Multiple fractured horizontal wells (MFHWs) are considered as the most effective stimulation technique to improve recovery from low permeability reservoirs particularly tight and shale assets. The understanding of the complex flow behaviour and predicting Productivity Index (PI) of these wells are vital for exploitation of such reservoirs. These data also affect the optimum hydraulic fracture design and the long term well performance.
The, analytical or semi analytical, models previously proposed cannot accurately describe the flow behaviour around MFHWs due to lack of capturing the complexity of the flow especially the fracture-to-fracture interference effects. The fine grid three dimensional (3D) simulation approach is also costly and cumbersome. In this work, we followed a novel approach to develop a new equation that can predict MFHWs performance under pseudo-steady state flow conditions in tight reservoirs.
An in-house programming code, which automatically creates batch files, reads input data and stores relevant output data for each simulation, was coupled with a fine grid 3D reservoir model to generate the required large data bank. For these simulations, the pertinent parameters (matrix permeability, number of fractures and fracture permeability, spacing, width, length and conductivity) were varied over wide practical ranges based on the full factorial experimental design method.
The overall as well as the individual impacts of the parameters on PI, as the output variable, were evaluated by various statistical analyses techniques, including Spearman's rank correlation coefficient, under different prevailing conditions. It is shown, for instance, that increasing the fracture width and permeability does not result in a significant monotonic increase in PI while changing fracture length, spacing and numbers influences PI greatly.
Moreover, a new expression is proposed that relates MFHWs-PI to PI of the horizontal well with a single fracture and to number of fractures and dimensionless fracture spacing parameters by applying the symbolic regression technique. The cross validation results show that the proposed equation is general, reliable and simple for prediction purposes because it benefits from limited and appropriate dimensionless numbers with excellent values of fitting indices.
This study expands our understanding of flow behaviour in tight reservoirs and provides an invaluable engineering tool that can facilitate simulation of flow around MFHWs and quickly predict their well performance. The new IPR equation can also be used for optimising MFHWs design.