Compaction-induced production decline is treated in the framework of open-system geomechanics of petroleum reservoir as of a system with variable mass.Variables of state are chosen as mass and strain (undrained variables) whereas pore pressure and porosity are considered as functions of state, and are expressed in terms of state variables. The model accounts for pressure depletion and permeability degradation due to compaction. Evolution of production rate, reservoir pressure and porosity is formulated via approximate "bulk" production equation. Production decline vs. time is found to be either power-like (on the earlier stage) or exponential. Power-like decline is linked to permeability-porosity dependence. This approach provides explicit dependence of production rate and decline time on such rock parameters as fluid and bulk compressibilities.
As pointed out by Cleary (1978) and others, temporal response of fluid-saturated porous medium can include at least three characteristic regimes. Generally, at a very fast loading rate, porous medium exhibits a stiffer response in the elastic range and lower ultimate load capacity, whereas a very slow loading rate, the excess pore pressure is adequately dissipated and the solution converges to the conventional uncoupled (i.e. without solid-fluid coupling) non-linear mechanics solution. It can be observed that there is a smooth but non-linear transition in ultimate load capacity from slow loading rate to the fast loading rate. However, there is no yet analytical solution for transient behavior during elasto-plastic compaction. One more transient time in petroleum reservoirs is time of production decline. Despite many empirical scenarios of decline rates in petroleum reservoirs, substantiated theoretical models of decline rate were predominantly developed for gas- and water-drive depletion (Fetkovitch et al, 1996). At the same time, it is known that compaction drive mechanism may account for significant part of total recovery (Merle et al, 1976; Dake, 2002). Compaction-induced depletion time is qualitatively different from pseudo-steady state time, tpss=(φμCtA/k), which is well known in reservoir engineering (μ=viscosity, k=permeability, φ=porosity, Ct=total reservoir rock/fluid compressibility A=flow area). The physical difference between these two characteristic times is that the pseudosteady state time is the time of reaching steady-state flow into wellbore inside quasi-constant pressure (far-field) boundary which can be imposed either by natural limits such as faults or by neighboring wells. The depletion time is the characteristic time of variation of the pressure at those boundaries. The assumption is that pseudo-steady state time is smaller than characteristic time of variation of the pressure at those boundaries. Because compaction-drive-induced production is due to mechanical interaction between reservoir and country rock, it significantly depends on rock parameters. It is important to understand how rock properties measurement, carried out in laboratory experiments, can be used in prediction of production decline in compaction-drive-petroleum reservoirs.
Petroleum reservoirs present an example of open systems, which exchange mass with exterior.
Variation of pressure under variation of stress.
