Research On Modeling And Optimal Control Of Alkali-surfactant-polymer Flooding

Alkali-surfactant-polymer(ASP)flooding is an important tertiary oil recovery technique.It can enhance the oil recovery evidently by fully using the synergistic effect among three displacing agents(alkali,surfactant and polymer)to change properties of reservoir.But the mechanism of ASP flooding is too complex,and there is lack of comprehensive model to describe the flooding process.What's more,the price of displacing agents is expensive,and the exploitation period is very long.To make development scheme scientifically and obtain the maximal economic benefit,a study on modelling and optimal control for ASP flooding was carried out in this dissertation.The mathematical model of ASP flooding is firstly established based on the complex oil-displacement mechanism.Then the full implicit finite difference method is applied to discretize and solve the three-dimensional model.Further,the optimal control model of three-dimensional ASP flooding is given,which takes the net present value as the performance index,the ASP flooding model as the governing equation,the injection concentration of displacing agents,slug length and terminal flooding time as the control variables,the consumption and concentration restriction of displacing agents and the physicochemical algebraic equation as the constraints.Finally,the discrete necessary condition for this optimal control problem is inferred by maximum principle.On account of the discontinuities of slug-injection strategy and control variable in ASP flooding,an adaptive orthogonal function approximation(AOFA)method is presented.From the perspectives of Gaussian pseudo-spectral and rationalized Haar function,the algorithm process is: convert all path constraints into one terminal state constraint by constraint aggregation;discretize the problem into a nonlinear programming(NLP)by multi-stage problem transformation and orthogonal function approximation;solve this NLP with seqential quadratic programming.To identify the discontinuity of control and improve the accuracy,the adaptive strategy and control structure detection method with optimality verification are introduced.Simulation on the optimal control of ASP flooding with injection concentration and slug length as controls verifies the effectiveness of proposed method.To deal with the huge computation burden and low computation efficiency of AOFA,the dynamic programming(DP)is researched.On the one hand,since the slug length is an integer time variable,a dynamic scale mixed-integer iterative dynamic programming(DSMI-IDP)is presented,in which an integer truncation strategy is introduced to deal with the integer variables,an dynamic adjustment strategy is brought in to update the constriction factor and adjustment factor.Then DSMI-IDP is used to solve the optimal control of ASP flooding with injection concentration,slug length and terminal flooding time as controls to test the effectiveness.On the other hand,an approximate dynamic programming based on actor-critic frame is proposed,in which the approximation of control strategy and value function is realized by constructing linear basis function,the weight coefficient of value function is calculated by temporal difference learning algorithm,all parts are integrated into one by actor-critic frame,and the optimal control is searched by spectral conjugate gradient method.Simulation result on solving the optimal control of ASP flooding,in which only the injection concentration is chosed as the control,proves that the proposed method is effect.Considering the multiple fuzzy index in ASP flooding,a solution method for fuzzy multi-objective optimal control based on spiral optimization is presented.A hybrid spiral optimization algorithm(ISOA)is developed with the performance improved by Latin hypercube sampling and adaptive Cauthy mutation.In order to solve the fuzzy multi-objective problem,a new method combined with symmetry model and level cut set is introduced to transform the original problem into a deterministic problem,which can be solved by ISOA.The effectiveness is proved by solving the fuzzy multi-objective optimal control of ASP flooding with injection concentration as the control variable.Since ASP flooding involves a series of coupled partial differential equations,the solving process has low efficiency.Aming at one kind of system with distributed parameter input and state,and with lumped parameter output,an IDP algorithm based on biorthogonal spatial-temporal modelling is proposed.At first,build the identification model for ASP flooding: the lumped parameter Wiener model is expanded to a distributed parameter spatial-temporal model by biorthogonal decomposition,use this model to identify the relation between the input and state;the relation between state and output is built with ARMA model.Then,solve the optimal control problem based on identification model with IDP.At last,keep the slug constant and optimize the injection concentration,apply the proposed method to solve the optimal control of ASP flooding.