Jian Hou

A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems

In this paper, we propose a new mixed finite element method, called stabilized mixed finite element method, for the approximation of optimal control problems constrained by a first-order elliptic system. This method is obtained by adding suitable elementwise least-squares residual terms for the primal state variable y and its flux

Production analysis of sequential multi-well cyclic steam stimulation in heterogeneous heavy oil reservoir

sigma

Erratum to: A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems

σ. We prove the coercive and continuous properties for the new mixed bilinear formulation at both continuous and discrete levels. Therefore, the finite element function spaces do not require to satisfy the Ladyzhenkaya–Babuska–Brezzi consistency condition. Furthermore, the state and flux state variables can be approximated by the standard Lagrange finite element. We derive optimality conditions for such optimal control problems under the concept of Discretization-then-Optimization, and then a priori error estimates in a weighted norm are discussed. Finally, numerical experiments are given to confirm the efficiency and reliability of the stabilized method.

A method to recover natural gas hydrates with geothermal energy conveyed by CO2

The paper studies the particle retention and permeability impairment in porous media. This problem results from the re-injection of produced groundwater during oil production into the oilfields in order to reduce environmental damage. The lattice Boltzmann method (LBM) is used to simulate the fluid flow. The discrete element method (DEM) is adopted to simulate the particle motion. The fluid–solid interactions are simulated using the immersed moving boundary method (IMB). Based on the coupling LBM–DEM–IMB method, the paper studies the effect of particle diameter, flow rate, particle volume fraction and injection amount on the particle retention and permeability impairment. Results indicate that larger particle diameter, lower flow rate, higher volume fraction and more particle injection lead to more severe permeability impairment. In order to further study the effect of particle suspensions on heterogeneous reservoirs, a two-channel model with different permeabilities is established. The simulations show that smaller particles tend to retain in the low permeable channel and its permeability impairment is more severe. On the contrary, larger particles can reduce the permeability of high permeable channel, but they can protect the permeability of low permeable channel due to the mechanism of membrane filtration. Therefore, the sweep efficiency and oil recovery of the heterogeneous reservoirs can be improved by re-injecting produced groundwater after reasonable pretreatment. The re-injection also reduces environmental damage resulting from the large amounts of produced water in petroleum engineering. This paper provides some references for general studies on the flow of particle suspension in porous media.

Estimation of relative permeability curves using an improved Levenberg-Marquardt method with simultaneous perturbation Jacobian approximation

Sequential multi-well cyclic steam stimulation (CSS) performs better than conventional CSS in heavy oil reservoirs. It distributes all wells into two or more groups. Each group injects steam simultaneously while different groups inject one by one. This paper further studies the effect of heterogeneity on well grouping in sequential multi-well CSS and explains how it improves conventional CSS. Results indicate that the channelling wells should be put into a same group and injected simultaneously. This can expand heating area, increase moveable oil and replenish reservoir energy. After appropriate well grouping, injecting group by group can establish a pressure drop between injecting and producing groups. The pressure drop and oil displacement directions change periodically. These mechanisms improve the performance of sequential multi-well CSS in heavy oil reservoirs on both technical and economic sides. [Received: March 25, 2016; Accepted: July 24, 2016]

Production characteristic investigation of the Class I, Class II and Class III hydrate reservoirs developed by the depressurization and thermal stimulation combined method

Abstract We propose a stabilized mixed finite element approximation for optimal control problems governed by bilinear state equations. It is proved that the resulting mixed bilinear formulation is coercive and also continuous, which avoids the difficulty in choosing the mixed finite element spaces, i.e., the Ladyzhenkaya–Babuska–Brezzi matching condition for the mixed finite element spaces is unnecessary. Under pointwise bilateral constraint on the control variable, we deduce the optimality conditions at both continuous and discrete levels for the optimal control problems under consideration. Then an a priori error analysis in a weighted norm is discussed, with relatively low regularity requirements for the solutions to the optimal control problems. Finally, numerical experiments are given to confirm the efficiency and reliability of the proposed stabilized mixed finite element method.

Flow of Preformed Particle Gel through Porous Media: A Numerical Simulation Study Based on the Size Exclusion Theory

Example 6.2 For the second example, we consider the stabilized parameters μ = δ = 0.5. Table 2 shows that a first-order convergence is obtained for the control, which is well matched with the theoretical analysis. Figures 4, 5, and 6 show the approximate profiles of the control, the state, and the flux state, respectively, when the lowest order RT element is adopted for the approximation of the flux σ .