Injection of water into chalk hydrocarbon reservoirs has led to mechanical yield and failure. Laboratory experiments on chalk samples correspondingly show that the mechanical properties of porous chalk depend on pore fluid and temperature. In case of water-saturated samples, the concentration and nature of dissolved salts have an effect. Water has a significant softening effect on elastic properties of chalk as calculated from wave data, and the softening increases with increasing critical frequency as defined by Biot. The critical frequency is the highest frequency where elastic wave propagation is controlled by solid-fluid friction. The reference frequency is thus a measure of this friction, and we propose that the fluid effect on mechanical properties of chalk may be the result of liquid-solid friction. We reviewed 622 published experiments on mechanical properties of porouschalk. The data include chalk samples that were tested at temperatures from [Formula: see text] with the following pore fluids: fresh water, synthetic seawater, glycol, and oil of varying viscosity. The critical frequency is calculated for each experiment. For each specimen, we calculate the thickness to the slipping plane outside the Stern layer on the pore surface. For electrolytes, the thickness of this layer is calculated based on Debye-Hückel theory. The layer reduces the porosity available for fluid flow. We find that the Biot critical frequency based on pore scale data can be used to explain effects on the macro scale. We find that the effective yield stress and also the effective stress of failure in tension as well as in compression are log-linearly related to log reference frequency. This opens the possibility to predict yield and failure under reservoir conditions from mechanical tests made under laboratory conditions. It also opens the possibility of predicting the effects of water flooding on chalk stability.

We propose a combination of Biot's equations for effective stress and the expression for shear failure in a rock to obtain an expression for minimum pore pressure in a stable vertical well bore. We show that a Biot's coefficient calculated from logging data in the Hejre Field, North Sea, is significantly different from 1. The log‐derived Biot's coefficient is above 0.8 in the Shetland Chalk Group and in the Tyne Group, and 0.6–0.8 in the Heno Sandstone Formation. We show that the effective vertical and horizontal stresses obtained using the log‐derived Biot's coefficient result in a drilling window for a vertical well larger than if approximating Biot's coefficient by 1. The estimation of the Biot's coefficient is straightforward in formations with a stiff frame, whereas in formations such as shales, caution has to be taken. We discuss the consequence of assumptions made on the mineral composition of shales as unphysical results could be obtained when choosing inappropriate mineral moduli.

Development of high-pressure, high-temperature (HPHT) petroleum reservoirs situated at depths exceeding 5 km and in situ temperature of 170 °C increases the demand for theories and supporting experimental data capable of describing temperature effects on rock stiffness. With the intention of experimentally investigating temperature effects on stiffness properties, we investigated three sandstones from the deep North Sea Basin. As the North Sea Basin is presently undergoing substantial subsidence, we assumed that studied reservoir sandstones have never experienced higher temperature than in situ. We measured ultrasonic velocities in a low- and high-stress regime, and used mass density and stress–strain curves to derive, respectively, dynamic and static elastic moduli. We found that in both regimes, the dry sandstones stiffens with increasing testing temperature and assign expansion of minerals as a controlling mechanism. In the low-stress regime with only partial microcrack closure, we propose closure of microcracks as the stiffening mechanism. In the high-stress regime, we propose that thermal expansion of constituting minerals increases stress in grain contacts when the applied stress is high enough for conversion of thermal strain to thermal stress, thus leading to higher stiffness at in situ temperature. We then applied an extension of Biot’s effective stress equation including a non-isothermal term from thermoelastic theory and explain test results by adding boundary conditions to the equations.

No abstract

A fluid effect towards higher strengths for oil saturated chalk compared to water saturated chalk has previously been identified and labeled the water weakening phenomenon, but has not been further characterized physically until now. The hypothesis of this paper is that the Biot critical frequency can be used to explain this behavior on the pore scale and be extrapolated to the macroscale failure and pore collapse properties. A large set of previously published laboratory test results on chalk was collected. The data spans three different chalk types which were tested at temperatures from 20°C to 130°C with the following pore fluids besides dry chalk: fresh water, synthetic seawater of different chemical compositions, methanol, glycol, formamide, decane and crude oil of varying viscosity.The Biot critical frequency determines the transition from where an applied sound velocity is dominated by viscous forces to where it is dominated by inertial forces, i.e. when the pore fluid motion lags behind the applied frequency. It is therefore a measure of the internal surface friction between solid and fluid and is interpreted as a friction factor. The Biot critical frequency incorporates the porosity, permeability, fluid density and fluid viscosity, where the latter is highly temperature dependent. All these parameters are usually determined during laboratory tests and the fluid viscosity and density may be found in tabulated references. Besides the fluid effect there is an effect from the applied strain or stress rate on both the strength and yield properties. This phenomenon couples with the critical frequency through the use of a previously published study on the rate dependence.The data show that the Biot critical frequency can be used as a common friction factor and is useful in combining laboratory results. It is also inferred that the observed water weakening phenomenon may be attributed to the friction between solid and fluid. The scope for the applicability of the Biot critical frequency as a friction factor is in analysis of the compaction of chalk fields where the effect of different fluids and temperatures is relevant. IntroductionThe weakening effect of water in chalk is significant for North Sea reservoir subsidence and several experimental studies have focused on the subject. This paper reviews the results from these test series in order to match the theoretical considerations and find the governing physical properties. Gutierrez et al. (2000) found higher friction for oil saturated chalk (42˚) than water saturated (38˚) in simple tilt tests on a large test series on chalk samples submerged in either oil or water. The chalk studied is Lägerdorf chalk from a quarry in northwest Germany. While the solid-solid friction is one location for the friction forces in the submerged simple tilt test, the fluid-solid friction should thus be considered as well. This causes our focus on fluid-solid friction as a possible mechanism for weakening when assuming no alteration of the chalk surface and consequently no change i...