Multi-stage hydraulic fracturing is considered as a solution to low-productivity wells when the reservoir properties are not good enough to produce oil or gas naturally. The Inflow Performance Relationship (IPR) is the most common method used to evaluate well productivity. Many models have been introduced to estimate the IPR for horizontal wells. However, a significant error will result when they are applied for fractured horizontal wells. This work introduces a new IPR model to estimate gas production rates from multi-stage hydraulically fractured horizontal gas wells at different well pressures.

A single-horizontal-well simulation model was built to generate the production data, and several scenarios were created by changing different parameters, such reservoir permeability anisotropy and fracture properties (fracture dimensions, conductivity, and the number of fractures) to determine the parameters that significantly affect gas production rates from such wells. After the effective parameters were determined, 70% of the resultant data was used to develop the new IPR model using nonlinear regression techniques, while 30% of the data was used for testing. Afterward, a statistical study was performed to evaluate the proposed model to ensure its accuracy in estimating gas production rates using different statistical means, such as R-squared, mean percentage error, variance, and standard deviation.

The term dimensionless conductivity was introduced to simplify the model. This term is a combination of reservoir permeability, fracture half-length, and fracture conductivity. The gas production rate was found to be a strong function of the ratio between vertical and horizontal permeability, the number of fractures, and fracture conductivity, while the height of the fracture and the half-length had no significant effect on the dimensionless IPR curve. The new model showed an excellent performance in estimating gas production rates for hydraulically fractured horizontal wells with a mean percentage error of 3.06% and R-squared of 0.9966.

This study introduced a new simple and reliable IPR model that accurately estimates the gas production rates from multi-stage hydraulically fractured horizontal gas wells at different flowing bottom-hole pressures.

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