In this contribution, Real-Time Optimization with Modifier Adaptation and Quadratic Approximation (MAWQA) is experimentally applied to a pilot-scale 18 mm reactive extruder for the production of hydrophobically modified ethoxylated urethanes which are used as rheological paint additives. Standard model-based control is in this application not applicable because of the complex coupling of the chemical reaction, complex internal flows within the equipment, and a high sensitivity to external disturbances. The optimization is performed with the goal to minimize the specific energy requirement for the product by changing the overall throughput and the barrel temperature locally while meeting a hard constraint on the product quality. The product quality is determined by the viscosity of the product which is measured online with a capillary viscometer. In contrast to other work, the MAWQA method is applied here purely data-based without using a physical model. Despite the absence of a rigorous model, the method converged to the optimum after 6 initial probing moves and 4 iterations where the product quality constraints were already met.