Laboratory Investigation to Assess the Impact of Pore Pressure Decline and Confining Stress on Shale Gas Reservoirs

Four core samples of outcrop type shale from Mancos, Marcellus, Eagle Ford, and Barnett shale formations were studied to evaluate the productivity performance and reservoir connectivity at elevated temperature and pressure. These laboratory experiments were conducted using hydrostatic permeability system with helium as test gas primarily to avoid potential significant effects of adsorption and/or associated swelling that might affect permeability. It was found that the permeability reduction was observed due to increasing confining stress and permeability improvement was observed related to Knudsen flow and molecular slippage related to Klinkenberg effect. Through the effective permeability of rock is improved at lower pore pressures, as 1000 psi. The effective stress with relatively high flow path was identified, as 100-200 nm, in Eagle Ford core sample. However other three samples showed low marginal flow paths in low connectivity.


INTRODUCTION
and estimates based on clay content and pore-size distribution [3][4].A method developed for profiling permeability along a shale core sample, which was calibrated using pulse permeability measurements. As gas is produced and reservoir pressure declines, two different processes alter the permeability of the rock.
These processes can be categorized as stress effects and flow regime effects. The variation of permeability with effective stress has been studied fairly extensively for sandstones and carbonates [5][6][7]. This is sometimes referred to as slippage flow, in reference to molecules slipping past one another. [8] A common characteristic of all shale gas reservoirs is their extremely low intrinsic permeability. To produce gas at any significant rate, the rock must first be hydraulically fractured to create additional surface area and provide greater reservoir contact. Initially researchers [1][2] have studied the sensitivity of permeability to confining pressure at a single pore pressure. In later work intact plug permeability over a wide range of both pore and confining pressures was studied. Then researchers developed permeabilityporosity relationship for mudstones using a large data set consisting of both measured permeability values

BACKGROUND STUDY ON STRESS DEPENDENT PERMEABILITY
Stress-Dependent Permeability: Many physical properties of porous rocks (permeability, volumetric strain, porosity) vary as a function of confining pressure and pore pressure according to an effective pressure. This is known as Terzaghi's principle, defined as follows: Where C p is the confining pressure and P p is the pore pressure. When describing how volumetric strain varies with effective stress, the appropriate coefficient is defined as the Biot coefficient, α [9][10][11][12] and effective stress law defined as confining pressure and pore pressure combination identify the permeability of the rock through effective stress law as below: Where σeff is true effective stress and χ is the effective stress coefficient for permeability. Thus, χ determines the relative sensitivity of permeability to changes in confining pressure and pore pressure. Most rocks have been shown to have χ < 1, indicating that the rock is more sensitive to changes in confining pressure than pore pressure. However, a handful of studies of clay-bearing sandstones have found χ to be greater than 1, implying that changes in pore pressure have a larger impact on permeability than confining pressure [11][12]. In contrast to observations of χ > 1 in high-clay sandstones, [13]

FLOW REGIME EFFECTS ON PERMEABILITY
Expanding on the introduction above, flow in gas shale (and similarly tight rocks) is described by a combination of transport mechanisms acting at different scales [15][16]. It is common to denote transitions between these various flow regimes using the dimensionless Knudsen number, defined as: Where d P is the diameter of the pore and λ is the mean free path of a molecule moving through it, calculated as: Where KBoltz is the Boltzmann constant, T is the temperature, dm is the molecular diameter, and P is the pressure. The molecular mean free path becomes larger as pressure (gas density) decreases. The relationship between the Knudsen number, pore width, and pressure is displayed in Figs. 1-2.Flow in gas shale's lies mostly within the Darcy, slip, and transition flow regimes within the petroleum engineering literature, Klinkenberg[8] was the first recognize this [8].

XPERIMENTALMETHODOLOGY
All measurements were made using helium as the test gas. This was done primarily to avoid the potentially significant effects of adsorption and/or associated swelling that might impact permeability [17][18][19]   was pre-stressed for a period of 60-72 hrs at an effective stress 25% greater than the experiment design pressure.
A schematic of the hydrostatic permeability system used for plug permeability measurements is shown in Fig. 2.
The sample is wedged between two floating plugs attached to pore lines inside a Viton jacket. Confining pressure is controlled manually using the high-pressure generator shown on the far right in Fig. 3.
Confining pressure is measured using a Heise DXD pressure transducer accurate to 0.1% up to 10,000 psi Where, w is slit width, c is an empirical constant, μ is viscosity, R is universal gas constant, T is temperature, M is molar mass, and Kb is the Klinkenberg constant.

Sample Description
In

Results and Discussion
Plug permeability measurements were conducted for all six samples under study. Permeability was measured at pore pressures from 1000-4000 psi ( to be a very minor crack oriented along its axis, which seems to have enhanced permeability. Finally, notice that for each sample, permeability varies as a function of simple effective stress (C p -P p ) in a similar way, allowing for a single function to be fit to the whole data set. The data for each rock were fit to a unique permeability effective stress law as described previously. These results are presented in Fig. 5.
In all cases, χ was found to be less than 1, indicating that the rocks are more sensitive to changes in confining pressure than changes in pore pressure. Noting that permeability as a function of modified effective stress forms a trend enables us to attribute all permeability variation observed (for Pp> 1000 psi (6.9 MPa) thus far) to effective stress effects.
As previously mentioned, three of the six samples were chosen for further characterization at lower pore pressures This contrasts with the higher permeability Eagle Ford 2 sample, which has a lower K b and, thus, a smaller overall contribution of slip flow to total flow. The overall contribution of slip flow to total flow in these samples will be further considered in the discussion section.

CONCLUSION
A study has been conducted to impact of pore pressure decline and confining stress on shale gas reservoirs. The main conclusions in this paper are as follows: (i) It is observed through laboratory experiments on shale core samples examining the effects of confining stress and pore pressure of four out crop core samples were more sensitive changes in confining pressure than changes in pore pressure.
(ii) In addition to effective stress, permeability of the rock is significantly enhanced at a very low pore pressures (< 500 psi (< 3.4 MPa)) because of slippage effects.
(iii) Increasing slip flow at low pore pressures may help to relatively long and flat production tails observed in some shale plays in Eagle Ford.