The paper suggests a new approach to short-term forecasting of oil production at shale plays in the USA. It is based on the analytical solution of the differential equation of oil production. The concept of the production potential is introduced, which corresponds to the exponential, harmonic and hyperbolic curves of the base oil production from an individual well. The production potential is estimated using a stationary solution of the differential equation. Its value answers the question: how much production will be achieved over time, all other things being equal (a constant number of drilling rigs, their productivity and the rate of decline in basic production).

It is shown that production at US shale plays is best described by a harmonic potential with a lag of 6 months. Usage of this potential reduces the differential equation to the Riccati equation that allows expressing the solution of the Cauchy problem in elementary functions.

The robustness of the proposed forecasting method of oil production was investigated using the sensitivity analysis to the change of WTI oil price. It is established that the potential and the volume of shale oil production are proportional to the square root of the number of drilling rigs, and, therefore, to the oil price. This may indicate overestimated expectations of growth in the shale oil production for researchers who run the linear models. This could lead to understated expectations of oil future price.