Research On Skin Effect Of Induction Logging

The reserch on induction logging which pepole usually do base on the solution of the Maxwell's electromagnetic field equations of the space,and they have get some conclusions.However,the phsical essence of the skin effect occuring ,in other words,is the mutual inductance and self inductance has not been used for the pupose.By establishng a geological mode,we apply the mutual inductance principle for calculating the induced current of stratum.We get the formulas of the mutual inductance and inductace of the rings which are coaxial.Where mutual inductance M and inductance L have the following characteristics:①Mutual inductance between the coil become smaller as distance increases.②When the two coils radius ratio is closer to 1, the greater the mutual inductance.③The bigger of the radius of the current loop,the larger the mutal inductance and inductance.When we establishing the model,we consider it as a cylinder which has a limited radius and high .Here we need emphasize that although this boundary may get not very actual results ,it's enough in the range of induction logging.Taking into account the axial symmetry, we separated the whole into some series rings.The follows are the conditions and the ways.⑴If the radius of the rings are small enough,it's not only the skin effect can be ignored but the current density is uniform or only the function of radius.⑵In the primary the flux through a surface boundary by the ring only produce the primary current,there is no induction current in the stratum.Then we only consider the impact of the changed current but not the whole.⑶Although the inductance near the borehole is not actual,the current in any ring is the result of the sum of all the current in fomation,so it's can also be ignored. ⑷The same length of model which is divided into how many rings is not important,in fact only the width sastify the conditions which the formulas of the inductance and mutual inductance need.Considering the I is the product of the j and s,it's equal regardless if it's wide or narrow.⑸We consider the formation of mutual inductance value should clearly be a three-dimensional matrix, if the score is too fine ,matrix becomes very large, more than the memory of PC. In the actual processing we adopt the ways which must meet the preceding several conditions to divide the model.We will apply this method to the actual stratum and draw three types curves.One is that surrounding rock is mud rock and stratum is sand,thichess is fixed,and R is varying.The second is that thickness is varying and R is fixed.The third is that there is mud rock in the sand.We take those results with the results obtained by geometric factor theory for comparison so that we test the theory is right.On the other hand when the electrical conductivity is higher,differences proved the skin effect in induction logging.we expain the characters by the mutual inductance between currents.Although it has long been recognized for the phenomenon of mutual inductance,however,because the process is very complex so pepole have get little quantitative terms,we draw some conclusions based on some reasonable assumption.