Scaling of Capillary Imbibition Under Static Thermal and Dynamic Fracture Flow Conditions
Authors: Babadagli T. 
Published: December 2007

Abstract
Although laboratory investigations provide an insight into matrix recovery by capillary imbibition in naturally fractured reservoirs (NFR), an up-scaling of laboratory scale performance to reservoir condition is necessary for realistic recovery prediction. Owing to the numerous parameters involved, the formulation of scaling under thermal effect and dynamic conditions becomes highly complex. This study is aimed to incorporate two critical parameters; oil viscosity and the flow rate in fracture, into the capillary imbibition scaling formulations.
The decrease in oil viscosity during thermal applications in NFR's substantially affects the capillary imbibition recovery rate and should be considered in scaling studies. To investigate this effect, static imbibition experiments were conducted using four types of heavy-oil samples at different temperatures ranging from 20 to 90 C. Then, the recovery curves were analyzed for a possible scaling behavior considering the oil viscosity change under thermal effect. Scaling formulations reported previously were applied and compared to propose the most applicable one for particular oil-water pairs. The effects of wettability and thermal expansion on the scaling behavior were also discussed.
Another factor that has not been considered previously in the scaling of capillary imbibition is the flow rate in fracture. As the flow rate increases, contact time between matrix and fluid in fracture decreases causing less effective capillary imbibition. The results obtained through water injection experiments in artificially fractured core samples with matrix permeabilities ranging from 300 md to 0.075 md were used to verity the numerical model (dual-porosity) of core scale displacements. The numerical results were used to obtain a correlation between the convergence constant in Aranofsky's abstract recovery-time relationship and an imbibition group consisting of injection rate and matrix properties. It was observed that a good correlation exists implying a possible scaling.

Introduction
In naturally fractured reservoirs (NFR), great amount of oil is stored in matrix due to much higher storage capacity than fracture. Thus, the main target of an enhanced oil recovery application in a NFR is to recover matrix oil. Under water injection or strong water influx, the matrix oil is recovered mostly by capillary imbibition if the matrix is water wet. The suction of water by matrix releasing the oil due to capillary forces is governed by numerous parameters, namely rock, fluid and flow properties and boundary conditions of these properties. The effect of these parameters on the amount and the rate of the recovery has been clarified and this phenomenon has been formulated to scale up the laboratory scale data to reservoir scale in the past.
Due to complexity of the phenomenon, some of the properties are not included in the formulation of the process for scaling purpose. Therefore, the formulation is incomplete yet and the inclusion of additional parameters in the formulation requires experimental verifications.
As an example, capillary imbibition can be enhanced with an additional temperature effect when the matrix contains heavy-oil. In this case, the viscosity of oil, which is subject to change under temperature effect, needs to be incorporated in the formulation. Difficulties in the scaling formulation associated with the thermal effects were pointed out and discussed by Briggs et al. In fact, the relative permeability and capillary pressure curves should be same for the scaling law being valid but under the temperature effect both are expected to change. The scaling of capillary imbibition under thermal effect has been examined in a few studies. Reis reviewed the matrix recovery mechanisms for non-isothermal conditions and provided the characteristic recovery times for them. An attempt was made by Babadagli for scaling the capillary imbibition under temperature effect.