In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encoun...In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks,while giving poorer accuracy in the smooth regions.Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. In this paper, we investigate several shock-capturing schemes.The competency of each scheme was tested against onedimensional benchmark problems as well as published numerical experiments. The numerical results have shown good performance of high-resolution finite volume methods in capturing shocks by resolving discontinuities while maintaining accuracy in the smooth regions. Thesemethods along with Godunov splitting are applied to model proppant transport in fractures. It is concluded that the proposed scheme produces non-oscillatory and accurate results in obtaining a solution for proppant transport problems.展开更多
We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the author...We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.展开更多
基金the research funding for this study provided by NSERC through CRDPJ 387606-09
文摘In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks,while giving poorer accuracy in the smooth regions.Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. In this paper, we investigate several shock-capturing schemes.The competency of each scheme was tested against onedimensional benchmark problems as well as published numerical experiments. The numerical results have shown good performance of high-resolution finite volume methods in capturing shocks by resolving discontinuities while maintaining accuracy in the smooth regions. Thesemethods along with Godunov splitting are applied to model proppant transport in fractures. It is concluded that the proposed scheme produces non-oscillatory and accurate results in obtaining a solution for proppant transport problems.
文摘We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.
