ABSTRACT: Reservoir stress paths estimated from m situ measurements and on the basis of core data are often in apparent disagreement. Using synthetic rocks formed under stress, we show how stress dependent / plastic deformation and core damage may affect the predicted stress paths. Further, consequences of scale ef- fects in fractured reservoirs, and of Biot's a being different from unity, are demonstrated. In order to gain more insight into the response of reservoirs during depletion, the quantity and quality of in situ compaction and stress monitoring data need to be improved.
INTRODUCTION: THE STRESS PATH CONCEPT
By tradition, the oil industry has assumed that reser- voirs compact uniaxially with zero lateral deforma- tion. Recent developments, like in the North Sea Ekofisk (Teufel et al., 1991) and Shearwater (Kenter et al., 1998) as well as other (Addis, 1997) fields, indicate that deviations from this ad hoc stress path exist. The stress path has important implications for reservoir compaction and for the associated field production strategy. There is thus a need for predic- tion of stress path as an up-front exercise as well as an evaluation as a part of reservoir monitoring. The stress path of a depleting reservoir can be de- fined as the rate of change in horizontal stress rs. change in pore pressure; i.e.
[Equation available in full paper] (1)
In case of an elastic, isotropic formation, subject to uniaxial compaction (zero lateral strain), and where the entire weight of the overburden is felt by the reservoir at all times (constant vertical stress throughout production), the stress path is
[Equation available in full paper] (2)
Here a is the Blot coefficient (<1) and v is Pois- son's ratio. If the same reservoir is subject to a uni- axial stress path, then y= a, or if the stress path is isotropic, then ), = 0. Often a parameter describing the change in effective horizontal stress as a result of change in effective vertical stress is used instead; i.e,
[Equation available in full paper] (3)
For the special case of uniaxial compaction, tc is often referred to as Ko. Notice that
[Equation available in full paper] (4)
As pointed out by Addis (1997) the y-parameter estimated from Equation (2) is strictly valid only if the reservoir is reacting passively to the pore pres- sure decline. ff alteration of the local tectonic stress field occurs, then the pore pressure response should rather be estimated from say the Mohr-Coulomb failure criterion. y for normal faulting (the minimum stress perpendic? to the strike of the fault) is
[Equation available in full paper] (5)
Further solutions exist (Addis et al., 1998a), de- pending on boundary conditions, material behavior, and on the surrounding formations. In both cases above (Eqs. 2 and 5), stress arching by the overbur- den is neglected. If this occurs then ¾ should be higher than predicted by Eqs. (2) or (3).