Reduced order model and global sensitivity analysis for return permeability test

Abstract Return Permeability Test (RPT) is a laboratory procedure performed on core plugs for estimating the permeability reduction caused by the invasion of drilling and completion fluids into oil and gas reservoirs. Estimating the damage magnitude (i.e., permeability reduction and percentage of the plugged pore throats) from RPT is critical for accurately analyzing and optimizing wells’ production operations. Several parameters such as the extent and permeability of the invaded zone, production rate, and percentage of the open flow area (i.e., the ratio of the pore throats that remain unplugged after the test to total pore throat area of the rock) affect the estimations from RPT by impacting the pressure drop. Therefore, it is necessary to identify the dominant parameters systematically from the production point of view. Also, the numerical solution of the problem is complex and requires a software package, which often has an expensive CPU run time and might not be efficient for engineers all the time. To this end, we present a systematic global sensitivity analysis (GSA) using the Sobol method for two primary purposes. Firstly, to rank the dominant input variables that affect the variation of the inlet pressure of a core plug with a partially open area and a reduced permeability zone at the flow outlet. Secondly, we develop a reduced-order model (ROM) for this complex problem with a controlled error. As a global sensitivity analysis approach, one advantage of the Sobol technique over the local sensitivity analysis is its ability to account for simultaneous changes of multiple input parameters on the variation of the quantity of interest (QI). Another advantage is that the method can be used to create ROMs even in situations where the governing function is not explicitly known. In this study, we selected four variables as the input parameters of our GSA: the thickness and permeability of the invaded zone ( l f and k f ), production velocity v i , and percentage of the open flow area after the test r o . Since the function governing the relationship between the input and output parameters is not known, a Monte-Carlo simulation is used to carry out the required integrations. For this purpose, a total of 8,000 samples from combinations of the selected input variables are generated. The samples are selected from a range of interest for each variable using the Saltelli sample generation algorithm. Then, computational fluid dynamics (CFD) simulations are conducted on the selected input set to generate pressure (QI) at the core inlet. The results show that the internal cake permeability k f has the most significant impact ( ∼ 32%) on total pressure drop. The second and third most dominant first-order variations are the ratio of open flow area to the total core area r o ( ∼ 15%) and injection velocity v i ( ∼ 13%). Also, the combination (simultaneous changes) of r o and k f has the second most dominant effect between all variables ( ∼ 20%). Finally, we presented a ROM for this problem using the dominant input parameters that account for 96% of the changes in QI, and using several examples demonstrates that the error can be controlled. The result of this study is a model that is mathematically simple and runs much faster than the conventional CFD simulations with reasonable accuracy. It is also a tool to identify and rank the dominant input variables and their interactions regarding their impact on QI variations. The proposed methodology will provide useful guidelines for further analysis of RPT results and provide a simple tool for production engineers.