Characteristics of non-Darcy flow in low-permeability reservoirs

Well testing is recognized as an effective means of accurately obtaining the formation parameters of low-permeability reservoirs and effectively analyzing the deliverability. Well test models must comply with the particular characteristics of flow in low-permeability reservoirs in order to obtain reasonable well test interpretation. At present, non-Darcy flow in low-permeability reservoirs is attracting much attention. In this study, displacement tests were conducted on typical cores taken from low-permeability reservoirs. Two dimensionless variables were introduced to analyze the collected experimental data. The results of the dimensionless analysis show whether non-Darcy flow happens or not depends on the properties of fluid and porous media and the pressure differential. The combination of the above three parameters was named as dimensionless criteria coefficient (DCC). When the value of the DCC was lower than a critical Reynolds number (CRN), the flow could not be well described by Darcy’s law (so-called non-Darcy flow), when the DCC was higher than CRN, the flow obeyed Darcy’s law. Finally, this paper establishes a transient mathematical model considering Darcy flow and non-Darcy flow in low-permeability reservoirs, and proposes a methodology to solve the model. The solution technique, which is based on the Boltzmann transformation, is well suited for solving the flow model of low-permeability reservoirs. Based on the typical curves analysis, it was found that the pressure and its derivative curves were determined by such parameters as non-Darcy flow index and the flow characteristics. The results can be used for well test analysis of low-permeability reservoirs.