We present a framework of the application of Bayesian Optimization (BO) to well management in geological carbon sequestration. The coupled compositional flow and poroelasticity simulator, IPARS, is utilized to accurately capture the underlying physical processes during CO2 sequestration. IPARS is coupled to IBM Bayesian Optimization (IBO) for parallel optimizations of CO2 injection strategies during field-scale CO2 sequestration. Bayesian optimization builds a probabilistic surrogate for the objective function using a Bayesian machine learning algorithm, Gaussian process regression, and then uses an acquisition function that leverages the uncertainty in the surrogate to decide where to sample. IBO addresses the three weak points of the standard BO in that it supports parallel (batch) executions, scales better for high-dimensional problems, and is more robust to initializations. We demonstrate these algorithmic merits by an application to the optimization of the CO2 injection schedule in the Cranfield site using field data. The performance is benchmarked with genetic algorithm (GA) and covariance matrix adaptation evolution strategy (CMA-ES). Results show that IBO achieves competitive objective function value with over 60% less number of forward model evaluations. Furthermore, the Bayesian framework that BO builds upon allows uncertainty quantification and naturally extends to optimization under uncertainty.