Imbibition Model Studies on Water-Wet Carbonate Rocks
Authors: Parsons R.W. , Chaney P.R. 
Published: December 2007

Abstract
Oil recovery by the imbibition mechanism can be important in fractured carbonate reservoirs with a bottom water drive. Laboratory experiments were performed on water-wet carbonate rocks to model this process. The results are interpreted in light of the applicable scaling laws. The imbibition production behavior of a pillar of rock subjected to a slowly rising water table can be systhesized from data on total immersion experiments on small rock samples. If the rate of water table rise is slow enough and if the physical properties are such that the imbibition zone is of a small vertical extent, then only the final oil recovery on the small samples need to known. Applying laboratory imbibition data to a real reservoir should be done with caution because of possible wettability problems and the unknown behavior of two-phase flow in fractures.
Introduction
The spontaneous taking up of a preferential wetting fluid into a porous medium with the simultaneous expulsion of the contained fluid is termed imbibition. One of the many physical imbibition processes is the production of oil by the taking up of water into a water-wet reservoir rock. In certain types of heterogeneous reservoirs, e.g., fractured, it is realized that imbibition alone may be the dominant mechanism.
Theoretical studies of imbibition oil recovery have followed several lines of attack. The behavior of certain mathematically tractable and conceptually simple models have been analyzed. Birks considered a bundle of vertical capillaries model, while Perotti et al. and Kelemen used a model of a series of vertically oriented fractures. If the oil production behavior from a block of reservoir rock is known, then the cumulative behavior of a vertical stack of these blocks subjected to a rising water table can be determined by a method outlined by Aronofsky et al.
Knowing the capillary pressure and relative permeability functions should uniquely set the imbibition behavior for a given sample. Solutions of the partial differential equations describing the process, however, present some formidable problems. Digital computer techniques have been applied to displacement processes in which the capillary pressure has been included. More recently, similar techniques have been used by Blair to calculate countercurrent imbibition behavior. The fact that imbibition behavior is described by the usual fluid flow equations (Darcy's Law and continuity equation) implies that the derived scaling laws should apply equally to this situation. Use of model experiments to study imbibition has been employed by Graham and Richardson and Mattax and Kyte, who actually tested the scaling law applicability.
This study is concerned with scaled model imbibition experiments on water-wet carbonate rocks. Of particular interest is the slowly rising water table experiment. This simulates a highly fractured reservoir with the water table rising uniformly through the vertical fracture system. Experiments were performed on different sized samples and with different rates of rise of the water-oil interface surrounding the rock pillar. Total immersion imbibition experiments on smaller rock samples were performed to test the basic linear scaling laws arid to see if these simpler tests could be used to synthesize the rising water table experimental results.
THEORY IMBIBITION SCALING LAWS
Scaling laws for the flow of two incompressible immiscible fluids in a porous medium have been presented by Rapoport. These are derived directly from Darcy's Law for the individual phases and the continuity equation. Results from a laboratory model experiment will duplicate those from some reservoir prototype if a constant proportion is maintained among the three forces acting on the fluids - the capillary pressure gradient, the gravitational gradient and the flowing pressure gradient. Operation of the model (i.e., fluid injection or withdrawal) must be conducted in accordance with specific equations.
SPEJ
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