A model-based fault detection and accommodation scheme is introduced for a class of distributed parameter systems (DPS) described by coupled partial differential equations (PDEs). Actuator faults at the boundary condition are considered. A detection observer is proposed based on the linear PDE representation of the DPS by assuming that the state information is available. Upon detecting a fault, an adaptive term is added to the observer to estimate the fault parameter vector which is utilized for fault accommodation by reconfiguring the control input. An update law is proposed to estimate the unknown fault parameter vector. An explicit formula is proposed to estimate the time-to-accommodation (TTA) by using the parameter vector. Finally, an example to demonstrate the effectiveness of the proposed scheme is included.