A Semi-Analytical Model for the Simulation of Horizontal and Slanted Wells

Abstract

Abstract This paper presents a semi-analytical solution for the pressure draw down of horizontal or deviated wells in an infinite reservoir considering the well as a source of infinite conductivity. The solution is obtained using the concept of Green's functions applied to solve the diffuse equation in radial coordinates for a point in an infinite domain kept at a constant pressure. The solution is employed to generate dimensionless functions in order to investigate the behavior of horizontal or slanted wells. Others analytical solutions availablein the Literature are used for validation and comparison of results. Calculation procedures are illustrated in the Appendix A and B at the end of the paper. Introduction Horizontal and slanted wells have been drilled recently in many parts of the world and intensive research has been conducted in order to get a better understanding of the characteristics of the horizontal wells. The petroleum industry has developed drilling techniques for directional wells which allow the engineer to plan wells and to reach the reservoir targets under complexwell trajectories. Integrated reservoir studies performed through the use of a suite ofgeology, geophysical and engineering software have brought a much betterknowledge of the reservoir. In this scenario horizontal and slanted wellsalways appear as one of the most viable alternatives. The increasing world interest in horizontal well is also justified due to the higher productivity index exhibited by them when compared to conventional wells (verticals) and as possible solutions for gas coning problems, thin reservoirs, low productivity reservoirs due to low porosity/permeability and reservoirs showing big vertical/horizontal permeability contrast. In conformity with Broman, the costs of drilling and completion of the firsthorizontals wells in Prudhoe Bay Unit were 2.5 more expensive than the conventional ones. However the productivity for these wells were 2 to 3 timesgreater than the conventional ones. Beliveau also presented data on more than 1000 horizontals wells comparing their production to those vertical ones and found a very positive result for the productivity index. The indexes range from 2 to 4 and even more (about 7 to 8) in highly fractured fields. Modeling using analytical solution Modeling of horizontal well in order to make interpretations of well testsis a challenging task both for the analytical and the numerical approach. Different analytical solutions available for the analysis make the interpretation of the test a hard task. These difficulties according to Kuchuckare associated mainly with the directional behavior for the parameters searched.