New approach for predicting multiple fractured horizontal wells performance in tight reservoirs

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. Understanding of the complex flow behaviour and predicting Productivity Index (PI) of these wells are vital for exploitation of unconventional reservoirs. The analytical or semi analytical models previously proposed for their PI calculations cannot accurately describe the flow behaviour around MFHWs mainly due to lack of capturing the complexity of the flow especially the fracture-to-fracture interference effects. Many of them are also too complex and/or not general enough limiting their use. The fine grid three-dimensional (3D) simulation approach is also costly and cumbersome. In this work, we followed a new approach to develop a new equation that can predict MFHWs performance under pseudo-steady state (PSS) flow conditions in tight reservoirs. A programming code, producing the include files, was coupled with a fine grid 3D commercial reservoir simulator to generate a large data bank. For these simulations, the pertinent parameters (matrix permeability, the number of fractures and fracture permeability, spacing, width, length and conductivity) were varied over wide practical ranges based on the Latin Hypercube sampling method. The individual impact of the parameters on PI, as the output variable, was evaluated by a statistical analysis technique 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 influence PI greatly. A new equation is then proposed that relates MFHWs-PI to a limited number of parameters by applying symbolic regression technique. Here, the total productivity index of MFHWs is related to the PI of the horizontal well with a single fracture, the number of fractures and dimensionless fracture spacing. 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 good 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, their optimum design and their well performance prediction.