A Universal Formulation for the Prediction of Capillary Pressure

Abstract

Capillary pressure and associated relative permeability are special core analysis parameters which are vital in accurately describing fluid distributions and movement in porous media when two (or more) immiscible fluids are present. Conventionally, the determination of capillary pressure requires laboratory experiments, which are expensive and time consuming. Assuming that core material is available, typically a limited number of core plugs are considered for testing, often resulting in incomplete reservoir description. This situation then leads to motivation for developing mathematical capillary pressure models, as an alternative to adequately describing fluid behaviour in reservoirs.The well known Carman-Kozeny (C-K) equation (Carman 1937;Kozeny 1927) is commonly used to model permeability as a function of other pore structure parameters. More recently parametric groups were established for the C-K equation, which are in regular use in reservoir characterisation. Specifically, the determination of flow zone units for the description of distinct (litho)facies is now widely used in linking fluid flow to geological descriptions. In this paper, a new and innovative deployment of the C-K equation is investigated to derive capillary pressure relationships. The new mechanistic, drainage capillary pressure model uses the principle of "effective saturation", and is developed and validated with data sets from onshore and offshore Australian hydrocarbon basins, giving a good comparison with laboratory measurements and other established models. Most significantly, the new mechanistic formulation does not just fit capillary relationships but is able to predict drainage curves by knowing or assuming up to six properties: absolute permeability; effective porosity; irreducible water saturation; maximum capillary pressure, which may be related to a particular reservoir situation or laboratory standard; capillary entry pressure; and associated entry water saturation. The last two parameters are typically required for a higher permeability (or better quality) rock. Absolute permeability is incorporated indirectly. Furthermore, there is no requirement for correlation parameters or constants but the analysis determines two parameters which give a measure of heterogeneity of the sample being investigated.

Transition zones analysis using empirical capillary pressure model from well logs and 3D seismic data on ‘Stephs’ field, onshore, Niger Delta, Nigeria

“…From this capillary pressure log, the actual oil-water contact, transition zone, zone fully saturated with oil and the free water zone were delineated. The capillary pressure log was interpreted after Glover (2000), Larsen et al (2000) and Goda (Sam) et al (2011).…”

“…Two non-miscible fluids sharing the same porous space tend to occupy different positions depending on their density contrast (Glover 2000;Pascoal 2015). Vavra et al (1992), Hartmann and Beaumont (1999), Larsen et al (2000), Sarwaruddin et al (2001), Kumar et al (2002), Wiltgen et al (2003), Johan and Svein (2005), Okoli and Ujanbi (2007), Jamiolahmady et al (2007), Zhao et al (2008), Renzo et al (2010) and Goda (Sam) et al (2011) have employed a different approach to analyse the oil transition zone and saturation height above free water level using semi-empirical relationship from Leverett (1941), Skelt and Harrison (1995), Christiansen (2001), Wu (2004), amongst others, with special core analysis (SCAL) under laboratory conditions. Hydrocarbon saturation in a reservoir can be overestimated when the effect of mobile water occurring in the transition zones within the reservoir is not accounted for while estimating reserves (Fig.…”

“…From capillary pressure, hydrocarbon/water contacts, rock matrix type and pore throat structure, heights of transition zones within the reservoir can be determined. In this study, a universal empirical model by Goda (Sam) et al (2011) for obtaining the reservoir capillary pressure information of a field in the absence of core information was utilized and validated using well logs information from 'Stephs' field.…”

Build-up of capillary pressure curves and saturation parameter using residual water saturation factor by the example of Eastern Siberia carbonate deposits

“…На данный момент существует достаточно много моделей, описывающих связь кривой капиллярного давления с различными петрофизическими параметрами. Хронологический обзор основных моделей представлен в работе [8]. В России достаточно широкое применение получили модели Леверетта и Брукса -Кори.…”

“…где ркапиллярное давление; σмежфазное натяжение; θкраевой угол смачивания; K пр -коэффициент проницаемости; K п -коэффициент пористости; K в -коэффициент водонасыщенности; а и b -эмпирические константы. Сначала модель Леверетта рассматривалась применительно только к терригенным коллекторам, но, как показал дальнейший опыт, в определенных ситуациях ее можно использовать и для карбонатных коллекторов [8]. Как можно видеть из выражения (1), связь между капиллярным давлением р и текущей водонасыщенностью K в определяется шестью константами.…”