The mineral industry is comprised of several large-scale, complex processes that require tight control in order to operate appropriately. Among them, the thickening process is a solid-liquid separation unit operation whose highly nonlinear and slow dynamics pose challenges in obtaining an accurate process model. Consequently, model-based controllers, such as the model predictive controller (MPC), despite all its advantages, do not achieve their best performance in such an industrial environment. In this work, we investigate using a data-driven predictive control (DDPC) approach to control the thickening process, in which we integrate a predictive control formulation and a prediction technique called Lazily Adaptive Constant Kinky Inference (LACKI). The proposed method makes use of process data and a machine learning technique to supply the lack of an accurate model. Simulated results show that this approach performs satisfactorily in controlling the thickening process.