The spread between two related energy prices is a very important quantity throughout energy finance. Of particular interest are spreads between different energy types, different delivery points (location spreads) and different delivery times (calendar spreads). Each underlying price process may be modeled directly.At times, however, it is a useful simplification to consider the spread as a distinct process, which may itself be directly modeled. For this purpose, we investigate the continuous limit of a mean-reverting random walk and its extensions. Analytical results about the solution of this process, including its stationary distribution, are obtained. This new mean-reverting process is compared with the Vasicek process, and its advantages are discussed. We show that this new model for spread dynamics is capable of capturing kurtosis. It can also capture the possible skewness in the transition density of the price spread process. Since the analytical transition density is unknown for this nonlinear stochastic process, the local linearization method is deployed to estimate the model parameters. We apply this method to empirical data for modeling the spread between West Texas Intermediate (WTI) crude oil and West Texas Sour (WTS) crude oil.