History Dependent Modeling of Counter-Current Flow in Porous Media

Open Access
Li, Gaoming
Graduate Program:
Petroleum and Natural Gas Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
November 25, 2002
Committee Members:
  • Abraham S Grader, Committee Chair
  • Phillip Michael Halleck, Committee Chair
  • Turgay Ertekin, Committee Member
  • Derek Elsworth, Committee Member
  • Michael Adebola Adewumi, Committee Member
  • capillary pressure hysteresis
  • reservoir simulation
  • porous media
  • Counter-current flow
  • fluid bank
  • history matching
  • X-ray CT
Gravity-driven counter-current flow occurs in reservoir processes such as gas storage in an aquifer and certain secondary and tertiary recovery processes. In order to operate these processes effectively, it is important to understand and to be able to model the flow process. Both drainage and imbibition processes exist simultaneously when counter-current flow occurs. It has been difficult to model this type of flow process because of the impossibility of assigning a single capillary pressure curve applicable over the entire sample in this situation. The focus of this study is to find a method for accurately representing capillary pressure in counter-current flow. Gravity-driven counter-current flow experiments have been done in glass bead packs and the spatial and temporal saturation distributions of the core sample obtained with X-ray computed tomography (CT). With the aid of a deterministic reservoir simulator, capillary pressure and relative permeabilities were extracted by matching the saturation distribution with optimization methods (history-matching). This work applies a saturation-history-dependent approach to simulating counter-current flow. From the capillary hysteresis loop, a family of curves (called scanning curves) is constructed connecting the two branches. Each grid block of the sample is assigned a different scanning curve according to its current saturation and saturation history. This technique was used to simulate previous laboratory experiments in glass bead packs. The simulation reproduced two-dimensional saturation distributions over time with good accuracy. Similar simulations of experiments described in the literature were equally successful. In particular the simulation captured the fluid banks observed in counter-current flow experiments, which cannot be obtained through other methods.