Model Predictive Control of Heat Pump Water Heaters for Energy Efficiency
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We compare two approaches for building a statistical proxy model (metamodel) for CO₂ geologic sequestration from the results of full-physics compositional simulations. The first approach involves a classical Box-Behnken or Augmented Pairs experimental design with a quadratic polynomial response surface. The second approach used a space-filling maxmin Latin Hypercube sampling or maximum entropy design with the choice of five different meta-modeling techniques: quadratic polynomial, kriging with constant and quadratic trend terms, multivariate adaptive regression spline (MARS) and additivity and variance stabilization (AVAS). Simulations results for CO₂ injection into a reservoir-caprock system with 9 design variables (and 97 samples) were used to generate the data for developing the proxy models. The fitted models were validated with using an independent data set and a cross-validation approach for three different performance metrics: total storage efficiency, CO₂ plume radius and average reservoir pressure. The Box-Behnken–quadratic polynomial metamodel performed the best, followed closely by the maximin LHS–kriging metamodel.
Energy and particle transport rates are decoupled in the H-mode edge since the ion thermal transport rate is primarily set by the neoclassical transport of the deuterium ions in the tail of the thermal energy distribution, while the net particle transport rate is set by anomalous transport of the colder bulk ions. Ion orbit loss drives the energy distributions away from Maxwellian, and describes the anisotropy, poloidal asymmetry and local minimum near the separatrix observed in the Ti profile. Non-Maxwellian distributions also drive large intrinsic edge flows, and the interaction of turbulence at the top of the pedestal with the intrinsic edge flow can generate an intrinsic core torque. The primary driver of the radial electric field (Er) in the pedestal and scrapeoff layer (SOL) are kinetic neoclassical effects, such as ion orbit loss of tail ions and parallel electron loss to the divertor. This paper describes the first multi-species kinetic neoclassical transport calculations for ELM-free H-mode pedestal and scrape-off layer on DIII-D using XGC0, a 5D full-f particle-in-cell drift-kinetic solver with self-consistent neutral recycling and sheath potentials. Quantitative agreement between the flux-driven simulation and the experimental electron density, impurity density and orthogonal measurements of impurity temperature and flow profiles is achieved by adding random-walk particle diffusion to the guiding-center drift motion. This interpretative technique quantifies the role of neoclassical, anomalous and neutral transport to the overall pedestal structure, and consequently illustrates the importance of including kinetic effects self-consistently in transport calculations around transport barriers.
Reduced-order models provide a means for greatly accelerating the detailed simulations that will be required to manage CO 2 storage operations. In this work, we investigate the use of one such method, POD-TPWL, which has previously been shown to be effective in oil reservoir simulation problems. This method combines trajectory piecewise linearization (TPWL), in which the solution to a new (test) problem is represented through a linearization around the solution to a previously-simulated (training) problem, with proper orthogonal decomposition (POD), which enables solution states to be expressed in terms of a relatively small number of parameters. We describe the application of POD-TPWL for CO 2 -water systems simulated using a compositional procedure. Stanford’s Automatic Differentiation-based General Purpose Research Simulator (AD-GPRS) performs the full-order training simulations and provides the output (derivative matrices and system states) required by the POD-TPWL method. A new POD-TPWL capability introduced in this work is the use of horizontal injection wells that operate under rate (rather than bottom-hole pressure) control. Simulation results are presented for CO 2 injection into a synthetic aquifer and into a simplified model of the Mount Simon formation. Test cases involve the use of time-varying well controls that differ from those used in training runs. Results of reasonable accuracy are consistently achieved for relevant well quantities. Runtime speedups of around a factor of 370 relative to full- order AD-GPRS simulations are achieved, though the preprocessing needed for POD-TPWL model construction corresponds to the computational requirements for about 2.3 full-order simulation runs. A preliminary treatment for POD-TPWL modeling in which test cases differ from training runs in terms of geological parameters (rather than well controls) is also presented. Results in this case involve only small differences between training and test runs, though they do demonstrate that the approach is able to capture basic solution trends. The impact of some of the detailed numerical treatments within the POD-TPWL formulation is considered in an Appendix.
Aerial gamma ray surveys are important for those working in nuclear security and industry for determining locations of both anthropogenic radiological sources and natural occurrences of radionuclides. During an aerial gamma ray survey, a low flying aircraft, such as a helicopter, flies in a linear pattern across the survey area while measuring the gamma emissions with a sodium iodide (NaI) detector. Currently, if a gamma ray survey is being flown in an area, the only way to correct for geologic sources of gamma rays is to have flown the area previously. This is prohibitively expensive and would require complete national coverage. This project’s goal is to model the geologic contribution to radiological backgrounds using published geochemical data, GIS software, remote sensing, calculations, and modeling software. K, U and Th are the three major gamma emitters in geologic material. U and Th are assumed to be in secular equilibrium with their daughter isotopes. If K, U, and Th abundance values are known for a given geologic unit the expected gamma ray exposure rate can be calculated using the Grasty equation or by modeling software. Monte Carlo N-Particle Transport software (MCNP), developed by Los Alamos National Laboratory, is modeling software designed to simulate particles and their interactions with matter. Using this software, models have been created that represent various lithologies. These simulations randomly generate gamma ray photons at energy levels expected from natural radiologic sources. The photons take a random path through the simulated geologic media and deposit their energy at the end of their track. A series of nested spheres have been created and filled with simulated atmosphere to record energy deposition. Energies deposited are binned in the same manner as the NaI detectors used during an aerial survey. These models are used in place of the simplistic Grasty equation as they take into account absorption properties of the lithology which the simplistic equation ignores.
The research project aims to develop and validate an advanced computer model that can be used in the planning and design of stimulation techniques to create engineered reservoirs for Enhanced Geothermal Systems. The specific objectives of the proposal are to: 1) Develop a true three-dimensional hydro-thermal fracturing simulator that is particularly suited for EGS reservoir creation. 2) Perform laboratory scale model tests of hydraulic fracturing and proppant flow/transport using a polyaxial loading device, and use the laboratory results to test and validate the 3D simulator. 3) Perform discrete element/particulate modeling of proppant transport in hydraulic fractures, and use the results to improve understand of proppant flow and transport. 4) Test and validate the 3D hydro-thermal fracturing simulator against case histories of EGS energy production. 5) Develop a plan to commercialize the 3D fracturing and proppant flow/transport simulator. The project is expected to yield several specific results and benefits. Major technical products from the proposal include: 1) A true-3D hydro-thermal fracturing computer code that is particularly suited to EGS, 2) Documented results of scale model tests on hydro-thermal fracturing and fracture propping in an analogue crystalline rock, 3) Documented procedures and results of discrete element/particulate modeling of flow and transport of proppants for EGS applications, and 4) Database of monitoring data, with focus of Acoustic Emissions (AE) from lab scale modeling and field case histories of EGS reservoir creation.
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