Multirate-Transfer Dual-Porosity Modeling of Gravity Drainage and Imbibition

Summary We develop a physically motivated approach to modeling displacement processes in fractured reservoirs. To find matrix/fracture transfer functions in a dual-porosity model, we use analytical expressions for the average recovery as a function of time for gas gravity drainage and countercurrent imbibition. For capillary-controlled displacement, the recovery tends to its ultimate value with an approximately exponential decay (Barenblatt et al. 1990). When gravity dominates, the approach to ultimate recovery is slower and varies as a power law with time (Hagoort 1980). We apply transfer functions based on these expressions for core-scale recovery in field-scale simulation. To account for heterogeneity in wettability, matrix permeability, and fracture geometry within a single gridblock, we propose a multirate model (Ponting 2004). We allow the matrix to be composed of a series of separate domains in communication with different fracture sets with different rate constants in the transfer function. We use this methodology to simulate recovery in a Chinese oil field to assess the efficiency of different injection processes. We use a streamline-based formulation that elegantly allows the transfer between fracture and matrix to be accommodated as source terms in the 1D transport equations along streamlines that capture the flow in the fractures (Di Donato et al. 2003; Di Donato and Blunt 2004; Huang et al. 2004). This approach contrasts with the current Darcy-like formulation for fracture/matrix transfer based on a shape factor (Gilman and Kazemi 1983) that may not give the correct average behavior (Di Donato et al. 2003; Di Donato and Blunt 2004; Huang et al. 2004). Furthermore, we show that recovery is exceptionally sensitive to parameters that describe the physics of the displacement process, highlighting the need to make careful core-scale measurements of recovery. Introduction Di Donato et al.(2003) and Di Donato and Blunt (2004) proposed a dual-porosity streamline-based model for simulating flow in fractured reservoirs. Conceptually, the reservoir is composed of two domains: a flowing region with high permeability that represents the fracture network and a stagnant region with low permeability that represents the matrix (Barenblatt et al. 1960; Warren and Root 1963). The streamlines capture flow in the flowing regions, while transfer from fracture to matrix is accommodated as source/sink terms in the transport equations along streamlines. Di Donato et al. (2003) applied this methodology to study capillary-controlled transfer between fracture and matrix and demonstrated that using streamlines allowed multimillion-cell models to be run using standard computing resources. They showed that the run time could be orders of magnitude smaller than equivalent conventional grid-based simulation (Huang et al. 2004). This streamline approach has been applied by other authors (Al-Huthali and Datta-Gupta 2004) who have extended the method to include gravitational effects, gas displacement, and dual-permeability simulation, where there is also flow in the matrix. Thiele et al. (2004) have described a commercial implementation of a streamline dual-porosity model based on the work of Di Donato et al. that efficiently solves the 1D transport equations along streamlines.