A new method for calculating productivity of horizontal well in low-permeability heavy oil reservoir

On the basis of the characteristics of fluid flow in the horizontal well under the steady state conditions and the theory of the isobaric ellipsoidal and rotational surface proposed by Song Fuquan,the seepage field of horizontal well could be more accurately divided into three regions in the low-permeability heavy oil reservoir with the power-law fluid pattern,including inner,middle and outer.The productivity formula of the horizontal well under steady state for every region was derived respectively.According to the equivalent principle of the flow rates and pressures at the regional boundaries,the non-linear equations regarding to the pressures of boundaries were constructed.The Newton-Raphson method was adopted to get the numerical productivity values of the horizontal well.The comparison of the calculated productivity with the estimated maximum productivity showed the effectiveness and practicability of the new method for calculating the productivity of horizontal well.The analysis on the power-law exponent,start-up pressure gradient and length of the horizontal wellbore showed that those parameters had great effects on the productivity of the horizontal well when the power-law exponent n was over 0.8.There was a linear relationship between the productivity of horizontal well and the start-up pressure gradient.The length of the horizontal wellbore had no effect on the productivity change rate of the horizontal well,but it could be affected when the power-law exponent n was over 0.8.