A 2-D device model of the organic electrochemical transistor is described and validated. Devices with channel length in range 100 nm-10 mm and channel thickness in range 50 nm-5 mu m are modeled. Steady-state, transient, and AC simulations are presented. Using the realistic values of physical parameters, the results are in good agreement with the experiments. The scaling of transconductance, bulk capacitance, and transient responses with device dimensions is well reproduced. The model reveals the important role of the electrical double layers in the channel, and the limitations of device scaling.