A Method for Full-Range Young's Modulus Correction
- Wyatt Jackson Canady (Halliburton)
- Document ID
- Society of Petroleum Engineers
- North American Unconventional Gas Conference and Exhibition, 14-16 June, The Woodlands, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2011. Society of Petroleum Engineers
- 5.6.2 Core Analysis, 7.5.1 Ethics, 5.6.1 Open hole/cased hole log analysis, 5.5.2 Core Analysis, 1.14 Casing and Cementing, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 1.2.3 Rock properties
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Deriving rock moduli from acoustic velocities is the most common method for evaluating formation mechanical strength in the petroleum industry. While common, the accuracy of the method is hindered by the difficulty correcting the moduli, as measured by the acoustic logging tool to values representative of the actual moduli of the rock.
Analysts generally rely on simple empirical equations to provide the estimates for the corrections that must be made. These empirical equations are usually derived from wireline logs or from core analysis of samples taken from the formation of interest. The usefulness and accuracy of this method of modulus correction is hampered by the fact that the dynamic-to-static conversions are strongly non-linear. The method is also hampered by the rather narrow range of values available in a particular empirical function.
This paper presents an empirical method featuring a simple, single equation that provides estimates of static Young's modulus across the whole-range stresses and rock strengths that might be encountered in a reservoir.
Four regimes of formation consolidation define how acoustic velocities relate to rock strength:
Unconsolidated or Weakly Consolidated Formations. In these zones, the velocities of the propagating acoustic wave are dominated by the propagation velocity of its constituent liquids and solids rather than the mechanical stiffness of the rock itself. In these rocks, the measured modulus can be an order of magnitude greater than its actual modulus.
Consolidated Formations—Hetrogenuous Regime (Confining Pressures up to 2-3 KPa). Rocks in this regime generally have their constituent grains either welded together at their contact points or are bound by one or more cementing minerals. Porosities tend to be in the higher range (15-30%, depending on sorting). The cementation may be hetrogenuous, varying place to place in the formation, and, most significantly, may contain many "penny shaped?? fractures or microcracks (Simmons 1965) oriented either to the current stress field or else to a field present at the time of the fracture's creation. The presence of microcracks significantly reduces both the measured modulus and the rock strength. In this regime, actual rock strength may be on the order of 50% of its measured value. Rock mechanical property measurements in this regime are dominated by rock porosity, micro-fracture properties, population, and, to a minor extent, the moduli of the constituent minerals.
Consolidated Formations—Linear Regime. As burial depths increase, cracks begin to close up and are completely closed when the confining stress exceeds 2-3 KPa. Rocks in this regime generally respond according to Hooke's law and are said to be responding in a "linear?? manner.
Of the four regimes, the measured rock mechanical properties most faithfully represent the actual rock properties and are often referred to as the "intrinsic?? properties (Brace 1965). Closure of cracks under compressive stress tends to increase the effect elastic moduli of rocks (Mavko, Mukerji, and Dvorkin 2009a). Consolidated formations where acoustic velocity is primarily influenced by materials moduli and porosity. In this regime, the actual strength is often 70-90% of the measured value.
Consolidated Formations—Non-Linear Regime. At greater depths of burial, rocks cease responding to the stresses on it in a linear way. Porosity has largely been closed; the average distance between mineral molecules is approaching that of the distant between molecules of mineral in its crystal form. Some minerals have become chemically unstable and may undergo a chemical change. At these conditions, the velocity of the acoustic wave begins to be dominated by the tectonic stress.
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