7,028 research outputs found
Application of Fast Marching Methods for Rapid Reservoir Forecast and Uncertainty Quantification
Rapid economic evaluations of investment alternatives in the oil and gas industry are typically contingent on fast and credible evaluations of reservoir models to make future forecasts. It is often important to also quantify inherent risks and uncertainties in these evaluations. These ideally require several full-scale numerical simulations which is time consuming, impractical, if not impossible to do with conventional (Finite Difference) simulators in real life situations. In this research, the aim will be to improve on the efficiencies associated with these tasks. This involved exploring the applications of Fast Marching Methods (FMM) in both conventional and unconventional reservoir characterization problems.
In this work, we first applied the FMM for rapidly ranking multiple equi-probable geologic models. We demonstrated the suitability of drainage volume, efficiently calculated using FMM, as a surrogate parameter for field-wide cumulative oil production (FOPT). The probability distribution function (PDF) of the surrogate parameter was point-discretized to obtain 3 representative models for full simulations. Using the results from the simulations, the PDF of the reservoir performance parameter was constructed. Also, we investigated the applicability of a higher-order-moment-preserving approach which resulted in better uncertainty quantification over the traditional model selection methods.
Next we applied the FMM for a hydraulically fractured tight oil reservoir model calibration problem. We specifically applied the FMM geometric pressure approximation as a proxy for rapidly evaluating model proposals in a two-stage Markov Chain Monte Carlo (MCMC) algorithm. Here, we demonstrated the FMM-based proxy as a suitable proxy for evaluating model proposals. We obtained results showing a significant improvement in the efficiency compared to conventional single stage MCMC algorithm. Also in this work, we investigated the possibility of enhancing the computational efficiency for calculating the pressure field for both conventional and unconventional reservoirs using FMM. Good approximations of the steady state pressure distributions were obtained for homogeneous conventional waterflood systems. In unconventional system, we also recorded slight improvement in computational efficiency using FMM pressure approximations as initial guess in pressure solvers
Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model
Bayesian inference methods are applied within a Bayesian hierarchical
modelling framework to the problems of joint state and parameter estimation,
and of state forecasting. We explore and demonstrate the ideas in the context
of a simple nonlinear marine biogeochemical model. A novel approach is proposed
to the formulation of the stochastic process model, in which ecophysiological
properties of plankton communities are represented by autoregressive stochastic
processes. This approach captures the effects of changes in plankton
communities over time, and it allows the incorporation of literature metadata
on individual species into prior distributions for process model parameters.
The approach is applied to a case study at Ocean Station Papa, using Particle
Markov chain Monte Carlo computational techniques. The results suggest that, by
drawing on objective prior information, it is possible to extract useful
information about model state and a subset of parameters, and even to make
useful long-term forecasts, based on sparse and noisy observations
Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution
Bayesian analysis is widely used in science and engineering for real-time
forecasting, decision making, and to help unravel the processes that explain
the observed data. These data are some deterministic and/or stochastic
transformations of the underlying parameters. A key task is then to summarize
the posterior distribution of these parameters. When models become too
difficult to analyze analytically, Monte Carlo methods can be used to
approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC)
methods are particularly powerful. Such methods generate a random walk through
the parameter space and, under strict conditions of reversibility and
ergodicity, will successively visit solutions with frequency proportional to
the underlying target density. This requires a proposal distribution that
generates candidate solutions starting from an arbitrary initial state. The
speed of the sampled chains converging to the target distribution deteriorates
rapidly, however, with increasing parameter dimensionality. In this paper, we
introduce a new proposal distribution that enhances significantly the
efficiency of MCMC simulation for highly parameterized models. This proposal
distribution exploits the cross-covariance of model parameters, measurements
and model outputs, and generates candidate states much alike the analysis step
in the Kalman filter. We embed the Kalman-inspired proposal distribution in the
DREAM algorithm during burn-in, and present several numerical experiments with
complex, high-dimensional or multi-modal target distributions. Results
demonstrate that this new proposal distribution can greatly improve simulation
efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30
times for groundwater models with more than one-hundred parameters
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