Elementary Pore Network Models Based on Complex Analysis Methods (CAM): Fundamental Insights for Shale Field Development

Ruud Weijermars,Aadi Khanal

doi:10.3390/en12071243

Abstract

This paper presents insights on flow in porous media from a model tool based on complex analysis methods (CAM) that is grid-less and therefore can visualize fluid flow through pores at high resolution. Elementary pore network models were constructed to visualize flow and the corresponding dynamic bottomhole pressure (BHP) profiles in a well at reservoir outflow points. The pore networks provide the flow paths in shale for transferring hydrocarbons to the wellbore. For the base case model, we constructed a single flow path made up of an array of pores and throats of variable diameter. A passive ganglion (tracer) of an incompressible fluid was introduced to demonstrate the deformation of such ganglions when moving through the pores. The simplified micro-flow channel model was then expanded by stacking flow elements vertically and horizontally to create complex flow paths representing a small section of a porous reservoir. With these model elements in place, the flow transition from the porous reservoir fluid to the wellbore was modeled for typical stages in a well life. The dynamic component of the bottomhole pressure (BHP) was modeled not only during production but also during the drilling of a formation (with either balanced, underbalanced or overbalanced wellbore pressure). In a final set of simulations, the movement of an active ganglion (with surface tension) through the pore space was simulated by introducing a dipole element (which resisted deformation during the movement through the pores). Such movement is of special interest in shale, because of the possible delay in the onset of bubble point pressure due to capillarity. Capillary forces may delay the reservoir to reach the bubble point pressure, which postpones the pressure-drop trigger that would lead to an increase of the gas–oil ratio. The calculation of the estimated ultimate recovery (EUR) with an erroneous assumption of an early increase in the gas–oil ratio will result in a lower volume than when the bubble point delay is considered.

Highlights

Pore sizes in shale basins range from a few nm to several μm [1,2,3,4]
The purpose of this study is to apply recently developed algorithms based on complex analysis methods (CAM) to model the particle paths of fluid flowing through a network of pores
The algorithms are implemented to model the flow from a porous reservoir section into the wellbore

Summary

Introduction

Pore sizes in shale basins range from a few nm to several μm [1,2,3,4]. Pore size and pore networks control the porosity of a rock and connectivity between the pores controls the bulk permeability.Pores in shale are so narrow that the already reduced permeability of shale formations is further affected by the flow behavior in the reservoir, deviating from Darcy flow. Pore sizes in shale basins range from a few nm to several μm [1,2,3,4]. Pore size and pore networks control the porosity of a rock and connectivity between the pores controls the bulk permeability. Pores in shale are so narrow that the already reduced permeability of shale formations is further affected by the flow behavior in the reservoir, deviating from Darcy flow. Hydrocarbon reservoir fluids typically have molecular diameters on the order of 1 Angstrom or 0.1 nm. Various conceptual models exist to describe and quantify the behavior of fluids in nano-pores [5]. The effects include so-called molecular size filtration and sievage, which become relevant when the pore diameter drops from 10 to 5 nm [6,7].

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Conclusion