Calculation and Analysis of Fluid Flowing Patterns in the Well Cementation Second Interface
Authors: Liu Yikun , Cui Haiqing , Wu Guangxing , Gong Yujie , Sen Fan 
Published: December 2007

Abstract
The flow equations of a fluid passing through reservoirs, mud cakes and going up along the wall of a well are carried out by analyzing the second interface of well cementation, as well as applying theory of hydraulics and percolation mechanics. This paper educes the impact of influence factors on the fluid going up and possible channel forms in second interface by solving the equations and analyzing of the practical oil field conditions. The main factors influencing fluid outside crossflow are fissure opening degree, the distance between the middle part of reservoir and cement return height, and reservoir pressure, but the influence of reservoir permeability is relatively less. Calculated results indicate that the main factors influencing pressure gradient are flux, reservoir and mud cake permeability; the bigger the flux, the less the permeability and the bigger pressure gradient.
The channels of fluid flow are mainly the high pressure reservoirs, second interface cranny. Therefore, the flow patterns are that plane radial percolation exists horizontally in the reservoir and fissure percolation or pipe flow exists vertically in second interface.

Introduction
Daqing oil field is a nonhomogeneous sandstone structure. The long course of water injection production leads to a difficulty in cementing a well with a high quality. People were puzzled with the hard problems of "the leakage outside of casing", "the channeling among formations" and "hollow casing" in the past. All these problems seriously influence the normal oil well production and lower the production limitation period and the life expectancy. From the investigation and research experiment on these problems we can see that the defects existing in the well cementation second interface are the main cause. From the fluid model of fluid flow in second interface we know that the formation fluid first leaks into bore hole wall annulus space, and then moves up through those fracture or groove between mud cake or cement sheath and formation. this leakage leads to the accident of "the leakage outside of casing" and "the channeling among formations", etc. There was no quantitative ideas on the opening a fracture or a groove through which a fluid can flow in the past. Based on the calculation and analysis of fluid flowing patterns in the well cementation second interface, this paper makes this problem clear in theory.

Theoretical model
The mathematical model used in the calculation of fluid outside crossflow

Single phase fluid radial flow mathematical model.
According to the theory of mechanics of fluid through porous media, the radial flow leakage flow rate equation is:Equation (1)
We suppose there exist radial flow in one sector area in the formation, then the flow rate equation will be:Equation (2)
The mathematical model used in the calculation of fluid outside crossflow
Single phase fluid radial flow mathematical model.
According to the theory of mechanics of fluid through porous media, the radial flow leakage flow rate equation is:Equation (1)
We suppose there exist radial flow in one sector area in the formation, then the flow rate equation will be:Equation (2)
Single phase fluid radial flow mathematical model.
According to the theory of mechanics of fluid through porous media, the radial flow leakage flow rate equation is:Equation (1)
We suppose there exist radial flow in one sector area in the formation, then the flow rate equation will be :Equation (2)