The development of a simulator for homogeneous reservoirs with application in producer wells (represented by a sink) and the aquifer analysis is obtained by combining the Boundary Element Method (BEM), the Isogeometric Formulation using NURBS (Non-Uniform Rational B-Spline) as shape functions, and also the Axisymmetric Formulation. The Isogeometric Formulation makes the discretization of geometric model (mesh generation), which is the step of numerical analysis that is more time-consuming for the engineer, be no longer necessary, since the same functions that describe the geometry also approximate the field variables in the BEM. In other words, the same discretization used in the geometric model, generated in CAD (Computer Aided Design) modeling programs, also is used by the BEM. The oil and water reservoirs, as simplified models for validation of the new mathematical methodology, can be fully represented by the analysis of a plane passing through the axis of rotational (axial) symmetry. The dimension of the problem is reduced from three to two dimensions: radial and axial directions only, and all variables in the circumferential direction are assumed to be constant. When the geometry and the problem variables are both axisymmetric, then the problem is considered fully axisymmetric. The isogeometric and axisymmetric formulations are coupled to obtain the well simulator for the single and double phase case, i.e., one or two incompressible fluids inside the reservoir. The determination of boundary conditions for the model, including the analysis of fluids interface movement, is also presented. The final code is a new tool for the analysis of gas/water coning phenomenon and quick drawdown problem in homogeneous reservoirs, as validation models. Validation of the results is carried out by comparing with others numerical methods and analytical results.

通过结合边界元法（BEM），使用NURBS（非均匀有理B样条）作为等几何公式，获得了用于均质油藏的仿真器的开发以及在生产井中的应用（以汇表示）和含水层分析。形状函数，以及轴对称公式。等几何公式化使几何模型的离散化（网格生成）不再是必需的，因为几何模型的相同功能也可以近似地估算字段中的变量，而几何模型的离散化对于工程师来说是一个耗时的数值分析步骤。 BEM。换句话说，BEM也使用在CAD（计算机辅助设计）建模程序中生成的几何模型中使用的离散化方法。石油和水库，作为验证新数学方法的简化模型，可以通过对穿过旋转（轴向）对称轴的平面的分析来充分表示。问题的范围从三个维度减少到两个：仅径向和轴向，并且假定圆周方向上的所有变量都是恒定的。当几何形状和问题变量均为轴对称时，则认为该问题是完全轴对称的。等几何公式和轴对称公式被耦合以获得用于单相和双相情况的油井模拟器，即，油藏内的一种或两种不可压缩的流体。还介绍了模型边界条件的确定，包括对流体界面运动的分析。最终代码是一种用于分析均质油藏中的气/水锥化现象和快速下降问题的新工具，作为验证模型。通过与其他数值方法和分析结果进行比较来验证结果。