Toward Field-Scale Wettability Modification—The Limitations of Diffusive Transport

Summary Densely-fractured oil-wet carbonate fields pose a true challenge for oil recovery that traditional primary and secondary processes fail to meet. The difficulty arises from the combination of two unfavorable characteristics: First, the dense fracturing frustrates an efficient waterflood; second, because of the oil-wetness, the water pressure exceeds the oil pressure inside the matrix blocks, thus inhibiting spontaneous imbibition of water. In the past decade, using a new class of surfactants, enhanced oil recovery (EOR) researchers have studied the options to chemically revert the wettability of carbonate rock without drastically decreasing the oil-water interfacial tension. These chemicals, termed "wettability modifiers" (WMs), effectively reverse the sign of capillary pressure at the prevalent saturation. With the oil pressure exceeding the water pressure, the capillary pressure becomes the driving force for oil expulsion from the matrix and into the fracture system. Previous publications on chemical wettability modification focused on the performance of different chemical wettability modifiers for a chosen rock/oil/brine system. In some cases, they demonstrated an almost full oil recovery from core plugs. Little attention, however, has been given to the mechanism underlying the transport of the chemical into the matrix block and to the proper scaling of laboratory results to reservoir size. The present study aims to demonstrate that imbibition after wettability modification is diffusion-limited. To this end, the recovery profiles for spontaneous capillary imbibition, as well as for imbibition after wettability modification, are calculated. The results are then used to compare with the data of Amott cell imbibition experiments. It is confirmed that in both cases, the cumulative recovery is initially proportional to the square root of time. Imbibition after wettability modification, however, takes approximately 1,000 times longer than spontaneous capillary imbibition into a water-wet medium. The slow recovery observed in the case of imbibition after wettability modification is in excellent agreement with the assumption that, in the absence of significant spontaneous imbibition, the WM, to unfold its action, must first diffuse into the porous medium. In any diffusion process, the time scale is linked to the square of the length scale of the medium. Therefore, it would take up to 1,000 times longer (an equivalent of 200 years) before the same recovery is obtained from a meter-scale matrix block as is obtained from a centimeter-scale plug in a laboratory in 100 days. Consequently, unless a significantly faster transport mechanism for the wettability modifier is identified, or unless viscous forces or buoyancy enable forced imbibition, the chemical wettability modification of fractured oil-wet carbonate rock does not provide an economically interesting opportunity. Introduction Rock fractures provide comparatively highly permeable flow paths through oil reservoirs. In a densely fractured reservoir, the permeability contrast between the fracture network and the oil-bearing matrix can be significant. In that case, the viscous pressure differential across individual matrix blocks can be too small to release oil from the blocks under waterflood, thus leading to a poor recovery. Depending on the wetting state of the matrix and its initial water saturation, Swi, capillary action can cause imbibition of water up to a "spontaneous" equilibrium saturation, commonly denoted as Sspw. At this saturation, however, the capillary pressure inside the matrix block coincides with that in the fracture, and the recovery ceases. Experience has shown that carbonate fields often range from intermediate-wet to preferentially oil-wet (Treiber et al. 1972; Chilingar and Yen 1983), which is synonymous with Sspw being close or equal to Swi ; thus, they exhibit very limited recovery during primary and secondary production. Recently, a new EOR technique, designed specifically to tackle the challenges outlined previously, has been suggested by Austad and coworkers (Austad and Milter 1997; Standnes and Austad 2000a, b). In their pioneering work, these authors show that certain chemicals, when dissolved in the surrounding brine, can initiate water imbibition into oil-saturated core plugs and, hence, lead to the recovery of oil. One possible mechanism that explains these observations is the solubilization of adsorbed hydrocarbon components from the pore surface—as demonstrated by an atomic force microscopy study by Kumar et al. (2005), this exposes the intrinsically hydrophilic matrix. Another possibility is the formation of an additional chemical layer covering the adsorbed hydrophobic material. In either case, the pore surface becomes more hydrophilic, and the wettability of the matrix is thus modified. In a capillary rise experiment into parallel plates, Kumar et al. also observed different time scales for different types of wettability-modifying chemicals (2005). Using the cationic wettability modifier dodecyl trimethyl ammonium bromide (DTAB, also known as C12TAB), Standnes and Austad deduced that wettability modification was achieved through the comparatively slow process of partitioning the chemical into the oil phase, followed by desorption and solubilization of anionic hydrocarbon components (2000a, b). Shen et al. (2006) and Rao et al. (2006) measured the effect of surfactants on the relative water/oil permeabilities at different interfacial tensions. Wu et al. (2006) studied the properties and ranked the efficiency of chemical model compounds, based on their chemical structure, to modify the wettability and enhance recoveries. Several groups have taken initiative to model wettability modification in numerical simulators (Adibhatla et al. 2005; Delshad et al. 2006). So far, no significant attention has been given to time dependence and to the subsequent upscaling of the laboratory results to matrix block scale. This subject will be addressed in the present work. The structure of the article is as follows: In the Theory section, the basic results for countercurrent capillary imbibition will be briefly reviewed and compared to Fick's law of molecular diffusion. The oil recovery as a function of time for both capillary imbibition and imbibition after wettability modification will be predicted. The experimental approach to imbibition at different wetting situations will be described in the section Materials and Preparation. The recovery results will then be analyzed using the previously derived equations. Finally, tentative conclusions for the upscaling will be drawn.