Orthogonal fracture resistance-capacitance model of complex re-sistance of containing water coal seam

In view of the shortcomings of the Cole-Cole model (is widely used in CR),such as too many model param- eters and weak correlation with physical parameters,in order to develop the theory and technology of CR which is suit- able for evaluating the aquifer property and hydraulic fracturing effect of coal seam,the mechanism and resistance-ca- pacitance model are studied in this paper. According to the dielectric theory,the ions in water-bearing fissures will move and accumulate under the applied alternating electric field,and the movement of ions will generate electric re- sistance,the accumulation of ions will produce capacitance. Based on the theory of induced polarization and coal dualporosity medium,and referring to the rock capillary model,the coal seam pores and fissures are equivalent to orthogo- nal fractures. The resistance value of coal seam pores and fissures is the resistance value Rw of horizontal fracture,and the capacitance value is the capacitance value Cw of vertical fracture,the resistance of coal seam itself is Rc and the ca- pacitance is Cc . The model of water-bearing coal seam is composed of orthogonal fracture and coal seam,and a three- way parallel equivalent circuit consists of equivalent horizontal fracture Rw ,coal seam Rc ,equivalent vertical fracture Cw and coal seam Cc in series. Two kinds of metamorphic coal samples,e. g. ,fat coal and anthracite coal,were select- ed in laboratory,the real part Rs and imaginary part X of complex resistance of coal samples with different water satura- tion (Sw ) were measured,the model fitting was used to obtain the resistance and capacitance parameters and calculate the porosity. The results show that the Resistance-Capacitance model fits well with Rs and X,the model parameters R and C decrease with the increase of Sw ,and the extremum of X-curve with different Sw shifts to the right,has the same physical meaning as the model. The Orthogonal Fracture Resistance-Capacitance model of complex resistance based on the theory of induced polarization and dual-porosity medium has the advantages of clear physical meaning and simple mathematical calculation,the model parameters can predict coal seam porosity. This study lays a theoretical foundation for predicting the water content of coal seam and evaluating the hydraulic fracturing effect by CR.