Determination of Rock Properties from Logs I

UNCONFINED COMPRESSIVE STRENGTH

The production of sand from hydrocarbon reservoirs can result in various operational and safety issues. In addition to lost production from sand fill and or plugging, solids particles can cause significant erosion to both downhole tubulars and surface facilities.

Predicting the onset of sand production has always been a bit of a dark art requiring not just an understanding of geomechnics but also knowledge of petrophysical and mineralogical issues.

The first step in understanding the potential of failure of a formation is the determination of the rock mechanical properties. If we know how strong the rock is we can determine under what conditions we might expect it to fail. There are a number of mechanical properties that we can assess either by direct measurement from core samples or utilising logging information. The key properties that we are trying to determine are:

Unconfined Compressive Strength (UCS)
Poisson’s Ratio (ν)
Shear Modulus (G) – The Modulus of Rigidity
Young’s Modulus (E) – The Modulus of Elasticity
Bulk Modulus (K) – The Modulus of Compressibility
Biot’s constant

This short post discusses the determination of UCS using sonic logs. The derivation of the other properties will be discussed in the second part of this post.

UCS

The Unconfined Compressive Strength (UCS, also sometimes denoted as C₀ which refers to a zero confinement pressure) is simply the pressure which a sample of the rock can withstand before it fails – see Figure 1. In the oil and gas industry this is usually given in pounds per square inch (psi). Values of rock strength measured this way can very significantly from a few hundred psi for very unconsolidated formations to several thousand psi.

UCS from Logs

As stated earlier, one method of obtaining rock properties is to use well logs in conjunction with mathematical correlations. These can then be calibrated against physical measurements of UCS taken from core samples. The two main logs used for this purpose are the sonic log and the porosity log and there are a significant number of correlations available for each. This article will focus on the use of the sonic log for deriving the formation UCS.

There are a number of correlations available to calculate UCS from sonic logs and just a few of these are listed below.

McNally (1987)

$$C_0$ = 185213 e^{(-0.037*Dt)}$

Modified McNally

$$C_0$ = 838825 e^{(-0.057*Dt)}$

Rahman et al (2008)

$$C_0$ = 40847 e^{(-0.0268*Dt)}$

FORMEL (Raaen et al. 1996)

$$C_0$ = 145 * (140 - (2.1*Dt) +(0.0083*Dt^2))$

Chang et al (2006)

$$C_0$ = 2.05 x 10^9 * Dt^{-3}$

It is confusing to know when looking at these equations which one should be used for a given formation or field. A direct comparison yields some interesting results as shown in Figure 3 which considered values of sonic transit times between 55 and 110 μs/ft.

Figure 3 UCS v Sonic Transit Time for Various Correlations

Clearly at the lower end of the transit time range, there is a wide discrepancy with the various models. Note that a low transit time is equivalent to a high velocity of the sonic wave through the formation. This is an indication of higher density and thus higher rock strength. Rahman, FORMEL and Chang all predict lower values than the McNally and the modified McNally correlations. While this might be conservative on the part of Rahman, FORMEL and Chang, the values of UCS are more aligned with the higher levels observed by the other two correlations.

Between 70 μs/ft and 90 μs/ft there is a close relationship between Rahman, FORMEL and Chang, and above 100 μs/ft the Modified McNally gives a good result.

In the next part in this series of posts I will discuss the use of logs in deriving some of the other rock properties as listed at the start of this post.

Useful Links

https://geoloil.com/computingGeomechanics.php

References

SPE 121972, Rock Strength from Core and Logs: Where We Are and Ways To Go, A. Khahsar et al. 2009.

Z Hamdi et al Oil well compressive strength analysis from sonic
log; a case study. 2019 IOP Conf. Ser.: Mater. Sci. Eng. 495 012077

M. Fakir, M. Ferentinou & S. Misra An Investigation into the Rock Properties Influencing the Strength in Some Granitoid Rocks of KwaZulu-Natal, South Africa. Geotechnical and Geological Engineering, Vol. 35, No. 3

Jean-paul Mouchet & Alan Mitchell Abnormal Pressures While Drilling: Origins, Prediction, Detection, Evaluation (Fundamentals of Exploration & Production), Elf Aquitaine (Amazon UK link)