Determination of Effective or Relative Permeability Curves From Well Tests

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Abstract

This work presents a procedure for estimating effective or relative permeability curves directly from well-test pressure data obtained from a well producing a pressure data obtained from a well producing a solutiongas-drive reservoir. The basic procedure developed and discussed in this work combines computed effective permeability versus pressure values with nonlinear regression permeability versus pressure values with nonlinear regression analysis techniques to determine the parameters involved in Standing's relative permeability correlations. The advantage of the proposed method is that it does not require direct knowledge or computation of oil saturation as a function of pressure. It is shown that, in many cases, the pressure data obtained from drawdown (single or two-rate) and buildup tests is sufficient to determine accurate estimates of the parameters involved in Standing's relative permeability correlations. In particular, the computational procedures presented can be used to determine estimates of the pore size distribution index, connate water saturation, critical gas saturation and the effective (or relative) permeability of the non-wetting phase at irreducible wetting phase saturation. Once these parameters are determined, effective or relative permeability curves as a function of saturation can be generated without the direct knowledge or computation of sandface oil saturation.

Introduction

For solution-gas-drive reservoirs, Refs. 1-4 have provided methods for approximating the oil and gas effective provided methods for approximating the oil and gas effective permeabilities as a function of pressure directly from permeabilities as a function of pressure directly from pressure drawdown and buildup data. Refs. 5 and 6 have pressure drawdown and buildup data. Refs. 5 and 6 have presented modifications of the methods of Refs. 1-4 for presented modifications of the methods of Refs. 1-4 for cases where wellbore storage effects exist. Here, we develop a new computational procedure that enables one to obtain the oil and gas effective permeability as a function of oil saturation by using Standing's relative permeability correlations in conjunction with the methods of Refs. 1-4. The results assume two-phase radial flow of oil and gas to a well in an infinite-acting solution-gas-drive reservoir.

The results of Refs. 1-6 show that, once wellbore storage effects become negligible, we can obtain good estimates of KKro and KKrg from pressure drawdown data by applying the following equations:

(KKro)Pwf = (1)

and (kkrg)Pwf = (2)

Eq. 1 assumes that Qo is constant and equal to the sandface flow rate. In Eq. 2,Qg(t) denotes the sandface flow rate of free gas in scf/day, i.e.,

Qg(t) = Qgt -RsQo, (3)

where Qgt is the total gas flow rate (free gas plus solution gas) at standard conditions. As shown in Refs. 2 and 3, during the infinite acting period, Eqs. 1 and 2 typically yield reasonably good estimates of effective permeabilities except at very early times. Here, we show that the ratio of the effective permeabilities obtained from Eqs. 1 and 2 is exact even when permeabilities obtained from Eqs. 1 and 2 is exact even when Eqs. 1 and 2 yield inaccurate estimates of individual phase effective permeabilities. Dividing Eq. 2 by Eq. 1 and using Eq. 3 gives

KKrg = KKro (4)

which is equivalent to

R = Rs + (5)

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