Commonality between MAR water drainage and gas oil gravity drainage: the case of a fractured rock

A.R.Kacimov,  Sultan Qaboos University,   anvar@squ.edu.om
S.Al-Jabri, Sultan Qaboos University,   salemj@squ.edu.om
S.Schoofs,   Petroleum Development Oman, stan.schoofs@pdo.co.om
S.Sufyan, Petroleum Development Oman, sufyan.as.shihab@pdo.co.om

In MAR schemes planned in Oman, seasonal retrieval of water  from aquifers during summer incorporates drainage of highly conductive fractures and adjacent rock blocks (clay lenses) of low permeability. Similarly, in enhanced oil recovery  by Gas-Oil Gravity Drainage (GOGD) oil rapidly drains through fractures and slowly retreats from matrix blocks (Boerrigter et al., 2007). In both MAR and GOGD one immiscible phase displaces another in an essentially spatially non-uniform manner (on the scale of an individual block!)  with the following controlling factors: block/fracture sizes/aperture, capillary-pressure  function, relative permeabilities and phase viscosities-densities. The difference between MAR and GOGD is in the perception of aquifer (water): in groundwater hydrology it is a sacred entity to be replenished and protected, in GOGD it is a nuisance (e.g., upconing) causing deterioration in  oil production. In this work we try to bridge the gap between hydrological (MAR) and reservoir (GOGD) engineering.  We model the drainage of rectangular blocks (vertical cross-section) with left and right faces contacting a film flow of a heavy fluid (liquid), which re-imbibes into the block through the upper segment of the matrix-fracture contact surface and re-drains through a lower segment, providing the subjacent-superjacent blocks are separated by impermeable barriers. For a stack of GOGD blocks the winding paths of liquid result in recovery that is controlled by the upper most block only and in MAR multiple-block flow topology implies much  longer residence time of groundwater than can be expected from a standard double-porous medium model. Analytical solutions for steady state, essentially 2-D liquid motion are obtained for the Vedernikov model of capillarity by conformal mappings and solution of boundary-value problems involving singular integrals. A critical block size demarcating a flow regime with an  internal “phreatic surface bubble” attached to the block roof is found.  Numerical solutions are  obtained by HYDRUS2D for Van Genuchten capillarity-permeability functions. In both solutions  the mobility of gas is assumed to be infinite. Total capillary uptake by the block, streamlines, pressure/hydraulic head distributions within the block and Darcian velocity fields are plotted for a typical fractured rock in MAR and GOGD. Transient problems of  phreatic surface drainage from a single block are solved by the linear potential theory of Polubarinova-Kochina and compared against groundwater mound dynamics observed and modelled in Kacimov et al. (2009).

Boerrigter P.M.,  Verlaan, M.L. and  Yang D., 2007. EOR methods to enhance gas oil gravity drainage. SPE/EAGE Reservoir Characterization and Simulation Conference, 28-31 October 2007, Abu Dhabi, UAE. SPE paper 111403.

Kacimov A.R., Al-Jabri, S., Sherif M.M., Al-Shidi S., 2009.  Slumping of groundwater mounds: revisiting the Polubarinova-Kochina theory and modeling by analytic element method.  Hydrological Sciences Journal, 54(1), 174-188.