Geosteering is a sequential decision process under uncertainty. The goal of geosteering is to maximize the expected value of the well, which should be defined by an objective value-function for each operation.In this paper we present a real-time decision support system (DSS) for geosteering that aims to approximate the uncertainty in the geological interpretation with an ensemble of geomodel realizations. As the drilling operation progresses, the ensemble Kalman filter is used to sequentially update the realizations using the measurements from real-time logging while drilling. At every decision point a discrete dynamic programming algorithm computes all potential well trajectories for the entire drilling operation and the corresponding value of the well for each realization. Then, the DSS considers all immediate alternatives (continue/steer/stop) and chooses the one that gives the best predicted value across the realizations. This approach works for a variety of objectives and constraints and suggests reproducible decisions under uncertainty. Moreover, it has real-time performance.The system is tested on synthetic cases in a layer-cake geological environment where the target layer should be selected dynamically based on the prior (predrill) model and the electromagnetic observations received while drilling. The numerical closed-loop simulation experiments demonstrate the ability of the DSS to perform successful geosteering and landing of a well for different geological configurations of drilling targets. Furthermore, the DSS allows to adjust and reweight the objectives, making the DSS useful before fully-automated geosteering becomes reality.
The formation of capillary bridge formed by a liquid adsorbate is one of the main reasons for agglomeration in multiphase flows. Agglomeration takes place when the relative momentum of two colliding particles is fully consumed by the bridge. This article presents a theoretical study of the collisions of particles with adsorbed liquid taking into account the influence of capillary and viscous dissipative forces. The article proposes an approximate analytical solution for the dynamics of the bridge formed during the collision, together with a more complete numerical model, which is validated with experimental data. The restitution of the relative momentum of the colliding particles, depending on a series of dimensionless parameters characterizing the bridge, is investigated. A criterion for prediction of agglomeration, or "collision efficiency," in a flow involving cohesive particles is given. An expression is proposed for the coefficient of restitution for the case of collision via a liquid bridge. _ ext 50, v A 0 520:052, v S 0 50:052.The arrows indicate the direction of particle movement.
Abstract. The standard approximation for the flow-pressure relationship in porous media is Darcy's law that was originally derived for infiltration of water in fine homogeneous sands. Ever since there have been numerous attempts to generalize it for handling more complex flows. Those include upscaling of standard continuum mechanics flow equations from the fine scale. In this work we present a heterogeneous multiscale method that utilizes fine scale information directly to solve problems for general single phase flow on the Darcy scale. On the coarse scale it only assumes mathematically justified conservation of mass on control volumes, that is, no phenomenological Darcy-type relationship for velocity is presumed. The fluid fluxes are instead provided by a fine scale Navier-Stokes mixed finite element solver. This work also considers several choices of quadrature for data estimation in the multiscale method and compares them. We prove that for an essentially linear regime, when the fine scale is governed by Stokes flow, our method converges to a rigorously derived homogenization solution-Darcy's law. Moreover the method gives the flexibility to solve problems with faster nonlinear flow regimes that is important in a number of applications, such as flows that may occur near wells and in fractured regions in subsurface. Those flows are also common for industrial and near surface porous media. The numerical examples presented in the paper verify the estimate and emphasize the importance of good data estimation.
Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We present a methodology to construct a deep neural network (DNN) model trained to reproduce a full set of extra-deep EM logs consisting of 22 measurements per logging position. The model is trained in a 1D layered environment consisting of up to seven layers with different resistivity values.A commercial simulator provided by a tool vendor is utilized to generate a training dataset.The dataset size is limited because the simulator provided by the vendor is optimized for sequential execution.Therefore,we design a training dataset that embracesthe geological rules and geosteering specifics supported by the forward model. We use this dataset to produce an EM simulator based on a DNN without access to the proprietary information about the EM tool configuration or the original simulator source code.Despite employing a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multi-layer synthetic case and a section of a published historical operation from the Goliat Field.The observed average evaluation time of 0.15 milliseconds per logging position makes it also suitable for future use as part of evaluation-hungry statistical and/or Monte-Carlo inversion algorithms within geosteering workflows.
Quantitative workflows utilizing real-time data to constrain ahead-of-bit uncertainty have the potential to improve geosteering significantly. Fast updates based on real-time data are essential when drilling in complex reservoirs with high uncertainties in pre-drill models. However, practical assimilation of realtime data requires effective geological modelling and mathematically robust parameterization. We propose a generative adversarial deep neural network (GAN), trained to reproduce geologically consistent 2D sections of fluvial successions. Offline training produces a fast GAN-based approximation of complex geology parameterized as a 60-dimensional model vector with standard Gaussian distribution of each component. Probabilistic forecasts are generated using an ensemble of equiprobable model vector realizations. A forward-modelling sequence, including a GAN, converts the initial (prior) ensemble of realizations into EM log predictions. An ensemble smoother minimizes statistical misfits between predictions and real-time data, yielding an update of model vectors and reduced uncertainty around the well. Updates can be then translated to probabilistic predictions of facies and resistivities. The present paper demonstrates a workflow for geosteering in an outcrop-based, synthetic fluvial succession. In our example, the method reduces uncertainty and correctly predicts most major geological features up to 500 meters ahead of drill-bit.
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