Reducing cost and improving computability of reservoir simulation is an important goal in the process of enabling CCS (Carbon Capture \& Storage) as a large-scale technology for mitigating CO2 emissions. In terms of computation time data-driven approaches have potential to outweigh the performance of numerical reservoir simulators, learning instead of solving an approximation of the subsurface physics. In this research a Graph Neural Network (GNN) is trained on 2D reservoir model samples to construct a ML autoregressive reservoir simulator. As such the aim of the model is to integrate a spatiotemporal learning task in a graph representation learning problem. Where GNNs have shown their potential in various graph representation and node classification tasks, their use in a reservoir simulation setting is practically unexplored. Graph methods are studied in this setting because of their potential to handle data in non-Euclidean space, which is desired in reservoir simulation to efficiently handle unstructured grids. A simple GNN autoencoder is introduced, implementing the common GCN (Graph Convolutional Network) layer as a locally-operating message-passing operator. The model does not work with spatial graph information, accepting arbitrary graph sizes and structures in 2D or 3D. The model is trained, validated and tested against 2D simulated datasets, generated with the INTERSECT numerical reservoir simulator. The trained model remains numerically stable and makes correct predictions for >140 autoregressive steps. It also shows capability to translate point-source information (the injection rate at the injection well) correctly into a CO2 saturation propagation pattern and corresponding pressure field across the reservoir grid. The model exhibits the correct behaviour around geological layers with variable permeability/porosity, indicating the model successfully adapts to geological variability in the subsurface. Finally the model shows it can infer on totally new reservoir structures. The latter showcases the local method's potential to train a ML reservoir simulator for arbitrary reservoir grids by training it with small generalized subsurface samples, dismissing the need to fully (re)train on usual reservoir grid sizes. Predicting using the GNN methods gives a 60x speed-up compared to the numerical simulator on the small training grids, which likely improves for larger grids given the complexity scaling of numerical simulators. As expected, capturing the elliptic behaviour of the PDE governing pressure is challenging for the local GNN method. While the resulting expressiveness of pressure is passable, ideas for improvement are suggested which can be incorporated using the same proposed GNN architecture.