Application of Physics-Informed Neural Networks (PINNs) for Real-time Interpretation of Porous Plate Capillary Pressure Tests

Summary The porous plate method is perhaps the best practice method for measuring capillary pressure curves in porous materials including geological reservoir rocks. Such curves are critical for designing secure CO2 storage, estimating hydrocarbon reserves and optimizing hydrocarbon production. However, these tests suffer from prolonged durations of months, which is costly especially when performed at reservoir conditions. During the test, two (generally different) fluid pressures are assigned on each side of the system and fluid production is measured as a response. When the production has stabilized, the system has obtained a saturation corresponding to a capillary pressure equal to the assigned pressure difference. To maximize the test value, many pressure steps are performed within the available time. We propose utilizing Physics-Informed Neural Networks (PINNs) for real-time history-matching, interpretation and decision-making for porous plate experiments. Continuously in time we match the obtained data, accounting for the possible range of solutions, and predict the optimal time at which to change the pressure setting and what the next pressures should be. The approach is compared to a predefined strategy and a rule-of-thumb strategy using first synthetic pressure-production data generated by real CO2-water curves from sandstone and then by direct application to real experimental pressure-production data. The results were compared with those obtained from conventional numerical methods. The strategy leverages the physics of two-phase flow in porous media and underlying initial and boundary conditions with multi-fidelity observational data. Random Fourier embedding effectively captures non-linearities. Training via random collocation point resampling gave more reliable and efficient computations. The results demonstrate the effectiveness of the applied strategy in calculation of capillary pressure curve, via real-time history-matching of the experimental data and reporting the uncertainties behind the evaluations. These types of experiments are usually associated with high uncertainty in the relative permeabilities. An advantage of our uncertainty-based approach is the ability to determine saturation intervals where the curves can be determined accurately. The approach also predicts the future states of the system and provides suggestions about the later pressure steps of the experiment. Consequently, both time and financial resources are conserved without compromising quality. In fact, the proposed approach assists deciding the best subsequent experimental setting to further optimize information gained, without significant supervision. Additionally, it empowers scientists to optimize the decisions, automize the calculations, reduce test durations and consequently lower the project expenses.