An Empirical Approach To Derive Single-Phase Kh From Two-Phase Tests
Authors: Antsey T.W. 
Published: December 2007

Antsey, T.W., Member SPE-AIME, ADPC Ltd.

Abstract
Pressure buildup and fall-off tests in a large Middle East oil reservoir with significant gas saturations have been affected by two-phase flow. Empirical correlations have been obtained and used to derive single-phase kh values from these two-phase tests. The values so derived have been used to construct a consistent single-phase kh map of the reservoir.

Introduction
Abu Dhabi, which is one of the seven Emirates that make up the United Arab Emirates, is located at the south of the Arabian Gulf. Abu Dhabi Petroleum Co. is the interim operator of the onshore concession. This paper is based on a study carried out on one of the reservoirs operated by ADPC (Fig. 1).
The reservoir is in a large limestone anticline of Lower Cretaceous age. The area encompassed by the oil-water contact is some 900 sq km. The rock properties of porosity and permeability show properties of porosity and permeability show considerable, but regular, areal variations, and there are also quite predictable vertical variations in permeability.
The reservoir has a large gas cap covering some 200 sq km. Oil properties are depth related, so that at the oil-water contact the bubble-point pressure was originally over 1,000 psi below pressure was originally over 1,000 psi below reservoir pressure.
The reservoir was brought onstream in 1964, and now has been producing for over 13 years. With reservoir pressure in the producers initially little above local bubble point, all producers have been flowing at or below bubble point from the first day. In order to minimize the amounts of unassociated gas produced, the oil rates have been kept relatively produced, the oil rates have been kept relatively low. There is now a pressure sink in the most heavily produced area of the reservoir, and a pressure maintenance scheme, by water injection, was pressure maintenance scheme, by water injection, was commissioned in 1974. The scheme consists of two lines of injectors, one on each side of the pressure sink - the inner line is near the gas-oil contact, and the outer line is near the oil-water contact.
Pressure buildup tests (PBU's) have been made in producers before and throughout the producing life of producers before and throughout the producing life of the reservoir, and pressure fall-off tests (PFO's) have been made in the injectors since the commissioning of the water injection scheme. It should have been simple to map these test kh's, but it was not a straightforward exercise because the kh values derived from successive tests in the same well generally have declined with time — by factors of up to 70 percent. Therefore, a study was undertaken to try to rationalize the apparently inconsistent test kh data in order to construct a kh map for use in a model.
In virtually all producers the sand-face pressures on the straight-line sections of the pressures on the straight-line sections of the Horner plots of the PBU's are now less than the local bubble point, and in the majority of wells this always has been the case. Hence, the kh values derived from these PBU's have been affected by two-phase flow in the reservoir. The analyses of these PBU's have been based on oil production rates, and so the analyses are presumed to have been yielding (kh) kro rather than single-phase kh.
The main concern of this paper is to describe how the analysis of PBU's and PFO's has been extended to correct for the effects of two-phase flow. The emphasis is on the analyses of PBU's based on oil rates, so the two-phase flow corrections are made via kro. However, the producing gas-oil ratios often have been in excess of the solution gas-oil ratio, and so a section is included at the end of the paper that discusses the extended analysis based on production rates of this unassociated gas leading to production rates of this unassociated gas leading to possible corrections via krg. possible corrections via krg.

RE-ANALYSIS OF TESTS
The general equation for calculating kh from a Horner plot is
. . . . . . . . . . . . (1)