Dynamic multi-linear modeling of fractured horizontal wells in heterogeneous formations considering stress–sensitivity and slip flow

Reservoir petrophysical properties exhibit complex spatial and temporal variations under multiple interacting mechanisms, including reservoir heterogeneity, fracture stress–sensitivity, rock stress–sensitivity, and rarefied gas flow, resulting in highly nonlinear partial differential equations that control fluid flow. A dynamic multi-linear semi-analytical technique has been developed to stimulate the fluid flow behaviors in low-permeability formations stimulated with multi-stage fractured horizontal wells. Multi-linear models are built accordingly to investigate the variation of production rate under the interaction of multiple mechanisms. In the multi-linear modeling, a formation is first divided into subsystems based on the distribution of hydraulic fractures and each subsystem is further divided into many flow regions. Each region is assigned an independent set of initial petrophysical properties and governed by simple linear flow. Petrophysical properties of the flow regions are updated at the end of each time step according to the pressure distribution throughout the formation. Multi-linear modeling results support that fracture stress–sensitivity and rock stress–sensitivity weaken the impact of heterogeneity on well performance, while the potential rate enhancement introduced by gas rarefaction could supplement the rate loss caused by stress–sensitivity. Among the interplay of following mechanisms, reservoir heterogeneity, gas rarefaction, fracture stress–sensitivity, rock stress–sensitivity, the latter two play a dominant role in productivity reduction. When time reaches one year, under fracture and rock stress–sensitivity as well as gas-slippage effect, the cumulative production loss is 17%. The proposed technique provides a fast way of weakening the strong nonlinearity with maintaining accuracy, which can be applied in quick production analysis and fracturing design.