An Improved Response Equation of Dual Laterolog in Dual Porosity Reservoirs and Its Solution Scheme and Applications in Fractured Reservoirs

Many fractured reservoirs are dual porosity reservoirs including matrix pores and fractures, which both contribute to the porosity. However, previous studies either ignored the effect of pores or fractures on dual laterolog, or had special application conditions. Considering the joint contribution of pores and fractures, a response equation of dual laterolog in dual porosity reservoirs is established. First, based on a borehole model with a vertical fracture in dual porosity reservoirs, fracture porosity equations are established in the investigation depths of deep and shallow laterologs, respectively. Using Archie's equations, the response equations of deep and shallow laterolog resistivities are derived, respectively. Then, the response equation, which is similar to the traditional equation of dual laterolog in fractured tight reservoirs, is established. It contains three unknown parameters, i.e. fracture width, fracture cementation exponent and matrix cementation exponent. To solve the equation, a virtual core model is proposed to estimate the fracture cementation exponent by fracture width. The estimation method of matrix cementation exponents is established by empirical formulas. Then, the response equation can be transformed into a nonlinear equation with one unknown parameter of fracture width, and conventional iterative methods can be employed to solve it and obtain the fracture width. Using the response equation and the solution scheme, the change characteristics of fracture cementation exponents in different fractured reservoirs are first analyzed. It shows that the fracture cementation exponents increase with the fracture widths, and they decrease with the increase of the ratio of formation water resistivity to unfractured reservoir resistivity. The applications indicate that the equation and solution scheme can obtain relatively accurate fracture widths quickly in dual porosity reservoirs, and they are recommended for dual porosity reservoirs with high fracture angel (>70 degrees) and low fracture density (<1/3.78 m-1). The findings of this study can help better understanding of the different contributions of fractures and pores to dual laterolog responses in dual porosity reservoirs, and they can provide an alternative solution for evaluating dual porosity reservoirs.