field data from eight channel optical sensors were used for the formation-testing case. Model runs were performed in 50 to 60 combinations of model parameters, which were normally distributed around the best-guess values at the initial step. For both cases, only two to three iterations of the algorithm were sufficient to obtain values of the matching parameters.