(181a) Real-Time Determination of Well and Formation Parameters Using Ensemble Kalman Filters

This paper discusses applications of the Ensemble Kalman Filter (EnKF) for the real-time quantification of sensor-generated data in two examples: the analysis of the declining production curve and zonal pressure sensor data for evaluating the matrix permeabilities and processing of multichannel optical to monitor the cleanup of hydrocarbon fluid samples in oil-based muds during formation-tester sampling.

The EnKF algorithm is an elegant and effective method used to optimize model parameters based on differences in predictions of model and measurement data. This paper explains how the same EnKF algorithm can be successfully applied to segmented multichannel sensor data in two very different applications: declining total production and zonal pressure data in a synthetic example of a fracture-stimulated wellbore, and field data obtained from multichannel optical density sensors showing the gradual transition from oil-based mud (OBM) filtrate to native formation fluids during formation-tester sampling stations. In the first case, the pressure depletion and production is simulated using an effective 2-D fracture production model, while 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 test the algorithm, a MATLAB code was developed, proving the high efficiency of the suggested method. At each time step, approximately 100–150 sampling data points from the multichannel sensors were processed. Synthetic (simulated) pressure flow rate data was used in the production decline case, while the actual field data from 8‑channel optical sensors were used in the formation-testing case. Model runs were performed in 50–60 combinations of the model parameters, which were normally distributed around the best-guess values at the initial step. In both cases, only 2–3 iterations of the algorithm were sufficient to obtain the values of the matching parameters.

In the case of the fracture system, the zonal permeabilities, which varied within an order of magnitude, were effectively found, with accuracy defined by the accuracy set for the measured pressure and flow rates. In the formation-testing case, the spectral optical densities, instant values of the OBM volume fraction, and the endpoints (spectral densities of mud and oil) were determined. The algorithm has shown to converge for all test runs, and an average accuracy of approximately 5 percent has been achieved.

Currently, both dynamic history matching for fracture modeling and formation-tester analysis are being carried out manually, making real-time analysis difficult. The suggested method combines advantages of modern multichannel data acquisition and advanced data science. The algorithm is universal, fast, stable, and can be applied to a variety of different workflows and models incorporating multichannel data and run in real time, thereby enhancing the operators’ ability to make timely decisions during operations.