Study of Scale Dependence of Dispersion Using Higher Order Schemes

Open Access
Connolly, Michael
Graduate Program:
Petroleum and Natural Gas Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 26, 2013
Committee Members:
  • Russell Taylor Johns, Thesis Advisor
  • Turgay Ertekin, Thesis Advisor
  • Li Li, Thesis Advisor
  • dispersion
  • miscible gas flooding
  • TVD
Miscible gas flooding is capable of recovering large volumes of in-situ oil by achieving high displacement efficiency. The efficacy of miscible gas flooding is compromised by hydrodynamic dispersion, which consists of both molecular diffusion and velocity-dependent dispersion. Hydrodynamic dispersion dissipates concentration fronts, causing early breakthrough and weakening the strength of the injected solvent. Dispersion can cause two-phase flow to develop in displacements that are otherwise multi-contact miscible, resulting in the formation of a residual oil phase. Dispersion is a scale dependent phenomenon that has been shown to increase with increasing heterogeneity, mobility ratio, correlation length, aspect ratio and distance traveled. Generally, dispersion is not modeled explicitly in reservoir simulation and physical diffusion is almost never modeled. At typical reservoir flow rates diffusion is expected to be much smaller than dispersion. Numerical dispersion in reservoir simulation is usually used as a proxy for true physical dispersion. Large grid blocks used in reservoir simulation can result in gross over-estimates of in-situ mixing. Higher order methods can be used to attenuate numerical dispersion in reservoir simulation, allowing for more accurate modeling of concentration gradients. The key objectives of this research were to: -Develop a higher-order flux-limited TVD code; -Use this code to study the scale dependence of reservoir mixing, particularly at high mobility ratios and high correlation lengths; -Explicitly model the effects of diffusion and determine the impact of various levels of diffusion on dispersion in reservoir simulation. This thesis details the development and use of a higher order flux-limited simulator with ``TVD-like" properties. The simulator was purpose-built to fulfill the requirement for a fast, high-resolution model that would not create excessive numerical dispersion. This simulator has been used to study the scale dependence of hydrodynamic dispersion. In this work over 1600 FCM displacements were simulated on heterogeneous grids. Both mobility ratio and longitudinal correlation length were varied across a wide range. Physical diffusion was modeled as part of this work. The simulation code was used to automatically calculate local dispersivity by fitting the 1D CD equation to the concentration history at each grid block and taking the log average across a vertical cross section. It was hypothesized that dispersivity would increase with increasing correlation length and mobility ratio. It was also envisaged that dispersivity would eventually decrease as mobility ratio became extremely adverse and/or correlation length became very long. Diffusion was predicted to have no significant impact on dispersivity in reservoir simulation because diffusion is much smaller in magnitude than numerical dispersion. Dispersivity behaved as predicted in the absence of input physical diffusion: increasing correlation length and mobility ratio resulted in increases in dispersivity, before causing it to decrease. Highly correlated, layered media and highly adverse mobility ratios appeared to be conducive to the development of channel-dominated flow. However, dispersivity was shown to peak at higher mobility ratios and correlation lengths as physical diffusion was progressively added. Diffusion was shown to significantly increase dispersivity. Dispersion is scale dependent, increasing with mobility ratio and correlation length. High resolution, fine-grid simulation models predict a decrease in dispersivity as mobility ratio and correlation length become very large, and flow appears to become channel-dominated. In reality, the presence of diffusion is likely to delay the onset of channel-dominated flow. Dispersion is likely to continue increasing even as mobility ratios become highly adverse and reservoirs become highly layered. In these scenarios diffusion plays an important role in initiating dispersion across sharp concentration gradients. In high resolution, fine-scale reservoir simulation models, numerical dispersion is unlikely to be sufficiently large to initiate dispersion. Flow may be erroneously modeled as channel-dominated, when in fact it is dispersion-dominated. Chapter 1 of this thesis is a literature review that details the nature of hydrodynamic dispersion. Chapter 2 provides an explanation of the mathematical principles used in this research. In Chapter 3 the simulation model is described. Chapter 4 provides details on the simulation study and an analysis of results. Chapter 5 includes the conclusions made in this work and recommendations for future research.