Horizontal Wells Mathematical Model Calculation And Well Test Analysis

Horizontal well technology is one of the most important technological mean on development of oil and gas fields in the world. The economic benefits one single well is the same as a 3 to 8 times of the same single well developed vertical wells. Horizontal well test analysis is the key mining technology, which runs through the entire development process. At present, the mathematical model for the Laplace transform, Newman product method and the source function method and other methods are commonly used in the horizontal well testing. Moreover the pressure is the amount of flow which is as a known quantity. But these studies do not consider how to calculate the pressure at the time when the uneven distribution of flow as the unknown quantity. In this paper, a new calculation method is proposed to solve the pressure and draw a well test interpretation curve.The results of the paper are as follows:1) Based on basic theory of the porous flow theory, Mathematical physics equations, point resource function, and so on, the three-dimensional reservoir vertical and horizontal wells mathematical model of unsteady flow have been further improved.When the flow distribution is a known quantity, the paper did not use the Laplace transform method but used orthogonal transformation, the precise point source solution for the transient flow, superposition principle to obtain the exact solutions of the pressure of three-dimensional reservoir vertical and horizontal wells mathematical model of unsteady flow.2) When the exact solution of horizontal well pressure is known, the paper used numerical methods and VB programming to draw the pressure and pressure derivative of the double logarithm of time curve, to divide the various flow period of horizontal well, to discuss the vertical position of horizontal well, the length of dimensionless wellbore and the effect of horizontal position of the source lines towards the horizontal well pressure transient curves of the dynamic characteristics.3) When the uneven distribution of flow is a unknown quantities, this paper proposed a new method. Flow function and stress expressions constitute the inverse problem of partial differential equations. First by numerical integration, iterative linear equations and convergence of infinite series method to calculate flow. And then the pressure can be determined by the flow of different time.