MULTI-WELL ANALYTICAL SOLUTION FOR CONING UNDER SIMULTANEOUS STEADY-STATE FLOW OF THREE PHASES

Open Access
Author:
Ahn, Eunnam
Graduate Program:
Petroleum and Mineral Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
May 09, 2018
Committee Members:
  • Russell Taylor Johns, Thesis Advisor
Keywords:
  • analytical solution
  • coning
  • vertical equilibrium
  • steady-state
  • multi-well
  • three-phase flow
Abstract:
A large amount of unwanted water and gas production from upward or downward coning can significantly erode profits in oil recovery processes. Simulation estimates of the magnitude and timing of coning can be erroneous owing to unknown reservoir heterogeneity, large grid blocks near the wells, and inaccuracies in simulation well models, such as that from Peaceman. This may lead to a failure to accurately calculate the critical oil rate in a given case. Thus, a good understanding of coning behavior is required for an effective water and gas control. An improved analytical water and gas control solution helps facilitate the computation of the critical rate and avoidance of unwanted water and gas. The solution may lead to a significant reduction in operating cost during oil production. This thesis presents a multi-well steady-state analytical solution for coning of three phases (water, oil, and gas) flowing simultaneously. The solution for multiple wells is developed using the principle of superposition with a potential function that includes capillary pressure and relative permeability. The assumption of vertical equilibrium (VE) is made, which gives maximum vertical crossflow and therefore the largest possible coning. Any model for relative permeability and capillary pressure can be used, although we used Stone 2 for relative permeability and Brooks-Corey for capillary pressure. We give dimensionless inflow performance windows (IPW) to show the allowable physical window of three-phase rates and the maximum oil rate as a function of the water and the total well flow rate. The new potential functions are also used to demonstrate superposition for several well patterns with no-flow boundaries. Besides estimating critical oil rates, the solution could be important to benchmark numerical solutions and improve the accuracy of Peaceman’s well model.