Formation-Resistivity Theory: How Archie Equations, Shaly-Reservoir Models, Conductive Rock-Matrix Model, and Dual-Triple-Porosity Models Are Related
- Philip C. Iheanacho (Smart Drilling Services Limited)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2014
- Document Type
- Journal Paper
- 141 - 151
- 2014.Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 4.1.2 Separation and Treating, 5.8.2 Shale Gas, 4.1.5 Processing Equipment, 5.6.1 Open hole/cased hole log analysis
- well log analysis interpretation
- 3 in the last 30 days
- 742 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The estimation of hydrocarbon pore volume (HCPV) from resistivity logs can be quite troublesome in some complex heterogeneous reservoirs. Most water-saturation/formation-resistivity models that work well for some reservoirs give unreliable results for others. No single model works for all types of reservoir scenarios. This paper presents the theory of formation resistivity in porous media. The paper develops the theory from the parallel-resistivity model and then extends it for the series-resistivity model. When applied for clean sand, the theory derives Archie equations from the first principle. The derivations show that both porosity exponent and saturation exponent are of the same origin and should have the same name. A better name for both parameters should be the tortuosity exponent of a component with respect to its fraction in a control volume. It is also advantageous to treat as a single parameter rather than two separate parameters. In addition, this theory derives new shaly-sand models for estimating HCPV. These new shaly-sand models can be used for different types of shale distribution by adjusting the value of a single parameter in the models. The formation-resistivity theory is also used to derive formation-resistivity models for conductive rock-matrix reservoirs and dual-triple-porosity reservoirs. A new equation for calculating the composite-porosity exponent is also developed. Field data are used to validate this work. The theory, when applied for each scenario, derives formation-resistivity models for estimating the reliable HCPV of different reservoir scenarios and types. Moreover, the strength of this theory is its ability to generate models that closely resemble models that have proved to work well for the reservoir cases for which they were developed. Although this work does not test the theory for the cases of tightsand, shale-gas, and other unconventional reservoirs because of the unavailability of such data, the author is of the opinion that the theory can easily be extended for such reservoirs if the necessary data are available.
|File Size||379 KB||Number of Pages||11|
Aguilera, R. and Aguilera, M.S. 2003. Improved Models for Petrophysical Analysis of Dual Porosity Reservoirs. Petrophysics 44 (1): 21–35.
Aguilera, R.F. and Aguilera, R. 2004. A Triple Porosity Model for Petrophysical Analysis of Naturally Fractured Reservoirs. Petrophysics 45 (2): 157–166.
Aguilera, C.G. and Aguilera, R. 2006. Effect of Fracture Dip on Petrophysical Evaluation of Naturally Fractured Reservoirs. Paper CICP 2006-132 presented at the Petroleum Society’s 7th Canadian International Petroleum Conference (57th Annual Technical Meeting), Calgary, Alberta, Canada, 13–15 June.
Al-Ghamdi, Behmanesh, H., Qanbari, F. et al. 2011. An Improved Triple-Porosity Model for Evaluation of Naturally Fractured Reservoirs. SPE Res Eval & Eng 14 (4): 377–384. http://dx.doi.org/10.2118/132879-PA.
Archie G.E. 1942. The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics. Trans. AIME 146: 54–62.
Berg, C.R. 2006. Dual-Porosity Equations From Effective Medium Theory. Paper SPE 101698 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. http://dx.doi.org/10.2118/101698-MS.
Clavier, C., Coates, G., and Dumanoir, J. 1984. Theoretical and Experimental Bases for the Dual-Water Model for Interpretation of Shaly Sands. SPE J. 24: 153–168. http://dx.doi.org/10.2118/6859-PA.
Herrick, D.C. 1988. Conductivity Models, Pore Geometry, and Conduction Mechanisms. Paper D presented at the SPWLA 29th Annual Logging Symposium.
Owen, J.E. 1952. The Resistivity of a Fluid-Filled Porous Body. Trans. AIME. 195: 169–174.
Tiab, D. and Donaldson, E.C. 1996. Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, second edition, 706. Houston, Texas: Gulf Publishing Co.
Towle, G. 1962. An Analysis of the Formation Resistivity Factor-Porosity Relationship of Some Assumed Pore Geometries. Paper C presented at the SPWLA Symposium on Logging, Houston, Texas, 16–18 May.
Waxman, W.H. and Smits, L.J.M. 1968. Electrical Conductivities in Oil-Bearing Sands. SPE J. 8: 107–122.
Winsauer, W.O., Shearin Jr., H.M., Masson, P.H. et al. 1952. Resistivity of Brine-Saturated Sands in Relation to Pore Geometry. AAPG Bull. 36: 253–277.
Woodhouse, R. and Warner Jr., H.R. 2004. Improved Log Analysis in Shaly Sandstones—Based on and Hydrocarbon Pore Volume Routine Measurements of Preserved Cores Cut in Oil-Based Mud. Petrophysics 45 (3): 281–295.
Wyllie, M.R.J. and Rose, W. 1950. Some Theoretical Considerations Related to the Quantitative Evaluation of the Physical Characteristics of Reservoir Rock From Electric Log Data. J. Pet Tech 2: 105.