It is well known that in higher-permeability natural gas reservoirs turbulence, at times referred to as non-Darcy effects, may become the dominant influence on production. For vertical wells turbulence has been relatively well understood, deliverability equations have been adjusted to account for the phenomenon and, correlations have been presented a long time ago. Furthermore, field-testing techniques have been established to obtain the non-Darcy coefficient.
Surprisingly, similar work has not been done for horizontal wells. One of the reasons is that horizontal wells have been the completion of choice in North America primarily for very low permeability reservoirs where turbulence effects are of no consequence.
However, as the international petroleum industry starts looking at high-permeability gas reservoirs, turbulence effects in horizontal wells can no longer be ignored. Past work on the subject has been sketchy and in the one or two literature sources where it was addressed, the calculations are demonstrably wrong, not taking into account the crucial near-well effects. Also, quite important is that the few turbulence correlations used in the past, for some unexplainable reason have ignored the porosity.
We present here appropriate correlations to account for turbulence effects in horizontal wells and show that while horizontal wells, even with turbulence, provide considerably higher performance than vertical wells, the reduction from ideal expectations can be substantial. For example, at a permeability of 100 md, while for vertical wells the reduction between real and ideal production may approach 40%, for horizontal wells, it may approach 30%. The influence of porosity is considerable and can account for another 30% deviation among reasonable porosity values.
We finally offer a large range of parametric studies that involve reservoir thickness, permeability anisotropy and horizontal well length. Turbulence effects have a tendency to reduce the expected beneficial ideal effects from longer wells or permeability isotropy because of the implicit "suicide" effects deriving from higher production rates.
Horizontal wells outside of the former Soviet Union started in the 1980s and, eventually, were widely introduced in the early 1990s. Since then, they have proliferated and have become essential in oil and gas production (Economides and Martin, 2007). The main advantages of horizontal wells are (Joshi, 1991, Cho and Shah, 2001):
To increase productivity as the wellbore is longer than that of vertical well;
To reduce water or gas coning;
To reduce turbulence in gas wells (emphasis ours);
To intersect fractures in naturally fractured reservoirs and drain reservoirs more effectively;
To improve drainage area per well and reduce the number of vertical wells in low permeability reservoirs;
To increase injectivity of an injection well and enhance sweep efficiency.
There are quite a few important publications related to horizontal well performance (Celier et al., 1989, Dikken, 1990, Joshi, 1991, Norris et al., 1991, Ozkan et al., 1999, Economides et al., 1994, Cho and Shah, 2001), but few of them had addressed turbulence effects on well performance. Of those that discussed turbulence, most assumed that turbulence is small and can be neglected. Their assumption is that the horizontal well length (L) is a lot longer compared to the vertical well height (h) and therefore, they concluded that turbulence is smaller in horizontal wells compared with that in vertical wells and could be neglected. This is true when the reservoir is isotropic and the permeability is small. But when permeability increases, well deliverability increases, and turbulence effects can no longer be neglected. Based on our study, the production loss due to turbulence could account for 30% in horizontal wells. When the reservoir is anisotropic, it gets even worse.