Time-Domain Difference Modeling Of The Electromagnetic Wave Logging

The method of Finite Difference Time Domain, or (FDTD), is a new electromagnetic field numerical solution. FDTD disperses two Maxwell's Curl equations directly, that is, Faraday electromagnetic induction theorem and Ampere loop theorem, by central difference in space and time, and gets a group of explicit electromagnetic field recursive equations. As a electromagnetic field numerical method, in recent years it has been more widely used.As the development of the secondary and tertiary recovery of oil production in the oil industry, the water layer with low or high resistivity is not uncommon, sometimes it fails to distinguish oil layer and water layer with conductivity. In the high-frequency conditions, the permittivity of water is bigger than other media`s permittivity which are often encountered in well logging at least an order of magnitude, but not with changes in salinity. So to distinguish oil layer and water layer with permittivity sometimes is more effective than conductivity.Electromagnetic wave logging is also called dielectric logging, it can measure the conductivity and permittivity of the formation around the hole. Owing to the effect of electromagnetic wave propagation, in the process of the spread of electromagnetic waves, the phase of electromagnetic wave will be changed and the amplitude will be attenuated, so that the signal of two receive coil (or antenna) has difference in phase and amplitude. By recording phase difference and amplitude ratio, it can be effective to calculate the formation`s conductivity and permittivity.In this paper, it is used of FDTD to make forward modeling of electromagnetic wave logging, respectively, according to the actual situation it simulates electromagnetic wave logging-response curve (phase difference and amplitude ratio curve) about the horizontal layer in two-dimensional cylindrical coordinate system (TE-and TM mode) and logging-response curve (decay rate and the time difference curve) in three-dimensional cylindrical coordinate system. Specifically speaking:In cartesian coordinate system, introduces the principle of the FDTD method and the numerical stability conditions, numerical dispersion conditions, excitation source set method, Mur second order absorbing boundary conditions, and verifies the Mur second order absorbing boundary conditions on the electromagnetic wave absorption; In cylindrical coordinate system, under the conditions of the underground lossy isotropic medium deducts FDTD equation in two-dimensional TE mode, two-dimensional TM mode and three–dimensional mode, further research numerical stability conditions, numerical dispersion conditions, excitation source set method when used FDTD in cylindrical coordinate system. In addition, deducts Mur first order, second order absorbing boundary conditions in cylindrical coordinate system and processing method under the corner of the approach in two-dimensional TE mode and two-dimensional TM mode, verifies that it is good for the electromagnetic wave absorption.In order to carry out the forward modeling of electromagnetic waves logging, prepares three main types of programs in VC++6.0 platform, including realization of FDTD method in two-dimensional TE mode and two-dimensional TM mode, as well as three-dimensional mode. Specifically there are nine programs, the achievements of their function are: simulation of the electromagnetic logging response curve of formation (single and double layer) in two-dimensional TE mode according to the actual measured process; the mutual relationships between phase difference,amplitude ratio and underground medium`s conductivity,permittivity in two-dimensional TE mode; the impact of bed thickness on logging response in two-dimensional TE mode; simulation of the electromagnetic logging response curve of formation (single and double layer) in two-dimensional TM mode according to the actual measured process; the mutual relationships between phase difference,amplitude ratio and underground medium`s conductivity,permittivity in two-dimensional TM mode; the impact of bed thickness on logging response in two-dimensional TM mode; the impact of wellbore for logging response in two-dimensional TM mode (the changes of conductivity of bore mud,permittivity of bore mud and wellbore diameter ); the mutual relationships between decay rate,time difference and underground medium`s conductivity,permittivity in three-dimensional mode; the response of logging of EPT at the interface of the formation in three-dimensional mode. At the same time, compares the analytical solution with numerical solution (at the underground uniform medium) in the program which achieves the mutual relationships between phase difference,amplitude ratio and underground medium`s conductivity,permittivity in two-dimensional TE mode, the results is in good agreement.According to the results of programming it can be concluded that response of logging is very sensitive and change of logging curve is clear when use FDTD to make forward modeling of electromagnetic wave logging. On this basis, can draw the following conclusions:⑴,Phase difference and amplitude ratio about Electromagnetic waves logging increase as the conductivity of underground media increasing;⑵,In the high-frequency conditions, the shape of the phase difference curve is much better than the amplitude ratio curve, it reflects the true distribution of the formation parameters better, so analyses the impact of bed thickness primarily based on phase difference curve. When formation thickness is greater than or equal to the length of coil (electrode), logging response is obvious at the interface of the formation, it can distinguish the interface of the formation exactly; When formation thickness is less than the length of coil (electrode), there lacks obvious signs of logging response at the interface of formation so that it makes a certain impact on distinguishing formation;⑶,Because of using a relative measure for electromagnetic wave logging, the changes of conductivity of bore mud and permittivity and the changes of wellbore diameter have a smaller impact on logging response of electromagnetic wave logging. When conductivity of bore mud is small, it is no need to correct the impact of wellbore. When conductivity of bore mud is big, the decay of electromagnetic wave is big in the hole, the impact of wellbore increases, it need to correct the impact of wellbore;⑷,The logging response of the electromagnetic wave propagation logging has the following characteristics: At the interface of formation the time difference curve has obvious characteristic points, from the time difference curve it can distinguish the interface of formation exactly, nevertheless, the interface of formation basically corresponds to the half amplitude point of the decay rate curve.In the process of forward modeling of electromagnetic wave logging, it makes the efficiency of calculating be greatly improved by using the FDTD method to calculate the response of formation in the condition of axial symmetry in two-dimensional cylindrical coordinate system. in addition, it makes the results of calculating more realistic and more accurate by using the FDTD method to calculate the response of formation in the condition of non axial symmetry in three-dimensional cylindrical coordinate system. Using the FDTD method to make forward modeling of electromagnetic wave logging lays a good foundation for the future research of the logging response of electromagnetic wave logging in all cases.