Modeling Water Leak-off Behavior in Hydraulically Fractured Gas Shale under Multi-mechanism Dominated Conditions

Abstract

Fracturing-fluid leak-off in fractured gas shale is a complex process involving multiple pore/fluid transports and interactions. However, water leak-off behavior has not been modeled comprehensively by considering the multi-pores and multi-mechanisms in shale with existing simulators. In this paper, we present the development of a comprehensive multi-mechanistic, multi-porosity, and multi-permeability water/gas flow model that uses experimentally determined formation properties to simulate the fracturing-fluid leak-off of hydraulically fractured shale gas wells. The multi-mechanistic model takes into account water transport driven by hydraulic convection, capillary and osmosis, gas transport caused by hydraulic convection, and salt ion transport caused by advection and diffusion. The multi-porosity includes hydraulic fracture millipores, organic nanopores, clay nanopores, and other inorganic micropores. The multi-permeability model accounts for all the important processes in shale system, including gas adsorption on the organics’ surface, multi-mechanistic clay/other inorganic mineral mass transfer, inorganic mineral/hydraulic fracture mass transfer, and injection from a hydraulically fractured wellbore. The dynamic water saturation and pressure profiles within clay and other inorganic matrices are compared, revealing the leak-off behavior of water in rock media with different physicochemical properties. In sensitivity analyses, cases with different clay membrane efficiency, volume proportion of source rock, connate water salinity, and saturation are considered. The impacts of shale properties on water fluxes through wellbore, hydraulic fracture and matrix, and the total injection and leak-off volumes of the well during the treatment of hydraulic fracturing are investigated. Results show that physicochemical properties in both organic and inorganic matrices affect the water leak-off behavior.

Appendix 1

This appendix presents the determination basis of the three shape factors involved in the proposed model.

$\textcircled {1}$ Shape factor between the hydraulic fracture and other inorganic matrix, $\alpha _1$

Denoting that the pressure at the surface of hydraulic fracture is p, then within an element with dimensions of $\Delta x$, $\Delta y$, $\Delta z$, the water-phase flux from hydraulic fracture to the surface can be expressed as

$$\begin{aligned} q_\mathrm{w}^{Fs} =\frac{\rho _\mathrm{w} k^{F}k_{\mathrm{rw}}^F \Delta x\Delta z}{\eta _\mathrm{w} \frac{\Delta y}{2}}\left( {p_\mathrm{w}^F -p} \right) \end{aligned}$$

(38)

And the water-phase flux from the surface to other inorganic matrix within the element can be expressed as

$$\begin{aligned} q_\mathrm{w}^{sm1} =\frac{\rho _\mathrm{w} k^{m1}k_{\mathrm{rw}}^{m1} \Delta x\Delta z}{\eta _\mathrm{w} \frac{\Delta y}{2}}\left( {p-p_\mathrm{w}^{m1} } \right) \end{aligned}$$

(39)

According to Eq. (2), the water flux between the hydraulic fracture and other inorganic matrix within the element is defined as

$$\begin{aligned} q_\mathrm{w}^{Fm1} =\frac{\alpha _1 \rho _\mathrm{w} k^{F}k_{\mathrm{rw}}^F }{\eta _\mathrm{w} }\left( {p_\mathrm{w}^F -p_\mathrm{w}^{m1} } \right) \end{aligned}$$

(40)

On the basis of the continuity of flux, $q_\mathrm{w}^{Fs} =q_\mathrm{w}^{sm1} =q_\mathrm{w}^{Fm1}$. Combining these three equations, the shape factor between hydraulic fracture and other inorganic matrix can be deduced as

$$\begin{aligned} \alpha _1 =\frac{2}{\left( {1+\frac{k^{F}k_{\mathrm{rw}}^F }{k^{m1}k_{\mathrm{rw}}^{m1} }} \right) \Delta y^{2}} \end{aligned}$$

(41)

$\textcircled {2}$ Shape factor between the clay and other inorganic matrix, $\alpha _2$

The Kazemi model is used to describe the flow between clay and other inorganic matrix (Kazemi et al. 1976). The shape factor is related to the matrix block size:

$$\begin{aligned} \alpha _2 =4\left( {\frac{1}{l_x^2 }+\frac{1}{l_y^2 }+\frac{1}{l_z^2 }} \right) \end{aligned}$$

(42)

where $l_x$, $l_y$, $l_z$ are typical X-, Y-, and Z-dimensions of the matrix blocks.

$\textcircled {3}$ Shape factor between the wellbore and the hydraulic fracture, $\alpha _3$

The fluid from wellbore enters hydraulic fracture in the form of radial flow, and the injection rate is defined as (Bian et al. 2012)

$$\begin{aligned} \hat{{q}}_\mathrm{w} =\frac{2\pi \rho _\mathrm{w} \Delta yk^{F}k_{\mathrm{rw}}^F }{\eta _\mathrm{w} B_\mathrm{w} \ln \left( {\frac{r_e }{r_\mathrm{w} }} \right) \Delta x\Delta y\Delta z}\left( {p_{wf} -p_\mathrm{w}^F } \right) \end{aligned}$$

(43)

and

$$\begin{aligned} r_e =0.14\left( {\Delta x^{2}+\Delta z^{2}} \right) ^{1/2} \end{aligned}$$

(44)

According to Eq. (28), the inner boundary condition is

(45)

Thus, $\alpha _3$ is expressed as

$$\begin{aligned} \alpha _3 =\frac{2\pi }{\ln \left( {\frac{r_e }{r_\mathrm{w} }} \right) \Delta x\Delta z} \end{aligned}$$

(46)