This paper investigates the optimal load-sharing problem of serial gas compressors in the presence of plant-model mismatch. The problem is formulated as a static real-time optimization task that is solved via modifier adaptation for interconnected systems. The proposed approach guarantees optimal operation of the plant upon convergence. Furthermore, it is shown how the specific problem structure can be exploited during process operation for the efficient estimation of plant gradients with respect to local inputs. A simulated case study demonstrates the effectiveness of the proposed real-time optimization approach.