The research of different kinds of permeable non-Newtonian fluid flow is increasing day by day owing to the development of science,technology and production modes.It is most common to use power rate equation to descri...The research of different kinds of permeable non-Newtonian fluid flow is increasing day by day owing to the development of science,technology and production modes.It is most common to use power rate equation to describe such flows.However,this equation is nonlinear and very difficult to derive explicit exact analytical solutions.Generally,people can only derive approximate solutions with numerical methods.Recently,an advanced separating variables method which can derive exact analytical solutions easier is developed by Academician CAI Ruixian（the method of separating variables with addition）.It is assumed that the unknown variable may be indicated as the sum of one-dimensional functions rather than the product in the common method of separating variables.Such method is used to solve the radial permeable power rate flow unsteady nonlinear equations on account of making the process simple.Four concise（no special functions and infinite series） exact analytical solutions is derived with the new method about this flow to develop the theory of non-Newtonian permeable fluid,which are exponential solution,two-dimensional function with time and radius,logarithmic solution,and double logarithmic solution,respectively.In addition,the method of separating variables with addition is developed and applied instead of the conventional multiplication one.It is proven to be promising and encouraging by the deducing.The solutions yielded will be valuable to the theory of the permeable power rate flow and can be used as standard solutions to check numerical methods and their differencing schemes,grid generation ways,etc.They also can be used to verify the accuracy,convergency and stability of the numerical solutions and to develop the numerical computational approaches.展开更多
机械钻速(rate of penetration,ROP)是钻井作业优化和减少成本的关键因素,钻井时有效地预测ROP是提升钻进效率的关键。由于井下钻进时复杂多变的情况和地层的非均质性,通过传统的ROP方程和回归分析方法来预测钻速受到了一定的限制。为...机械钻速(rate of penetration,ROP)是钻井作业优化和减少成本的关键因素,钻井时有效地预测ROP是提升钻进效率的关键。由于井下钻进时复杂多变的情况和地层的非均质性,通过传统的ROP方程和回归分析方法来预测钻速受到了一定的限制。为了实现对钻速的高精度预测,对现有BP (back propagation)神经网络进行优化,提出了一种新的神经网络模型,即动态自适应学习率的粒子群优化BP神经网络,利用录井数据建立目标井预测模型来对钻速进行预测。在训练过程中对BP神经网络进行优化,利用启发式算法,即附加动量法和自适应学习率,将两种方法结合起来形成动态自适应学习率的BP改进算法,提高了BP神经网络的训练速度和拟合精度,获得了更好的泛化性能。将BP神经网络与遗传优化算法(genetic algorithm,GA)和粒子群优化算法(particle swarm optimization,PSO)结合,得到优化后的动态自适应学习率BP神经网络。研究利用XX8-1-2井的录井数据进行实验,对比BP神经网络、PSO-BP神经网络、GA-BP神经网络3种不同的改进后神经网络的预测结果。实验结果表明:优化后的PSO-BP神经网络的预测性能最好,具有更高的效率和可靠性,能够有效的利用工程数据,在有一定数据采集量的区域提供较为准确的ROP预测。展开更多
基金supported by National Natural Science Foundation of China(Grant No.50876106)
文摘The research of different kinds of permeable non-Newtonian fluid flow is increasing day by day owing to the development of science,technology and production modes.It is most common to use power rate equation to describe such flows.However,this equation is nonlinear and very difficult to derive explicit exact analytical solutions.Generally,people can only derive approximate solutions with numerical methods.Recently,an advanced separating variables method which can derive exact analytical solutions easier is developed by Academician CAI Ruixian（the method of separating variables with addition）.It is assumed that the unknown variable may be indicated as the sum of one-dimensional functions rather than the product in the common method of separating variables.Such method is used to solve the radial permeable power rate flow unsteady nonlinear equations on account of making the process simple.Four concise（no special functions and infinite series） exact analytical solutions is derived with the new method about this flow to develop the theory of non-Newtonian permeable fluid,which are exponential solution,two-dimensional function with time and radius,logarithmic solution,and double logarithmic solution,respectively.In addition,the method of separating variables with addition is developed and applied instead of the conventional multiplication one.It is proven to be promising and encouraging by the deducing.The solutions yielded will be valuable to the theory of the permeable power rate flow and can be used as standard solutions to check numerical methods and their differencing schemes,grid generation ways,etc.They also can be used to verify the accuracy,convergency and stability of the numerical solutions and to develop the numerical computational approaches.
