The Wellbore Temperature Test and Simulation Analysis for Liquid Carbon Dioxide Fracturing Management

Since physical parameters of CO2 are affected heavily by temperature and pressure, including density, specific heat capacity, thermal conductivity and viscosity, the calculation of wellbore temperature distributions during CO2 fracturing is different from hydraulic fracturing, in which those physical parameters are regarded as constants. In this paper we consider those physical parameters as variables in order to get more precise distributions of wellbore temperature during CO2 fracturing management. A wellbore temperature distribution model during CO2 fracturing process is established in this paper. The math model is based on the energy balance equation and the momentum balance equation and solved by finite difference method. In the calculating process, we considered the effects of temperature and pressure on physical parameters of CO2. Span-Wagner model and Vesovic model are used to calculate those parameters including density, specific heat capacity, thermal conductivity and viscosity. MATLAB is used here to implement those algorithms. Data of H79-31-45 well, a liquid CO2 fracturing well in Ji Lin-Field, is used to compare the calculated temperature with the measured data. This well use 0°C liquid CO2 as fracturing fluid to fracture the formation in depth of 1600 meters. The result shows that in the depth of 1000m and 1600m where the detectors are located, the relative errors between calculated data and measured data are less than 2% both at the beginning and the ending of the management. And as the injection time increases, the temperature of the wellbore has a significant decline, which illustrates very good agreement with result of the calculation. It indicates the precision of the simulation satisfies engineering requirement. In general, since the established model has a high accuracy, sensitivity analysis can be undertaken to analyze the effects of different parameters like the injection rate and injection time on wellbore temperature and the results can provide insights for designing fracturing schemes.