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Summary During the production life cycle of a reservoir, absolute permeability can change in response to an increase in the net effective stress. This paper focuses on stress-dependent permeability in unconsolidated, high-porosity sand reservoirs (offshore turbidites) and moderate- to low-porosity consolidated reservoirs, including tight-gas sands. Specifically we address fundamental controls on stress-dependent permeability, rock-based log modeling of stress-dependent permeability in cored and noncored wells, and, finally, implications for production rates and recovery volume based on data from reservoir simulation. Results demonstrate that the rate of reduction in permeability with an increase in stress is a function of the pore geometry in both consolidated and unconsolidated sand reservoirs. A practical, rapid, and cost-efficient methodology is presented to improve evaluation and enhance the productivity and management of stress-dependent reservoirs. Several cases are presented of a conceptual, single-well model of an overpressured, tight-gas sandstone reservoir that include stress-dependent permeability. Results of simulation analyses for varying conditions of reservoir stress demonstrate the importance of stress-dependent permeability in more accurate forecasting of reserves and predicting optimum wellbore-producing conditions. Introduction During the production life cycle of a reservoir, absolute permeability at any given location may change in response to localized changes in stress within the rock pore system owing to depressurization during production. Reservoir depressurization can increase the net effective reservoir stress (overburden pressure minus pore pressure) which can alter the detailed pore geometry of the reservoir rock, specifically the shape and the dimensions of the pore bodies and the pore throats.1 The rate of permeability decline with increasing stress is highly variable. This fact is well documented in the petroleum engineering and rock mechanics literature.2–19 The change of permeability with increasing stress is exponential, and the greatest variation of permeability occurs dominantly at low pressure (0 to 3,000 psi).2-4,12 In this low-pressure range, rocks can lose between 10 and 99% of their original permeability. Because of the high degree of variability inherent in this exponential relationship, it is difficult to predict permeability from a knowledge of pressure. From a practical viewpoint, this variability results in significant variations in reservoir characteristics related to permeability, such as abandonment pressure, even within a single reservoir. Production problems related to stress-dependent permeability occur in fractured and nonfractured reservoirs, in unconsolidated reservoirs with high-matrix porosity and permeability, and in consolidated reservoirs that are characterized by low-matrix porosity and permeability. Previous works have presented multiple, often contrasting, reasons to explain the complex and variable relationship between permeability and stress, including pore shape and sorting,1,5,11 lithology (specifically the volume of shale),3 rock mineralogy,13 initial permeability value,6,8,12 and various aspects of pore structure.14,15 While all of these characteristics may, to some degree, influence permeability at stress on a case-by-case basis, they do not explain the fundamental reasons for the variability inherent in the relationship. Further, most of these studies are based on analysis of a relatively small number of samples (<20). This review of previous work supports the recent contention that "in stress-dependent reservoirs that are depressurizing, there is a need to understand and to model dynamic permeability change such as pressure-dependent permeability."20 A primary objective of this paper is to develop an understanding of dynamic permeability change as a function of stress in nonfractured, unconsolidated, and consolidated sandstone reservoirs. The specific objectives of this work are:To determine fundamental controls on stress-dependent permeability, as identified through analysis of core samples.To develop a methodology that allows for prediction of permeability at any value of reservoir stress.To document the implications of stress-sensitive permeability for production (rate and total volume) and reserve computations, based on reservoir simulation. The results of this work allow us:To present a unified theory for the relationship between permeability and stress in matrix pore systems.To demonstrate that permeability can be predicted for any given value of stress.To present evidence from reservoir simulation that production and reserve estimates are significantly improved when permeability is considered as a dynamic variable. Physical Compaction of Sandstones Stress-related physical changes that affect relationships among individual sand grains are well documented in the geological literature21,22 and include the following areas. Grain Slippage and Rotation. The physical movement of sand grains in relation to one another occurs most commonly and most significantly at low stress levels, when grains are loosely packed and unconsolidated. This is the first response of unconsolidated sediments to increasing stress and is common in rocks characterized by loose packing and concomitantly high values of porosity (generally >25 to 50%). Changes in Grain Shape. Ductile "soft" sand grains, such as micas, shale fragments, and weathered grains, alter their shape in response to increased levels of stress and the resulting pressure exerted by surrounding nonductile grains (such as quartz). Changes in grain shape can occur over a wide range of stress values, depending on the relative ductility of the grains. Mica and shale fragments, for example, are highly ductile and deform readily at low values of stress. Other sand grains, such as multimineralic rock fragments, require higher stress levels for deformation. Grain Fracturing. Brittle sand grains, such as feldspars and occasionally quartz, can fracture at high stress levels. Intragrain fractures occur most commonly in grains characterized by cleavage (feldspar) and multimineralic grains with internal boundaries between different mineral components (rock fragments). Grains that lack cleavage (such as quartz) fracture only at very high levels of stress.

During the production lifecycle of a reservoir, absolute permeability at any given location may change in response to an increase in the net effective stress and a concomitant decrease in the value of in-situ permeability. This paper focuses stress dependent permeability in unconsolidated, high porosity sand reservoirs (offshore turbidites) and consolidated reservoirs (tight gas sands). Specifically we address:fundamental controls on stress dependent permeability, as identified through analysis of core samples,rock-based log modeling of stress dependent permeability in cored and non-cored wells, andimplications for production based on data from reservoir simulation. This work reveals a fundamental difference between the stress dependent permeability behavior of unconsolidated and consolidated sand reservoirs. In unconsolidated sand reservoirs, the greatest permeability reduction with stress occurs in the sands with the highest values of porosity and permeability. In cemented sandstone reservoirs, the opposite is the case: most of the reduction in permeability occurs in sandstones with the lowest values of porosity and permeability. This difference in behavior between unconsolidated and consolidated reservoir sands is controlled by pore geometry. We present a practical, rapid and cost efficient methodology to improve evaluation and enhance the productivity and management of stress-dependent reservoirs. The method is based fundamentally on the identification of "Rock Types" (intervals of rock with unique pore geometry). Thin section evaluation, together with integrated nuclear magnetic resonance and SEM-based image analysis of core material is used to quantitatively identify various Rock Types. Rock Type data is integrated with measurements of permeability at various levels of stress. Results demonstrate that, within a particular field, some Rock Types lose <10% of original permeability while others lose >90% of original permeability as a function of increasing stress. Rock Types are then identified using routine suites of wireline logs, allowing for field-wide determination of the net footage and distribution of each Rock Type in all wells and the foot-by-foot calculation of permeability at any value of net effective stress. Based on geological input, the reservoirs are divided into flow units (hydrodynamically continuous layers) and grid blocks for simulation. Several cases are presented of a conceptual, single well model of an overpressured, tight gas sandstone reservoir that include stress dependent permeability. Results of simulation analyses for varying conditions of reservoir stress demonstrate the importance of stress dependent permeability in more accurate forecasting of reserves and predicting optimum well bore producing conditions.

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