In this talk, we investigate a coupled continuum pipe flow (CCPF) model which describes the fluid flows in karst aquifers. After generalizing the well-posedness of the forward problem to the anisotropic exchange rate case which is a space-dependent variable, we present the uniqueness of this parameter by measuring the Cauchy data. Besides, the uniqueness of the geometry of the conduit by the Cauchy data is verified as well. Finally, some regularization schemes are provided to solve one proposed Cauchy problem.