Effective Medium Resistivity Model For Applied Research In Areas Of High Mud

Based on the effective medium HB resistivity models in laminated or dispersed shaly sands proposed by Berg, the general effective medium HB resistivity model in laminated and dispersed shaly sands is established. In the derivation of the model we assume that clay-bound water fraction is included in total pores, clay-bound water and formation water have the same resistivity, and yet the difference of electrical properties between the two waters is incorporated into clay grain conductivity. After deriving Swt from the model, we find out that the water saturation equation is a quadratic equation about Swt, so its solution is very simple and obtained by using the standard quadratic-root formula. By analyzing parameters of the model, we find out that shale distribution largely affects water saturation calculated by the model, the less the resistivities of sand grains or clay grains, the more largely the resistivities of grains affect the relation between Ct and Swt, the effect of m on the relation between Ct and Swt is increased with Swt. Testing on artificial samples with conducting rock grains it proves that the model can be applied in clay-free porous rocks with conducting grains, but formation water resistivity must be less than rock grain resistivity. Testing on rock sample data in dispersed shaly sands it shows that adding another parameter (n) to the model can decrease the relative error of fitted Co. However, when we consider the difference of electrical properties between clay-bound water and formation water in the model, although another parameter (Qv) is added to the model, the relative error of fitted Co is increased slightly. Testing on logs in laminated shaly sands it demonstrates that the model can be applied in laminated shaly sands. Testing on effects of Rdc. and Vdc representing clay resistivity and fraction or dry clay resistivity and fraction on water saturation calculated by the model it proves that it is very reasonable for Rdc to be clay resistivity and Vdc to be dry clay fraction, so the model derived from the paper can be used to evaluate shaly sands.Based on the parallel conductance between laminated shale and dispersed shaly sand, while dispersed shaly sand can be described with SATORI resistivity model containing four components (conducting rock matrix grains, nonconductive hydrocarbons, dispersed clay particles and water), the generalized effective medium SATORI resistivity model in laminated and dispersed shaly sand is established. By studying the solution to generalized effective medium SATORI resistivity model in laminated and dispersed shaly sand, it shows that there is a local minimum of the function about w derived from the model in the range from 0 to , and the w corresponding to the minimum varies with or w as well as other parameters, therefore, in order to ensure the iteration convergence, here, we adopt a hybrid algorithm combining Newton and bisection, and the calculated result shows that using the hybrid algorithm to solve the equation about W is convergent. It is pointed out that shale distribution largely affects water saturation predicted by this model. The curvatures of the curves between total formation conductivity C, and total water saturation Swt, are greatly affected by formation matrix conductivity Cma, while it is less affected by clay conductivity Ccl. The curvatures of the curves between C, and Swt are only affected by w, a factor number that is related to relative volume of water content in the formation, while is not much affected by the matrix factor number ma. When Ct is kept to be constant, Swt increases ash ma increases, and decreases as w increases. The experiments of artificial samples with conducting rock grains show that the model may be applied in clay-free porous rocks with conducting rock grains, with a condition of formation water conductivity being larger than rock grain conductivity. Rock sample data in dispersed shaly sands and well logging data in laminated shaly sands shows that this model may be applied not only in dispersed s...