Dynamic workflow adjustment studies how to minimally adjust existing user-task assignments, when a sudden change occurs, e.g. absence of users, so that all tasks are being attended and no constraint is violated.In particular, we study two key questions: (i) Will the workflow still be satisfiable given a change? (ii) If the answer is yes, how to find a satisfying assignment with the minimum perturbation to the old system? We consider various types of changes, including absence of a user, addition of a separation-of-duty constraint, addition of a binding-of-duty constraint, and revocation of a user-to-task authorization, study their theoretical properties and formulate them into the well-studied Boolean satisfiability problem, which enables a system engineer without much technical background to solve problems by using standard satisfiability solvers. A step further, towards more efficient solutions for our specific problems, we propose customized algorithms by adapting and tailoring the state-of-art algorithms inside standard solvers. Our work would have implications for business process management, staffing, and cost planning.