Gas flow in mudrocks depends on the complex, multiscale connectivity among nanopores, microfractures and macrofractures. Hydraulic fractures stimulate reservoir volume near a horizontal well and create other fractures at all scales. Elsewhere, we have described the Stimulated Reservoir Volume (SRV) as a fractal with its own fracture network that accesses the organic-rich matrix. In the practically impermeable mudrock, the known volume of fracturing water (and proppant) must create an equal volume of fractures at all scales. Thus, we can constrain the physical structure of SRV, i.e., the number of macrofractures and surface area created after hydrofracturing. Nanopores in the organic matrix act as the source of almost all gas. Here, we present a comprehensive, physics-based microscale model of (a) the increased permeability to gas flow in a mudrock and (b) the effects of smallest nanopores on well production rates and gas storage capacity in this mudrock.
We introduce a physical quantity, the microscale source term, s to study numerically the interactions between microfractures and nanopores. Interactions of this term with the characteristic permeability of multiscale fractures, kf , defines the productivity and economic viability of gas wells. Most researchers explain enhancements of gas production from shales by invoking slip flow in the nanopores at high Knudsen number, Kn. However, molecular gas dynamics simulations, experimental results in carbon nanotubes, and the calculated Klinkenberg and Browns slippage factors discredit gas slip at high subsurface pressures (P>3000 psi) and with rough pore surfaces. We propose a model of flow of the high-pressure shale gas, and explain the increased permeability in mudrocks without slip flow and Knudsen diffusion. We predict enhanced gas flow at the outlet of a single micropore, caused by an additional gas influx from the numerous nanopores connected to that micropore. We then extend the single micropore model to a network of micropores, each fed by many nanopores. This network idealizes a microfracture network in contact with organic matrix in a mudrock. The overall permeability increase depends on the nanopore radii, flow rate in the microcapillaries, and the persistence of pressure difference between the nanopores and microcapillaries. A no-flow-reversal condition for the micropore network imposes limits on the nanopore radii and pressure differentials along the nanopores.
As the average radius of the nanopores feeding the micropore network increases, the ratio of the volumetric flow rates in the micropores, Qout/Qin, increases faster, because the additional gas influx depends on 4th power of the nanopore radius. An increase of the flow rate into a micropore network reduces the effect of the nanopore influx in the system. Qout/Qin is also highly sensitive to the difference between the pressure in the kerogen and that in the micropores. Isolated nanopores in the organic matrix can feed a micropore for only a few milliseconds, demonstrating that the kerogen matrix has a well-connected nanopore network. A small value of the microscale source term, s, gives additional numerical justification for the concept. The effect of the smallest nanopores with the radii ¡ 1nm on the gas storage capacity is highlighted. A mere 5% of such nanopores can maintain a long tail of slow production rate from the mudrock reservoirs.
Our analytical solution captures the experimentally observed enhanced flow rate in mudrocks. It presents a numerical justification for a well-connected nanopore network in the organic matrix, and the impact of the smallest nanopores on the long-term production rate from a horizontal well.