Fast Modelling of Gas Reservoirs Using POD-RBF Non-Intrusive Reduced Order Modelling

Abstract

We demonstrate that the non-intrusive reduced order model (NIROM) based on proper orthogonal decomposition and radial basis function interpolation is capable of gas reservoir simulation predictions with computational speed-ups of at least an order of magnitude and potentially many orders of magnitude. It can estimate 3-dimensional spatial pressure and saturation distributions as well as production data for unseen gas reservoir simulation scenarios produced at constant bottom hole pressure or gas rate control. The NIROM is created from a series of training simulations performed using a commercial simulator. These simulations produce "snapshots" of the pressure and saturation distributions at equally spaced time intervals. Proper Orthogonal Decomposition (POD) is then used to project these data into a higher dimensional hyperspace. Radial basis functions (RBF) are then used to both estimate the dynamics of the system and the behaviour for unseen inputs (such as well BHP or rate). The approach is demonstrated using 3 different reservoir models, including a realistic reservoir model using data taken from the Norne field. The NIROM simulations produce satisfactory predictions when compared to a commercial simulator, provided the unseen inputs are within the range of training parameters and time scale covered by the simulation. On average, these results were obtained using 10 training runs. The overall improvement in speed is insensitive to reservoir model complexities, such as local grid refinement, water coning or the presence of aquifers. Reservoir models with significant water production require more NIROM simulation subspace vectors to estimate performance, compared with cases without water production. Furthermore, we show that although NIROM works well for constant well controls over time it is less accurate when estimating behaviour when the imposed well rate changes quickly at different times in the simulation. This is the first time that POD-RBF NIROM has been applied and evaluated for pressure depletion problems, such as occur in gas reservoir performance prediction.

Order reduction of special valve models based on pod method

“…This method requires low computational cost, has a certain stability, and can maintain some basic properties of the original system. Currently, the POD model reduction method has been widely used in fluid mechanics [5], oil and gas transportation [6], structural dynamics [7], heat conduction [8], and other fields. Among them, in fluid mechanics, due to the high dimensionality of flow field information, POD can obtain the dominant mode of data by decomposing the data, reducing redundant information, and making the POD method applicable to the reduction of flow field models [9].…”