Forward And Inverse Study For Estimating Anisotropic Permeability Utilizing Dipole Flexural Waves In A Borehole

Permeability is one of the most important parameter that estimates the reserves of formation. There are a lot of works to gained the permeability in long time. Biot established the two-phase medium elastic theory in 1956, indicate the parameters like permeability and porosity effects the acoustic character of hole medium. Rosenbaum use this theory on the side of acoustic well logging, found that permeability is closely related to Stoneley-wave. Kexie Wang had reviewed the permeability's and porosity's effect on the field of well acoustic in cylindrical model, established definitely that the attenuation of Stoneley-wave is the most sensitive to permeability. Jun Ma used the flexural wave to calculate the permeability of formation first, gained satisfactory result. In this paper, we use the dipole acoustic well logging data to calculate the permeability in the isotropy model and transverse isotropy model.Firstly, prove theory expressions the field of acoustic which is excitated by dipole source in isotropy and transverse isotropy hole model, and simulate in numerical value, draw the full wave picture which is excitated by dipole source. Analyse the mode wave in each model, research the guide wave which is toward the apices residua in apex wave number plane. Calculate the exact analytic formula from the dispersion formula of the guide wave, and make the program of it.Secondly, research the flexural wave's dispersion, attenuation and the range ratio of two wave in fast and slow formation of the two models, found that in isotropy model, the dispersion of flexural wave is sensitive to different porosities, but not to different permeabilities; in contrary that its attenuation is sensitive to different permeabilities but not to different porosities, so we believe that we can use the attenuation to calculate the permeability of formation. In transverse isotropy model, the dispersion of flexural wave is sensitive different porosities, but the distinction become little when in high frequency field, it is sensitive to neither horizontal nor vertical permeability. In fast formation, the attenuation is very sensitive to different horizontal permeabilities, but it does nothing to vertical permeability, even its change by different porosities is more obviously. In slow formation, the condition is better than fast formation, the attenuation is more sensitive to both horizontal permeability and vertical permeability. So we conjecture that it is feasible to use the attenuation of flexural wave to calculate the permeability of transverse isotropy formation, especially in slow formation. In fast formation, the horizontal permeability can be calculated also.Finally, we use the flexural wave which intercept from full wave as the sampling function and the flexural wave which is calculated by residua of pole formula as the theory model function, calculate the permeability by nonlinear ordinary least squares estimation. Research the square error between theory model function and sampling function's change along the permeability's change, approve that the curve has only one minimum point. When the permeability leave the point, the error ascends humdrum, show the dependability of the calculation. As the result that the error of the calculation is little than 5% from middle to high permeability field, and the slow formation's result is better than fast formation's, and the error is little along with the permeability's increase. In the transverse isotropy formation, the result of vertical permeability is not satisfaction in fast formation, but the horizontal permeability is better, the error is little than 10%. In slow formation, the result is also better than fast formation, when the two permeability's difference is not very much, the error is both little than 10%. So we believe the result is correct.