Uncertainty quantification for the impact of injection rate fluctuation on the geomechanical response of geological carbon sequestration

We study the effect of random injection rate fluctuations on pressure and geomechanical stresses during geological sequestration of carbon dioxide (CO₂). We first derive analytical solutions for the mean and variance of the pressure of CO₂ in the reservoir. Next, we use the Monte Carlo simulation (MCS) method to obtain the mean and variance of geomechanical deformation stresses and the maximum sustainable injection pressure based on shear-slip failure analysis. The MCS method is validated using the analytical solutions for mean and variance of the pressure. We demonstrate that for any Gaussian distribution of injection rate Q with given mean Q- and standard deviation e_Q, the coefficients of variation of the CO₂ pressure (εp=εp/p-), deformation (εu=εu/u-), and stresses (εσ=εσ/σ-) increase linearly with the coefficient of variation of the injection rate (εQ=εQ/Q-). We calculate coefficients of variation and show that the fluctuations have the most pronounced effect on the geomechanical stresses and, therefore, on the potential fracturing of the aquifer and caprock layers. We demonstrate that the maximum sustainable injection pressure can be determined based on shear-slip analysis with a given expected risk due to the injection rate fluctuations. We show that the injection rate fluctuations decrease the maximum sustainable injection pressure.