This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which posses...The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.展开更多
During injection treatments, bottomhole pressure measurements may significantly mismatch modeling results. We devise a computationally effective technique for interpretation of fluid injection in a wellbore interval w...During injection treatments, bottomhole pressure measurements may significantly mismatch modeling results. We devise a computationally effective technique for interpretation of fluid injection in a wellbore interval with multiple geological layers based on the bottomhole pressure measurements. The permeability, porosity and compressibility in each layer are initially setup, while the skin factor and partitioning of injected fluids among the zones during the injection are found as a solution of the problem. The problem takes into account Darcy flow and chemical interactions between the injected acids, diverter fluids and reservoir rock typical in modern matrix acidizing treatments. Using the synchronously recorded injection rate and bottomhole pressure, we evaluate skin factor changes in each layer and actual fluid placement into the reservoir during different pumping jobs: matrix acidizing, water control, sand control, scale squeezes and water flooding. The model is validated by comparison with a simulator used in industry. It gives opportunity to estimate efficiency of a matrix treatment job, role of every injection stage, and control fluid delivery to each layer in real time. The presented interpretation technique significantly improves accuracy of matrix treatments analysis by coupling the hydrodynamic model with records of pressure and injection rate during the treatment.展开更多
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
文摘The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.
文摘During injection treatments, bottomhole pressure measurements may significantly mismatch modeling results. We devise a computationally effective technique for interpretation of fluid injection in a wellbore interval with multiple geological layers based on the bottomhole pressure measurements. The permeability, porosity and compressibility in each layer are initially setup, while the skin factor and partitioning of injected fluids among the zones during the injection are found as a solution of the problem. The problem takes into account Darcy flow and chemical interactions between the injected acids, diverter fluids and reservoir rock typical in modern matrix acidizing treatments. Using the synchronously recorded injection rate and bottomhole pressure, we evaluate skin factor changes in each layer and actual fluid placement into the reservoir during different pumping jobs: matrix acidizing, water control, sand control, scale squeezes and water flooding. The model is validated by comparison with a simulator used in industry. It gives opportunity to estimate efficiency of a matrix treatment job, role of every injection stage, and control fluid delivery to each layer in real time. The presented interpretation technique significantly improves accuracy of matrix treatments analysis by coupling the hydrodynamic model with records of pressure and injection rate during the treatment.
