Ensemble-based well-log interpretation and uncertainty quantification for well geosteering

Abstract

Hydrocarbon reservoirs are often located in spatially complex and uncertain geological environments, where the associated costs of drilling wells for exploration and development are notoriously high. These costs may be reduced with an optimized well-placement strategy based on real-time geological information, known as well geosteering. To effectively place the well in an updated geomodel and support well geosteering decisions in real-time, we apply an iterative inversion approach based on the Levenberg-Marquardt form of the Ensemble Randomized Maximum Likelihood method. The method estimates geomodel properties together with their uncertainties by reducing the statistical misfit between the measurements acquired with well-logging tools and the predicted measurements from numerical simulations. Analyses of synthetic cases indicate that the method's reliability and computational speed depend on the distance from the logging tool to formation boundaries, the contrast of model properties, and the thickness of formation layers. The proposed method delivers reliable estimates of model properties with only 40 ensemble members and 2--10 iterations, hence it is approximately 10--125 times faster than Metropolis-Hastings Monte Carlo, which we use as a baseline condition given its proven track record. Likewise, the developed method is amenable to parallelization to further reduce computational times.Implementation of the method with a synthetic example inspired by a historical well geosteering operation yielded accurate formation evaluation and verified its accurate and reliable performance under complex geological conditions.

Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements

“…In the first test case, layer resistivities are estimated by the inversion of EM measurements using DNN as a forward model, while the boundary positions remain fixed. This test case allows us to evaluate the performance of the real-time inversion of EM measurements in the absence of pronounced multi-modality, where an ensemble method can avoid local minima [Jahani et al, 2022]. In the second test case, the top boundary location, layers' thicknesses, and resitivities are jointly estimated.…”

“…layer positions) and resistivities in the subsurface environment. Other petrophysical properties could also be implicitly inferred [Jahani et al, 2022, Luo et al, 2015. Mathematically, DeepEM signals can be represented as a vector function of the subsurface properties and can be written as follows:…”

“…In that context, Bayesian algorithms can be useful for real-time inversion because of the flexibility to account for non-uniqueness and uncertainties. Among those Bayesian algorithms, iterative ensemble filters/smoothers can be the best choice for real-time inversion due to the relatively low computational cost and the parallelizable nature of the algorithm [Chen et al, 2015, Jahani et al, 2022.…”

“…These model-errors are unknown and in general vary with the forward problem, the selected DNN architecture, training setting, and amount of training data. Despite that, previous attempts at inverting deep-learning models did not address the approximating nature of the DNN models [Jahani et al, 2022, Wang et al, 2021. During real-time inversion of electromagnetic (EM) measurements, the neglect of model-errors could produce bias in the estimated input parameters of the DNN model and result in sub-optimal decisions.…”

Real-Time Automated Geosteering Interpretation Combining Log Interpretation and 3D Horizon Tracking

“…Various information, such as formation porosity, water saturation, presence of hydrocarbons, etc., can be inferred from the resistivity well logs. In [14][15][16], the response of a resistivity tool to the formation rock is modeled as an electro-magnetic simulator and the ensemble Kalman filter (EnKF) is adopted to estimate the formation boundaries. More recent publications [13,[17][18][19] adopted sequential Monte Carlo techniques (i.e., particle filters) as a substitution of the Kalman filter.…”