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STABLE METHOD AND APPARATUS FOR SOLVING S-SHAPED NON-LINEAR FUNCTIONS U TILIZING MODIFIED NEWTON-RAPHSON ALGORITHMS
STABLE METHOD AND APPARATUS FOR SOLVING S-SHAPED NON-LINEAR FUNCTIONS U TILIZING MODIFIED NEWTON-RAPHSON ALGORITHMS
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机译：利用修正的牛顿-拉普森算法求解S形非线性函数的稳定方法和装置
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摘要
An apparatus and method are provided for solving a non-linear S-shapedfunction F = f(S) which is representative of a property S in a physicalsystem, such saturation in a reservoir simulation. A Newton iteration (T) isperformed on the function f(S) at SV to determine a next iterative value SV+1. It is then determined whether SV+1 is located on the opposite side of theinflection point SC fromSV. If SV+1 is located on the opposite side of theinflection point fromSV , then SV+1is set to S1, a modified new estimate. Themodified new estimate, S1, is preferably set to either the inflection point,SC, or to an average value between SV and S V+1 , i.e. , S1 = 0.5( SV+ S V+1).The above steps are repeated until SV+1is within the predetermined convergencecriteria. Also, solution algorithms are described for two-phase and three-phase flow with gravity and capillary pressure.
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机译：提供一种用于求解非线性S形的装置和方法函数F = f（S），代表物理性质S储层模拟中的饱和度。牛顿迭代（T）为在SV处对函数f（S）执行以确定下一个迭代值SV + 1。然后确定SV + 1是否位于电池的另一侧。拐点SC来自SV。如果SV + 1位于从SV拐点开始，然后将SV + 1设置为S1，即新的估计值。的修改后的新估计值S1最好设置为拐点，SC或SV与S V + 1之间的平均值，即S1 = 0.5（SV + S V + 1）。重复上述步骤，直到SV + 1处于预定收敛范围内标准。此外，还介绍了针对两相和三相的解决方案算法相流在重力和毛细压力作用下。
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