Experimental determination of the effective pressure coefficients for Brazilian limestones and sandstones

Abstract

ABSTRACT. There are numerous efforts to obtain information about saturation and pressure changes due to reservoir production from time-lapse seismic data. In spite of some good examples existing on the literature, there are a lot of approximations behind those studies. Generally, it is assumed that the seismic properties are functions of saturation and differential pressure P d (overburden minus fluid pressure). Actually, the stress that governs the seismic behavior is the effective stress P e f , which is not exactly equal to P d . In fact it is equal to the overburden stress minus n times the fluid pressure. Such coefficient (n) is known as the effective stress coefficient. Sometimes, depending on the circumstances, it might be identified as the Biot-Willis coefficient taking into consideration the bulk modulus of the porous media. In this paper, laboratory results in a tentative to quantify the n values for Brazilian limestones and tight sands will be presented. It is important to point out, that is the first effort to perform this sort of measurements on Brazilian rocks. The results have shown that the mentioned approximations can introduce errors on pressure estimations from time-lapse data even for high porosity rocks.Keywords: effective pressure, porepressure, seismic velocities, Biot-Willis coefficient, 4D seismic. RESUMO.Há vários esforços no sentido de obter informações sobre mudanças de saturação e pressão, devidasà produção dos reservatórios, a partir de dados sísmicos com lapso de tempo. A despeito de alguns bons exemplos existentes na literatura especializada, várias aproximações são feitas para a realização destes estudos. Geralmente,é assumido que as propriedades sísmicas são funções da saturação e da pressão diferencial P d (pressão de soterramento menos pressão de fluido). Na verdade, a tensão que determina o comportamento sísmicoé a tensão efetiva P e f , que nãoé exatamente igual a P d . De fato, estaé igualà tensão de soterramento menos n vezes a pressão de fluido. Tal coeficiente né conhecido como coeficiente de tensão efetiva. Eventualmente, a depender das circunstâncias, este pode ser identificado com o coeficiente de Biot-Willis considerando o módulo de compressão volumétrica do meio poroso. Neste trabalho serão apresentados resultados de medidas em laboratório procurando quantificar os valores de n para calcários e arenitos fechados brasileiros.É importante salientar que esteé o primeiro esforço de realização deste tipo de medidas em rochas brasileiras. Os resultados mostram que as aproximações mencionadas podem introduzir erros nas estimativas de pressão a partir de dados de monitoramento sísmico mesmo para rochas muito porosas.Palavras-chave: pressão efetiva, poro-pressão, velocidades sísmicas, coeficiente de Biot-Willis, sísmica 4D.

Porosity and permeability development in compacting chalks during flooding of nonequilibrium brines: Insights from long‐term experiment

“…The Biot coefficient, which relates the pore pressure to the effective stress estimate, is linked to the consolidated area across grain contacts (see, e.g., Nermoen et al [2013] for a discussion). In the case of chalks, with a Biot coefficient on the order of 0.65-1.0 [see, e.g., Vasquez et al, 2009;Alam et al, 2012;[Nermoen et al, 2013;Omdal et al, 2009], this leads to a significant increase in the normal stresses at grain contacts, possibly up to 10-20 times the effective stress. Regardless of which local thermodynamic pressures have relevance for the local chemical potential at the grain contacts-either pore pressure in the lower end or contact stresses in the upper-these spatial stress differences may lead to varied solubility within the porous rocks.…”

The Influence of Rate of Change in Confining and Pore Pressure on Values of the Modulus of Compressibility of the Rock Skeleton and Biot’s Coefficient

“…The aforementioned publications [8][9][10] may be listed as examples (although certainly not exhaustive for the topic), these being core works aimed at giving a precise definition of terminology and research methodology. The following publications are similar in nature: [22], which includes a thorough analysis of the variability of Biot coefficient for various types of sandstone and limestone, and [23], which verified the method for determining Biot coefficient, previously proposed in [24]. Materials published by the American Rock Mechanics Association in 2013 include the work [25], related to phenomena occurring in rock during liquid saturation and pore pressure induction, as well as the paper [26] concerning the influence of the pore pressure on the value of Biot coefficient, and as a result, on the form of the effective pressure rule.…”

Measurements of the Effective Stress Coefficient for Elastic Moduli of Sandstone in Quasi-Static Regime Using Semiconductor Strain Gauges

“…However, despite the similarity in approach to the Gassmann theory, which is well confirmed by numerous experiments (see, e.g., the recent review by Sevostianov [ 30 ]), the effective stress model based on the equivalent homogeneous rock substitution has not found significant support in most published experimental studies, and, in particular, in studies devoted to measuring the effective stress coefficient for elastic moduli or velocities [ 20 , 21 , 22 , 31 ].…”

“…In recent decades, the concepts of the effective stress and effective stress coefficient have been subjects of intensive research of both theoretical (see, e.g., [12][13][14][15][16][17][18]) and experi-Sensors 2024, 24, 1122. https://doi.org/10.3390/s24041122 https://www.mdpi.com/journal/sensors mental natures [7,14,[19][20][21][22][23]. As was demonstrated in a number of studies [16,[24][25][26], all rock properties cannot be described by a single effective stress coefficient, and different values of the coefficient should be introduced for different physical quantities.…”