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.
Arps in 1944 developed decline curve equations for analyzing reservoir/well production decline and the estimated decline rate constant is used for production forecast. In making reservoir production forecast, the Arps equations are usually calibrated to match the reservoir historical production decline by adjusting the decline rate constant value. The decline rate constant indirectly influences the reservoir properties responsible for production decline. However, the value assigned to the decline rate constant might either overestimate or underestimate the uncertainties in the reservoir rock and fluid properties responsible for reservoir production decline. The decline rate constant in the Arps equation has no equation relating it to the reservoir properties that are responsible for the reservoir production decline hence; the direction of uncertainty quantification on these reservoir parameters is not explicit, therefore undermining the predictive power of the Arps equations. The impact of reservoir properties uncertainties on the production rate decline and forecast by Arps equations cannot be examined due to the empirical nature of the Arps equations. Also, the decline rate constant is not explicitly related to reservoir rock and fluid properties responsible for production decline. However, the predictive power of the Arps model can be greatly improved if the decline constant can be expressed as a function of the reservoir rock and fluid properties responsible for production decline. Hence, the impact of uncertainty on the production forecast by Arps models can be examined. The objective of this work is to introduce reservoir rock and fluid properties into the Arps decline curve equations. This will enable the imposition of reservoir physics on the decline curve equations and the impact of uncertainties in these properties on matching historical production decline and forecast. In addition, a relationship between the decline rate constant in the Arps equations and the reservoir rock and fluid properties that influence reservoir production decline has been developed. A mechanistic approach using dimensional analysis was used to develop the relationship. The decline rate was assumed to be proportional to the various reservoir rock and fluid parameters, such as permeability, porosity, net-to-gross, drainage area, fluid density, and viscosity, that could influence production decline and by unit dimensional analysis, a relationship was developed between the decline constant and these reservoir rock and fluid properties. The decline rate constant was directly related to the product of reservoir permeability, fluid density, and the square of the pressure difference but inversely proportional to the cubic power of fluid viscosity. The relationship developed for the decline constant in this work will give the modified Arps model strong predictive power and allows for the impact of uncertainties on the production forecast to be evaluated. The results obtained from the modified Arps equations give better reservoir properties dependent outcomes than the traditional Arps equations and enable analysis of the effects of reservoir rock and fluid properties uncertainties on the production decline and forecast.
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