Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media

This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.

Distributed Adaptive Formation Control for Underactuated Quadrotors with Guaranteed Performances

This paper investigates a distributed adaptive formation control problem for underactuated quadrotors with guaranteed performances. To ensure a robust and stable formation pattern with predefined behavior bounds, by transforming the original constrained formation synchronization error dynamics into an equivalent unconstrained one, a prescribed performance mechanism is introduced in the translational loop to render the formation regulation as a prior. Based on the graph theory and Lyapunov stability analysis, a state estimator-based minimal learning parameter (SE-MLP) neuroadaptive consensus strategy is developed for follower quadrotors to achieve a distributed cooperative formation with prescribed tracking abilities via exchanging local information with neighbors. The presented control scheme has the following salient merits: 1) the formation synchronization errors can be guaranteed within pre-assigned bounds with desired transient behaviors despite of uncertain disturbances; 2) by using a state estimation error to update neural network (NN) parameters, rather than the tracking error that widely applied in traditional NN approximators, and with the help of MLP technique, the proposed SE-MLP observer capable of decreasing the computational complexity can achieve a fast identification of lumped disturbances without causing high-frequency oscillations even using a large adaptive gain, and the transient solutions of L 2 norm of the differential of neural weights are established to illustrate the mechanism of SE-MLP observer in reducing chattering behaviors. Simulation results are given to validate the efficiency of developed technique.

Analytic transient solutions of a cylindrical heat equation

The principles of superposition and separation of variables are used here in order to investigate the analytical solutions of a certain transient heat conduction equation. The structure of the transient temperature appropriations and the heat-transfer distributions are summed up for a straight mix of the results by means of the Fourier-Bessel arrangement of the exponential type for the investigated partial differential equation.

PWR MOX/UO2 Transient Benchmark Calculation Using Monte Carlo Serpent 2 Code and Open Nodal Core Simulator ADPRES

This paper presents static and transient solutions for the PWR MOX/UO2 transient benchmark by Serpent 2 Monte Carlo code and open nodal core simulator called ADPRES. The presences of MOX fuels and burn-up variation in the benchmark’s reactor core pose challenges for reactor simulators due to severe flux gradient across fuel assemblies. In this work, the two-step method was used, in which the assembly level two-group constants were generated from single assembly calculations with zero net current boundary conditions using Serpent 2 Monte Carlo code, and later the core calculation was performed using ADPRES open nodal core simulator. Two types of diffusion coefficients were generated: the conventional B1 leakage corrected and Cumulative Migration Method (CMM). Finally, the solutions of Serpent 2/ADPRESS, including multiplication factor, power distribution, control rod worth, and critical boron concentration using both diffusion coefficients were compared against solutions from heterogeneous Serpent 2 calculations where the fuel and cladding are explicitly modeled. The reactor power during transients were also compared qualitatively against other nodal core simulators. The results showed that Serpent 2/ADPRES were able to predict the heterogeneous Monte Carlo solutions very well with reasonable differences. The transient solutions were also quite accurate compared to other nodal core simulators. As for the diffusion coefficients comparison, it was found that the CMM diffusion coefficient provide more accurate solutions for the benchmark compared to the B1 leakage corrected diffusion coefficients.