In this paper we propose a novel framework for the identification of a dynamic surrogate model (DSM) that can offer a fast and effective prediction of time-varying outputs (e.g., oil rates) of a Steam Assisted Gravity Drainage process. In the framework, the prediction at any given time consists of the addition of two components: a base model plus a correction term. The former is represented by a conventional one-step forecast nonlinear model(s) used recursively to make n-steps ahead forecast. The latter is modeled error term, rationalized under the assumption that the forecast error given by the base model is correlated with time due to the recursive strategy used. Since at every time step the input to the one-step forecast model is the prediction made by the same model in the previous time step, so an error accumulation is expected as the prediction time increases. This is analogous to the well-known geostatistical Kriging method, in which the basic assumption is that prediction errors are not constant, rather they are correlated with distance, and as a result, they can be modeled separately using covariance models. The identification of the base and correction model follows the typical surrogate model framework, i.e., design of experiments, evaluation of the samples, and construction of the models. In the context of DSM, the design of experiments represents the random selection of a set of steam injection policies in the preestablished production horizon. For each of these samples, a corresponding oil production rate time series is obtained using a reservoir simulation model; this model was built using publicly available data from Norther Alberta SAGD implementations. Afterwards, the base model and correction term are identified using Long-Short Term Memory neural networks. Results show that DSM significantly outperforms the conventional one-step forecast nonlinear models used recursively. In particular DSM offers, a significant increase of median R2 value of over 0.88 and a reduction of the median and standard deviation of Mean Absolute Percentage Error of over 67.0% and 80.1%, respectively. These results suggest that DSM is able to offer effective (low error and high R2) and efficient (relatively low number of samples) to identifying computationally inexpensive surrogate models for the prediction of time-varying outputs. Furthermore, the framework holds promise to be useful in SAGD optimization efforts, such as, finding the optimal steam injection policy.