Study On Sequential Method For Heavy Oil Recovery By Steam Flooding

Heavy oil has a significant proportion in the global oil and gas reserves.Steam flooding is a widely used technique in heavy oil recovery.During steam flooding,high pressure steam with suitable dryness fraction is injected into heavy oil stratum,and the properties of heavy oil will be greatly improved,typically a significant decrease of its viscosity under high temperature.By this means,the recovery of heavy oil can be further enhanced.Numerical simulation for steam flooding provides an effective way of predicting the production and designing the recovery schemes.However,performing high quality numerical simulation is a heavy task,since steam flooding is a complex thermal coupling process accompanied by the phase change and the release of latent heat.Physical quantities may be discontinuous in space,and it results in highly nonlinear governing equations,which are difficult to be solved numerically.The traditional fully implicit algorithm is often employed to solve the steam flooding problem numerically due to its high stability.However,its efficiency is quite low mainly because of the strong coupling of the mass and energy conservation equations and the obtained large-scale sparse coefficient matrix with wide bandwidth.How to decouple the mass and energy conservation equations within the allowable error and construct a corresponding numerical algorithm is important to improve the calculation efficiency.This thesis will focus on this,and the contents are as follows.1.The sequential method of decoupling the pressure and saturation variables in the mass conservation equations is reviewed.After decoupling,the pressure equation and the saturation equation can be solved independently and step by step.In this thesis,a decoupled pressure equation is constructed,which can be described as a specific linear combination of the control equations.The relevant imparts of the time derivatives of the other physical quantities except the pressure on the proposed pressure equation are eliminated effectively.In the decoupled saturation equation,the total flow velocity is employed.Then the high performance topological sorting algorithm is used to solve the saturation equation implicitly.By these approaches,high stability and high efficiency of the sequential method are achieved.2.A modified algorithm of solving the energy conservation equation in the sequential method is proposed in this thesis.The traditional sequential method is widely used in the component model,where the mass conservation is usually considered and the energy conservation is seldom involved.The traditional sequential method needs to be modified when considering the energy conservation.In order to obtain a high performance sequential method,the energy conservation equation also needs to be decoupled properly.It is found that an extra error,which is caused by the discrepancy of the mass conservation under temperature changes,is induced in the energy conservation equation.Through mathematical analysis of the expansion form of the original energy equation,this extra error term in energy equation is eliminated and an advanced energy equation is constructed correspondingly.Numerical tests indicate that the stability and the accuracy of the advanced energy equation are improved compared to the traditional one.3.The influence of the decoupled saturation equation on the stability of the sequential method is analyzed mathematically.It is known that the sequential method performs high stability if the total flow velocity is used during the construction of the decoupled saturation equation.However,if the phase velocity is used,numerical oscillations are likely to occur.In this thesis,the cause of this phenomenon is preliminarily discussed.It is found that an extra negative diffusion term is introduced into the discrete saturation equation if it is constructed by using the phase velocity,and this extra negative diffusion term will lead to the numerical oscillation under large time step.This finding reveals the cause of errors in the sequential method when the phase velocity is used in the decoupled saturation equation,and points out the direction of improving the sequential method.In summary,the sequential method for solving steam flooding in heavy oil recovery is investigated in this thesis.High performance decoupled mass and energy equation are achieved,and also,an advanced energy equation is obtained.In addition,the stability of the sequential method is preliminarily investigated.Based on the mathematical analysis,the necessity of using the total flow velocity during the construction of the discrete saturation equation is reaffirmed.