Abstract

Some simulation studies of unconventional wells with a declining flowing pressure show a significant increase (hump) in the oil rate at the time when the flowing pressure crosses the bubble point. This unexpected "oil-rate hump" is subsequently followed by the traditionally expected rate decline.

The unexplained rate hump raises various questions: The first question is: is it real or simply an artifact of the mathematics of numerical simulation? And if real, other question arise, including: how do reserve estimation methods that are based on rate decline apply to an increase? Or, does a rate increase mean one should produce the wells at pressures below the bubble point pressure to accelerate production of the oil associated with the rate hump? The main objective of this paper is to investigate whether a rate hump is a result of numerical errors of simulators especially as grid-blocks drop below bubblepoint pressure, or if it is an intrinsic response of formulations of two - phase flow under some conditions of flowing pressure, etc. And if the latter, what are the conditions that lead to a rate hump.

We start with the partial differential equations of two-phase (gas and oil) flow for transient linear flow and re-write them in a form similar to those of single-phase flow. This allows term-to-term comparison of the two-phase formulation with the corresponding single-phase one. Through this comparison and the analytical and numerical solutions presented, we suggest that the rate increase is not because of numerical errors, instead it is related to at least three groups of parameters(i) fluid properties impacting the ratio between single-phase and two-phase compressibility. (ii) flow parameters that reflect how efficiently the evolved solution gas displaces the oil, and (iii) the rate at which the pressure at the wellbore is declining.

Furthermore, a series of numerical simulations are conducted to:(i) investigate the effect of parameters of significance and (ii) extend the range of investigation to more practical cases such as those more common to completion in unconventional reservoirs. When we choose typical values for reservoir and fluid properties, and operating conditions from unconventional basins we observe significant rate increases that last for many months and could make a significant contribution to early production.

Next, we look for evidence of the "rate hump" in actual field data. Our review of field data did not result in any convincing data sets with clearly defined rate humps. While a more exhaustive review of field data may reveal this phenomenon to be real, we discuss conditions that may mask or negate the rate hump. We also provide preliminary guidelines for input parameters so that the simulation model does not exhibit the rate hump.

To the best of our knowledge, this is the first time that the rate hump is being investigated in the literature.

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