A Simple Molecular Kerogen Pore-Network Model for Transport Simulation in Condensed Phase Digital Source-Rock Physics

Abstract

Transport of small hydrocarbon molecules inside organic nanopores is of great interest in the oil and gas production from source rocks such as shale. Because of the small pore sizes, it is difficult to measure transport directly in the laboratory but require alternative approaches such as molecular simulation. Existing molecular models use nanoscale capillaries and do not describe the exact geometric structure of the organic nanopores in real source rocks, especially for mesopores (2–50 nm in diameter, defined by IUPAC), which widely exist in organic solids and are crucial for fluid transport in the source rocks. Here we present a new method to simplify the existing molecular kerogen models. Pore structures can be built to reflect the exact porous structure of hydrocarbon-bearing kerogen pores for fluid transport without losing accuracy. The kerogen pore-network skeleton can be populated based on 3D digital segments obtained from high-resolution TEM tomographs, combining with other material properties, including the elemental composition and density of the organic solid. The basic idea of the simplified molecular model is to ignore the detailed chemical information of the kerogen molecules and to use a uniform “representative” atom to replace all various atom types, while maintaining the geometric structure intact. To test the transport simulation accuracy using molecular dynamics for this simplified model, sample pore-network structures are populated with both the existing exact molecular model and the simplified model, and the permeability of reservoir fluid flowing through the media is simulated and compared. Specifically, simple reservoir fluids are charged into the space of the 3D porous networks with grand canonical Monte Carlo simulation at given subsurface condition; then, the fluids are driven by an external force field to flow through the network using non-equilibrium molecular dynamics simulation. The simplified kerogen model can be easily applied to larger organic porous material samples to reduce spatial uncertainty, provided enough computational resources.

Appendix

1.1 Force Field Parameters

In the flow simulation, OPLS-AA force field is used to describe fluid molecules, with bond, angles, dihedrals described in the equation forms below (Tables 2 and 3).

Table 2 Force field parameters used to calculate average parameters for the simplified molecular model

Table 3 Other force field parameters used in molecular simulations (Martin and Siepmann 1998, 1999; Makrodimitris et al. 2001)

$$ E = K\left( {r - r_{0} } \right)^{2} $$

(11)

$$ E = K\left( {\theta - \theta_{0} } \right)^{2} $$

(12)

$$ E = \frac{1}{2}K_{1} \left[ {1 + \cos \left( \phi \right)} \right] + \frac{1}{2}K_{2} \left[ {1 - \cos \left( {2\phi } \right)} \right] + \frac{1}{2}K_{3} \left[ {1 + \cos \left( {3\phi } \right)} \right] + \frac{1}{2}K_{4} \left[ {1 - \cos \left( {4\phi } \right)} \right] $$

(13)

1.2 Basic Information of Kerogen Building Blocks

See Table 4.

Table 4 Statistical information of kerogen building blocks (Ungerer et al. 2015)

1.3 Supplementary Interaction Terms for PCFF, CVFF Force Fields

To validate the simplified molecular model, CVFF and PCFF shall include more interactions to better describe the exact kerogen molecule building block. For CVFF force field, the equivalency table is slightly expanded to accommodate more interaction types; both CVFF and PCFF have included additional bond and angle coefficients based on similar bonds and angles. For dihedrals and improper dihedrals, which are not included in CVFF and PCFF, they are not taken into consideration. These parameters are listed in Tables 5, 6, 7, 8, and 9.

Table 5 Equivalency table for CVFF force fields

Table 6 Supplementary bond coefficients for CVFF

Table 7 Supplementary angle coefficients for CVFF

Table 8 Supplementary bond coefficients for PCFF

Table 9 Supplementary angle coefficients for PCFF