Analytical Design of Water-Free Production in Horizontal Wells Using Hodograph Method / Zastosowanie metody hodografu do określenia krytycznego wydatku poziomych otworów produkcyjnych

Horizontal well has been widely used as a solution for oil reservoir with underlain strong water drive. The advantage of horizontal well over vertical well is to increase the reservoir contact and thereby enhance well productivity. Because of that, horizontal well can provide a very low pressure drawdown to avoid the water coning and still sustain a good productivity. However, the advantage of the large contact area with reservoir will soon become the disadvantage when the water breakthrough into the horizontal well. The water cut will increase rapidly due to the large contact area with reservoir and it may cause the productivity loss of the whole well. Therefore, keeping the horizontal well production rate under critical rate is crucial. However, existing models of critical rate either oversimplify or misrepresent the nature of the WOC interface, resulting in misestimating the critical rate. In this paper, a new analytical model of critical rate is presented to provide accurate calculations on this subject for project design and performance predictions. Unlike the conventional approach, in which the flow restriction due to the water crest shape has been neglected; including the distortions of oil-zone flow caused by the rising water crest, the new analytical model gives an accurate simultaneous determination of the critical rate, water crest shape and the pressure distribution in the oil zone by using hodograph method combined with conformal mapping. The accuracy of this model was confirmed by numerical simulations. The results show that neglecting the presence of water crest leads to up to 50 percent overestimation of critical rates.