Study On Sequential Method Of Full Composition Model Of CO₂ Flooding In Low Permeability Reservoir

Low-permeability reservoirs are widely distributed in China.It is of great significance to improve the development techniques for increasing the oil production and storage in China.CO2 flooding is an important development technique for low-permeability reservoirs,which can result in a substantial increase in oil production.Numerical reservoir simulation for CO2 flooding thus become also important in petroleum production industry.In low-permeability reservoir,it can provide a reference for actual production.Traditional numerical methods usually encounter difficulties of huge reservoir size and too many component,resulting in unaffordable computation cost.To alleviate this,this paper focus on the study of high efficient numerical algorithm of CO2 flooding in low permeability reservoir.The sequential solution approach(SEQ)is a common method used in numerical reservoir simulation.When the traditional SEQ is employed to solve the full composition model during CO2 flooding,it may lead to some significant errors,and even worse,it fails sometimes.This is partly because that the component mass conservation equations are highly coupled,and the strong correlations among the coefficients,the phase pressure,the saturation and the component mole fractions make it difficult to construct an decoupled pressure equation.Besides,the traditional SEQ needs to solve the component mass conservation equations implicitly,which also further lows the calculation efficiency.In this thesis,the traditional SEQ will be modified and improved to meet the needs of practical numerical reservoir simulation.It is found that the influence of the time variation terms of saturation and mole fractions is much greater than the corresponding spatial variation terms,and based on this,an decoupled pressure equation is reconstructed with the help of Gaussian elimination considering that the parameters in the time variation terms are only related to the local grid.This reconstructed pressure equation is essentially a linear superposition of all the component mass conservation equations,and this operation can effectively eliminate the error induced by the time variations of saturation and the component mole fractions.Consequently,solving the reconstructed pressure equation directly can obtain high accuracy,and also ensures the stability for SEQ.After solving the decoupled pressure equation,the topological sorting algorithm can be employed to solve the saturation and component mass conservation equations due to their hyperbolic properties.For the two-dimensional plane flow,the velocity field of each phase(oil,water and gas)is irrotational,since the corresponding phase pressure field is potential.In this situation,the node equations can be decoupled and solved independently under the particular order from the upstream and downstream.In the three-dimensional case,a modified topological sorting algorithm is proposed based on the analysis of the swirling flow that may arise under the influence of gravity.The modified topological sorting algorithm is constructed according to the pressure gradient at the mesh interface,and the decoupling of the nodal saturation and component equations is realized,resulting in the great reduction of storage requirement and the significant improvement of calculation efficiency.The advanced SEQ for two and three dimensional cases is proposed in this thesis based on the combination of the construction of the decoupled pressure equation and the modified topological sorting algorithm for solving the saturation and the component equations.The usage of the decoupled pressure equation improves the accuracy and the stability of the whole solving process.The modified topological sorting algorithm sequential algorithm realizes the decoupling of the nodal saturation and component equations,and its computation amount is nearly proportional to the number of variables.This advantage of modified topological sorting algorithm results in great reduction of the storage requirement and improvement the calculation efficiency.With the increase of the number of grids,the efficiency increasement of the proposed SEQ is more obvious.Numerical tests for CO2 flooding are performed in this thesis,and the high efficiency of the proposed SEQ is indicated.In the two-dimensional case,the proposed SEQ can increase the calculation efficiency three to four times compared to the full-implicit algorithm under the same precision.In the three-dimensional case,the proposed SEQ can increase the calculation efficiency three to five times in spite of in the homogeneous or heterogeneous reservoir.