We develop a collocation spectral method (CSM) to address radiative transfer in a semitransparent anisotropic scattering cylindrical medium with graded index and space-dependent albedo. Accuracy and validity of the method is verified with exact solutions available in literature and other methods. CSM is found effective in obtaining radiative flux in graded index medium. And few nodes are enough to obtain accurate results.

Based on theory of fractal and assumption of continuity, a well test model for multiple fractured horizontal wells in fractal fractured shale gas reservoirs was established in which adsorption, desorption and cross flow between matrix and fractures are considered. Solution of the model was obtained with Laplace transform, point source solution and pressure drop superposition principles. Double logarithmic curves of dimensionless pressure changing over time were obtained. Characteristics of pressure of multiple fractured horizontal well in fractal fractured shale gas reservoirs and influence of parameters, such as fractal index and fractal dimension, on pressure and production curves were analyzed. It shows that the curves can be divided into 7 flow stages. Slope of unstable pressure well-test curves in the middle and late stages is greater with bigger fractal index or smaller fractal dimension.