Multiphase flow in tight formations

Abstract

Given the substantial growth of the shale industry over the last decade, understanding flow in confined spaces will play a primordial role in the future of the upstream petroleum sector. Most compositional simulators are designed for standard (unconfined) reservoirs. Additional physical phenomena occurring in confined spaces such as capillary pressure, diffusion and adsorption are not taken into account. Moreover, most studies conducted on this topic only focus on shale gas, without regards to the presence of a liquid phase. This thesis focuses on the effects of capillary pressure on a multiphase flow and describes the modified production profiles.
Recent studies have shown that elevated capillary pressure in confined spaces modifies the phase behavior of the hydrocarbon mixture, namely causing a reduction of the bubble point, which in turn affects the oil density and viscosity. These modifications will alter well produc- tion dynamics.
Standard compositional simulators couple a mass balance equation with conservation laws and thermodynamic equilibrium, which comes in the form of a nonlinear constraint describ- ing the equality of chemical potentials. This research work replaces the last condition with a modified K-value constraint. The K-value is simply the ratio of a component’s composition in its vapor phase to its liquid phase. The latter is specific to the pressure, temperature and the hydrocarbon sample’s molar composition; and is derived from equations of state (EOS) which are employed to describe the phase behavior of a system. Capillarity is introduced in the K-value by adding the Parachor model, which determines the interfacial tension and the Laplace equation to the EOS derivation.
The modified K-values are incorporated into Stanford’s Automatic Differentiation General Purpose Research Simulator (ADGPRS) based on a fully implicit approach. Other necessary modifications were made to include the effects of heterogeneity in the system. Simulations were ran in both simple one-dimensional reservoirs and more complex fractured models de- picting fractured shale reservoirs and compared to the production results generated by stan- dard compositional model.