Earth Resources Laboratory
http://hdl.handle.net/1721.1/67704
2015-01-14T14:12:50ZReal-time ensemble control with reduced-order modeling
http://hdl.handle.net/1721.1/90537
Real-time ensemble control with reduced-order modeling
Lin, Binghuai; McLaughlin, Dennis
The control of spatially distributed systems is often complicated by significant uncertainty about system inputs, both time-varying exogenous inputs and time-invariant parameters. Spatial variations of uncertain parameters can be particularly problematic in geoscience applications, making it difficult to forecast the impact of proposed controls. One of the most effective ways to deal with uncertainties in control problems is to incorporate periodic measurements of the systemâ€™s states into the control process. Stochastic control provides a convenient way to do this, by integrating uncertainty, monitoring, forecasting, and control in a consistent analytical framework. This paper describes an ensemble-based approach to closed-loop stochastic control that relies on a computationally efficient reduced-order model. The use of ensembles of uncertain parameters and states makes it possible to consider a range of probabilistic performance objectives and to derive real-time controls that explicitly account for uncertainty. The process divides naturally into measurement updating, control, and forecasting steps carried out recursively and initialized with a prior ensemble that describes parameter uncertainty. The performance of the ensemble controller is investigated here with a numerical experiment based on a solute transport control problem. This experiment evaluates the performance of open and closed-loop controllers with full and reduced-order models as well as the performance obtained with a controller based on perfect knowledge of the system and the nominal performance obtained with no control. The experimental results show that a closed-loop controller that relies on measurements consistently performs better than an open loop controller that does not. They also show that a reduced-order forecasting model based on offline simulations gives nearly the same performance as a significantly more computationally demanding full order model. Finally, the experiment indicates that a moderate penalty on the variance of control cost yields a robust control strategy that reduces uncertainty about system performance with little or no increase in average cost. Taken together, these results confirm that reduced-order ensemble closed-loop control is a flexible and efficient control option for uncertain spatially distributed systems.
2013-01-01T00:00:00ZEfficient characterization of uncertain model parameters with a reduced-order ensemble Kalman filter
http://hdl.handle.net/1721.1/90536
Efficient characterization of uncertain model parameters with a reduced-order ensemble Kalman filter
Lin, Binghuai; McLaughlin, Dennis
Spatially variable model parameters are often highly uncertain and di fficult to observe. This has prompted the widespread use of Bayesian characterization methods that can infer parameter values from measurements of related variables, while explicitly accounting for uncertainty. Ensemble versions of Bayesian characterization are particularly convenient when uncertain variables have complex spatial structures that do not conform to Gaussian descriptions. However, ensemble methods can be time-consuming for high-dimensional problems. This paper describes a reduced-order approach to ensemble characterization that is particularly well-suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform (DCT) to reduce the dimensionality of spatially variable time-invariant model parameters and a nonlinear extension of principle orthogonal decomposition (POD) to reduce the dimensionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step of a reduced-order ensemble Kalman fi lter. These concepts are illustrated in a subsurface solute transport problem using ensembles produced by full and reduced-order order models. These ensembles are very similar when there are no measurement updates. When the forecast ensemble is recursively updated with measurements the reduced-order Kalman fi lter does at least as well as the full-order fi lter in characterizing a dynamic solute plume, even though its augmented state dimension is only 2% of the dimension of the full-order state. This substantial increase in effi ciency implies that a reduced-order fi lter with the same ensemble size as its full-order counterpart can give comparable performance for orders of magnitude less computational e ffort or can use a much larger ensemble for the same computational e ffort. The possibility of substantial increases in ensemble size could lead to performance improvements through reductions in sampling error and in the rank of the ensemble null space. Also, a reduced-order model similar to the one described here could be used in ensemble real-time control applications, where it can decrease the eff ort required for both characterization and control.
2013-01-01T00:00:00ZEfficient Double-Beam Characterization for Fractured Reservoir
http://hdl.handle.net/1721.1/90535
Efficient Double-Beam Characterization for Fractured Reservoir
Zheng, Yingcai; Fang, Xinding; Fehler, Michael; Burns, Daniel R.
We proposed an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.
2012-06-01T00:00:00ZExperimental studies of the acoustic wave field near a borehole
http://hdl.handle.net/1721.1/90534
Experimental studies of the acoustic wave field near a borehole
Zhu, Zhenya; Liu, Xien; Gu, Chen; Toksoz, M. Nafi
A monopole or a dipole source in a fluid borehole generates acoustic waves, part of which propagate along the borehole and the other part enter the formation propagating as P- or S-waves. The refracted waves propagating along the borehole wall are used to determine P- and S-wave velocities. However, a significant fraction of the seismic energy radiates into the formation. In this laboratory study, we measure the acoustic waves in the borehole and the seismic waves in the formation at different distances from the borehole.
We use scaled borehole models made of Lucite and of concrete to simulate a soft and a hard formation, respectively. The waveforms are measured in the boreholes as well as in the formations with different radial distances from the axis of the borehole. The results show that the investigation depth of the wave measured in the borehole is less than one half of the wavelength. The seismic energy radiating into the formation and scattered from interfaces and heterogeneities can be used for imaging the formation.
2013-01-01T00:00:00Z