Simulation and interpretation of the pressure response for formation testing while drilling

Abstract

The most important stages of formation testing while drilling (FTWD) are mainly the pressure drawdown and build-up. Therefore, the main objectives of this research are to propose analytical solutions of the pressure response, verify the validity of the analytical model, and analyze the characteristics of the pressure response of FTWD tools via theoretical and experimental tests. The mathematical model of the pressure response is proposed, and the analytical solutions are obtained by application of successive integral transforms; the influences of heterogeneity, skin effect, storage effect, and supercharging effect are used to modify the analytical solution. The experimental apparatus was designed to verify the validity of the analytical model; the laboratory experiments of four types of representative samples were conducted. Finally, the characteristics of pressure response with varying formation permeability, heterogeneity, skin effect, storage effect, drawdown flow-rate, supercharging effect, etc. are discussed. The results indicate that the simulated pressure response curves are in good agreement with the laboratory experimental results, although the error is higher in the initial stage of pressure build-up (the maximum error is less than 20% for the ultra-low permeability formation), but the error of the calculated pore pressure, less than 10%, belongs to an acceptable range of error, i.e., the analytic model could be applicable in a wide permeability with the range from 1 mD to 100 mD. The pressure drawdown declines rapidly in the stage of withdrawing formation fluids and then recovers slowly to the original pore pressure during FTWD testing. The formation permeability and drawdown flow-rate have strong impacts, and the supercharging effect, skin effect, and heterogeneity have significant impacts; however, the storage effect has a relatively smaller impact on the pressure response of the FTWD tools. This analytical model is different from, but more practical than, the conventional method.