Modelling of Drainage Capillary Pressure: Using the Modified Carman-Kozeny Purcell Model to Identify the Type of Pore Throat Distribution Inherent in Laboratory Data

SPE Asia Pacific Oil &Amp; Gas Conference and Exhibition

Huu²,

Hoang

et al. 2016

Capillary pressure relationships (drainage) is of importance in both, reservoir engineering and petrophysics. Reservoir engineers use capillary pressure relationships in reservoir engineering calculations and petrophysicists use such relationships in saturation-height modelling. The overall objective of the study presented is to perform a comparative study of various capillary pressure models commonly used by the petroleum industry and to access their ability to match diverse laboratory data. Over the years many capillary pressure formulations have been proposed to match laboratory data, from the well-known Leverett J-function approach to more recent methods. Generally, formulations may be theoretical, semi-empirical, empirical or statistical basis. The comparative study presented involves the following analytical formulations: modified Leverett J-function, modified Brooks-Corey (MBC), Thomeer, Skelt-Harrison, Lambda (λ) and the more recently established, Modified Carman-Kozeny-Purcell (MCKP) model. Various types of pore structures may be modelled: homogeneous (narrow), broad (poorer sorting) and bimodal (two distinct distributions) where one of the distributions is often related to pore-fill, or a mixture of distribution types. Results presented in this paper compare application of the above-mentioned methods for homogeneous plugs. It is demonstrated that the MCKP method consistently outperforms the other methods and it is the only method that is able to identify the type of pore throat distribution without any further input data. The advantage of the MCKP method is that it does not contain any fitting parameters. The degree of accuracy of the MCKP model is typically R2 > 0.99. The MCKP model also lends itself very easily to predict capillary pressure relationships from more basic parameters. Presented are examples with data from two Australian fields, one offshore and one onshore.

Modelling of Drainage Capillary Pressure: A Comparative Study of Various Analytical Capillary Pressure Formulations in Matching Laboratory Results

SPE Asia Pacific Oil &Amp; Gas Conference and Exhibition

Huu²,

Hoang

et al. 2016

Capillary Pressure Drainage Curves: Modelling and Prediction of Capillary Entry Pressure

SPE/IATMI Asia Pacific Oil &Amp; Gas Conference and Exhibition

Kennaird²,

Bui³

et al. 2017

Capillary pressure (CP) measurements on core samples generally deploy one of three tests: porous plate (PP), centrifuge (CF) and mercury injection (MI). The first two mentioned tests are most often used to directly determine a CP relationship and the PP procedure most closely conforms to reservoir situations. CF test results may be superior for certain types of plugs and testing conditions, not to mention that testing is considerably faster. MICP tests are typically used for determining pore size distributions but may also be used to generate CP curves, with best results obtained by validation against the other two tests. MI tests also have the shortest timeline. CP curves have been modelled (fitted or matched) over the years with many alternative formulations, from the well-known J-function approach (Leverett, 1941) to more recent methods. Some formulations can realistically match the low pressures of CP profiles, including capillary entry pressure, while others do not cater for it at all. When the low-pressure part of CP curves exhibit a "roll-over effect (concave downward profile), entry pressure prediction may require high frequency data from MICP testing to give more definition. This paper examines several CP data sets, comparing PP and MI results, in light of pore throat distributions. Seven formulation are used to match entire CP profiles from PP data and are subsequentlyexaminedfor being able to represent capillary entry pressure. Various types of pore structures are discussed: homogeneous (narrow distribution), broad (poorer sorting) and bimodal (two distinct distributions) where the smaller pores are often related to pore-fill. It is shown that the Modified Carman-Kozeny Purcell (MCKP) formulation (Behrenbruch et al, 2011) is excellent in capturing the level of entry pressure for narrow pore throat size distributions or homogeneous plugs while entry pressure prediction for poorer sorted plugs tends to be less accurate, partially due to variation in samples.The detailed modelling of the roll-over effect requires a separate model. A new and improved correlation for (model) capillary entry pressure has been derived, showing results from Australian and other fields.

The Importance of Optimal Choice of Relative Permeability Relationships in Reservoir Simulation

SPE Asia Pacific Oil and Gas Conference and Exhibition

Hoang

Huu³

et al. 2018

Dynamic reservoir simulation models are used to predict reservoir performance, and to forecast production and ultimate recovery. Such simulation models are also used to match historic production. The success of such models depends critically on optimal gridding, particularly vertical definition and the choice of rock parameters, especially relative permeability. This paper compares simulation results as a function of utilising alternative relative permeability relationships as simulation input: Unaltered laboratory data Modified Brooks-Corey (MBC) relationships derived by fitting lab data (Lake,1989), including MBC and Sor extrapolation (Stiles, 1994) Relationships based on the more recently derived two-phase Modified Carman-Kozeny (2pMCK) formulation (Behrenbruch and Goda, 2006) For maximum clarity, comparisons are made on a single layer basis but covering a range of permeability and porosity values, and capillary pressure relationships are based on modelled lab data using the Modified Carman-Kozeny Purcell (MCKP) model (Goda and Behrenbruch, 2011). Study results show that very different production responses may be realised, depending on the validity of original lab data and choice of modelled relationships deployed. It is concluded that the use of the 2pMCK model in combination with auxiliary investigative tools is optimal in rationalising lab data. Some tested plugs show the influence of heterogeneity, as well as procedural shortcomings and even plug failure. It is shown how such test results can be identified by the 2pMCK model and then optimally modified. In comparison with the MBC model, it is also evident that the use of Corey coefficients may at times be too prescriptive, and even flawed when it is assumed that exponents are only a function of wettability rather than also considering plug heterogeneity and possible lab issues. Relative permeability and capillary pressure data sets are taken from lab results for the Laminaria and Corallina fields, Timor Sea.