| The geological reserves of oil and gas in tight reservoirs have a significant share of the total oil and gas resources.To improve the production and recovery of the tight reservoirs,unconventional methods such as fracturing are usually applied due to its low permeability.In order to evaluate the effect of fracturing and optimize the fracturing scheme,it is necessary to implement efficient and accurate numerical simulation for the fractured tight reservoir.After fracturing,the fracture system has typical multi-scale characteristics,including from micro-fractures and high conductive fractures with large scale.Different mathematical models are required to describe the flow in fractures of different scales.For micro-fractures,the dual-porosity model is usually employed.For high conductive fractures with large scale,the discrete fracture model is employed.Since the discrete fracture model has to be performed on unstructured grids to conform to the fracture geometry,its computational efficiency will be greatly reduced as the complexity of fracture geometry increases.The embedded discrete fracture model(EDFM)can use structured grids to mesh reservoirs,resulting in an improvement of efficiency.The EDFM has been widely used because of its high calculation efficiency and designed for the conductive fracture acting as a single source term.In the previous model,the transfer flow rates on the two sides of the fracture cannot be calculated separately,and therefore may cause error in the calculation of the multi-phase flow rates across matrix-fracture interface,especially when the discontinuity of physical quantities across the fracture occurs.To overcome this deficiency of the EDFM,some scholars have proposed some embedded discrete fracture models such as the projection-based embedded discrete fracture model,which can calculate the two-side transfer flow rates separately.At matrix-fracture interface,there exists complex flow phenomena due to a variety of mechanisms such as the heterogeneity of capillary force in matrix and fracture and so on,which adds difficulties on the construction of a highly accurate embedded discrete fracture model.This thesis carries out a research on the EDFM in tight reservoirs with fractures,and the main research contents are as follows.1.The fracturing shale gas well multi-scale model is applied to perform history matching or shale gas wells in the Weiyuan Shale Gas Field,Sichuan Basin China.Based upon the parameters obtained through history matching,the fracturing effects are evaluated.After fracturing,stimulated reservoir volume(SRV)with a large number of fracturing fractures are created near shale gas wells,and there is a multi-scale problem of matrix,micro-fracture network and conductive fractures.Outside SRV,the single shale gas flow is only considered.Inside SRV,the single shale gas flow is also considered in the matrix,and the capillary pressures has little effect on flow.In the study,fracturing shale gas wells are depleted wells,and directly connected with the conductive fracture.The shale gas and fracturing fluid flow into the production well through the conductive fracture,which acting as a single source term.The multi-scale model is established directly by using the EDFM proposed by Lee et al.The quantitative influence of the pressure-sensitive effects,especially of the pressure-sensitive effect of the relative permeability on the history matching results is carefully investigated.In order to obtain the history matching results with high accuracy,both the pressure-sensitive effect of the absolute permeability and of the relative permeability need to be considered fully.Furthermore,it is found that the pressure-sensitive effect of the relative permeability has a greater influence on the fitting of the fracturing fluid phase flow than on the fitting of the gas phase flow,and theoretical analysis is performed to explain this phenomenon.2.The CO2 flooding using the projection-based embedded discrete fracture model(pEDFM)is investigated.In the actual production process,high pressure CO2 is often injected to realize the displacement of various components in the tight reservoirs.The CO2 in miscible state reduces the effect of capillary pressure on flow and improves the recovery.In the state,the capillary pressure between the oil phase and the gas phase is very small.In the thesis,the effect of capillary pressure on oil-water two-phase flow was only considered.Considering the discontinuity of physical quantities across the fracture,the pEDFM uses projection method to calculate the transfer flow on both sides of the fracture,which improves the calculation accuracy.However,through theoretical analysis,two defects in the existing pEDFM are found.One defect is that the transmissibility value provided in the existing model is only half of the true one when the fracture is embedded closely to the corresponding matrix grid interface.If the permeability of the matrix grid with the fracture embedded in differs from the adjacent matrix grid,the error will be bigger.The other defect is that the choice of the projection direction in the existing model is not appropriate in the certain case when the fracture passes right through the center of the matrix grid.In this situation,the existing"minimum distance criterion" and "different side criterion" do not work,and the projection direction will be chosen randomly.However,projecting the embedded fracture to the downstream interface will bring extra calculation errors.To overcome the two defects mentioned above,an advanced pEDFM is proposed in this thesis.The series relationship of flow is clarified in the calculation of the transmissibility,and based on this,an improved algorithm of calculating the transmissibility is proposed.For the selection of projection direction,the "upstream priority criterion" is proposed.The numerical examples show that the advanced pEDFM can improve the accuracy of CO2 flooding simulation in tight reservoir after fracturing in both two and three dimensions.3.A modified embedded discrete fracture model is proposed.In tight reservoirs,there is a large capillary pressure difference between matrix and fracture.For oil-water two phase flow,the difference causes three flow patterns across the matrix-fracture interface,corresponding to three different interface conditions.When the pressure difference between matrix and fracture can overcome the capillary end effect,the two-phase fluids will both flow from matrix to fracture,and the water phase saturation at the matrix side of the interface is one.When the matrix pressure is higher than the fracture pressure,but the pressure difference cannot overcome the capillary pressure,only the oil phase will flow from matrix to fracture,and the water phase flow rate is zero.When the matrix pressure is lower than the fracture pressure,both the two-phase fluids will flow from fracture to matrix,and the ratio of water phase flow rate to oil phase is just the water-oil mobility ratio at the fracture side.The three flow patterns make it difficult to establish an accurate EDFM.Compared with Lee's model,there are two obvious features of the proposed one.First,each matrix cell with fracture embedded in is treated as two sub-cells to describe the discontinuity across the fracture.Under the treatment,the matrix-fracture transfer flow across the two sides of the fracture can be calculated separately.The second aspect of the proposed embedded discrete fracture model is that the 1D analytical solution of two-phase steady flow near matrix-fracture interface is employed to calculate the phase transfer flow rate.The analytical solutions for the three different patterns are derived and then employed to construct an alternative numerical scheme of calculating matrix-fracture transfer flow rate.The employment of the analytical solution can conquer the numerical difficulty induced by divergent physical quantity at matrix-fracture interface,and can provide accurate calculation of flow across the interface.Numerical tests show that the proposed embedded discrete fracture model can provide accurate results even on coarse grids. |
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