The Stress-Depletion Response Of Reservoirs
Authors: Addis M.A. 
Published: December 2007

Abstract
The minimum horizontal stress acting in a reservoir at depth is observed to decrease significantly with decreasing reservoir pore pressure. This stress decrease is referred to as the stress- depletion response of the reservoir. It particularly affects the stability of open-hole wellbores in horizontal and multilateral well completions and the onset of sand production, both of which are expected to become more likely with increased production. The stress-depletion response is studied for six reservoirs from different geological environments, all of which show a linear trend. Prediction of the stress-depletion response prior to production is normally performed using a passive basin relationship; this shows poor agreement with the field examples. Consequently, a number of relationships which take account of simple faulting are described and compared with the field responses. The best agreement between the predicted responses and the field data was obtained with using a passive basin relationship or a normal fault based relationship with the inclusion of the Biot coefficient.

Introduction
Lifetime considerations of some well completion types require that the stresses acting in the reservoir before initial production are taken into account in the design stage. If formation pressures decrease during production, the evolution of the stresses with production should also be considered, as stress and pore pressure magnitudes are intrinsically linked.
Stress magnitudes and ratios acting within reservoirs are responsible for defining the fracture gradient around wellbores and borehole stability. Stress magnitudes acting around wellbores and perforations in open-hole (Barefoot) and perforated completions which exceed the rock strength are also the primary mechanism for sand production. Furthermore, the fracture conductivity within naturally fractured reservoirs may potentially be dependent upon the stress magnitudes and ratios.
This paper discusses the decrease in the minimum horizontal stress accompanying production and depletion. The aim of this work is to identify the range of field responses to depletion and to account for the observed changes to enable prediction of the stress-depletion response. The current prediction methods are based on the assumption that the reservoir responds to depletion in a 'passive basin' manner. However, predictions based on this approach show poor agreement with the observed field values. In order to improve the prediction of the stress-depletion response, factors which are likely to affect these values are discussed, including geological structure of six field examples. Alternative theoretical relationships describing the stress-depletion response, which consider faulting, are described and compared with the field responses, with the aim of defining an improved predictive methodology with which to estimate the stress-depletion response of reservoirs prior to production.

Stresses Acting at Depth
The stresses acting within a reservoir can be represented by 3 orthogonal stresses which are normally considered to be orientated vertically and horizontally. This assumption of two horizontal stresses and one vertical stress is valid for flat lying laterally extensive reservoirs. In areas where there is considerable structure, at the foothills of mountain ranges or around salt diapirs, the stresses will be significantly rotated from the vertical and horizontal planes. The vertical stress at any depth is equivalent to the weight of the overlying sediments and rocks. The two horizontal stresses are a combination of the lateral effect of the overburden, the Poisson effect, plus any tectonic stress change, or geometric constraint which results in unequal horizontal stress magnitudes. The pore fluid pressure in the formation also affects the magnitude of horizontal stresses, both in the 'virgin' stress state and during production.
Only the more usual cases of near-vertical and near-horizontal stress orientation will be considered within this discussion, where the minimum stress measured during stress tests is assumed to be oriented in a horizontal direction.
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