**3. Osmosis**

Imbibition in tight formations is usually accompanied by osmosis, especially in highsalinity shale formations. Osmosis is a spontaneous net movement of solvent molecules toward a higher concentration region so as to minimize the concentration difference between two sides of a semi-permeable membrane. Solute–membrane interactions are more frequent on the higher solute concentration side than the low concentration side. Thus, more solute particles, such as salt, try to pass through the membrane, but they are excluded by the membrane due to its semi-permeable property. As those particles are pushed, a momentum is generated and pulls water molecules through the membrane from the lower concentration side [88].

Previously, osmosis was overlooked, since its effect is negligible during fluid flow in porous medium of conventional formations. However, in tight (unconventional) formations, which contain high clay mineral contents, a semi-permeable membrane can arise to generate osmosis. Neuzil and Provost [89] observed the anomalous fluid pressure in a

subsurface when they performed osmosis measurements on moderately compacted high clay content Pierre shale. This can be illustrated by electric double layer (EDL) theory [90]. Clay particles are naturally and commonly negatively charged. To neutralize the surface charges, cations or counter-ions will be attracted to the clay surface and form a diffuse double layer. However, the concentration of attracted ions decrease away from the clay platelets as electrostatic force weakens. If there is enough distance between clay platelets, there may exist a charge-neutral zone in the middle. However, due to some compaction effect, the diffused layers overlap each other, where the excessive charges accumulate. This overlap region carries charges and provides exclusion forces to any of the charged particles that try to pass through it but not water molecules [91–94].

Small pore sizes, which are a distinguishing characteristic of porous medium in tight formations, also contribute to osmosis occurrence. First, small rock pores with high clay contents can increase the quantity and quality of semi-permeable membrane. Second, the disassociated ions from salt in the aqueous solution are usually hydrated and complexed by water molecules. Thus, when the pore size is small enough, water molecules are more mobile than the larger-size hydrated ions, which will experience more restriction through the rock. Hence, as being excluded by the small rock pores, those hydrated ions may acquire enough momentum to overcome the diffusive flux and pull the water out of low concentration solution [95].

Hence, osmosis in tight formations has attracted research attention. Osmosis study in drilling engineering is mainly related to wellbore stability, which is strongly affected by water-based drilling fluid. When drilling fluid is invaded into formation rocks, it can decrease rock strength and elastic modulus and increase pore pressure, which are all causes of wellbore instability [96]. In shale formations, osmosis is considered as a significant mechanism to result in fluid invasion [97,98]. However, osmosis is a particular mechanism that allows fluid to have a bi-directional flow through controlling the salinity of the drilling fluid. Abass et al. [99] indicated that a designed drilling fluid can extract formation fluid out of shale to strengthen wellbore. The designed considerations are to increase osmotic flow to the wellbore, which requires increasing the salinity and fluid viscosity as well as reducing the shale permeability. High-salinity drilling fluid can induce osmotic flow to the wellbore. High viscosity and small permeability can inhibit capillary flow into formations. Membrane efficiency is also a consideration that is hard to control but should be considered when designing. Membrane efficiency is a ratio between actual osmotic pressure and theoretical osmotic pressure. Abass et al. [99] measured membrane efficiency in shale samples from the Zuluf field of Saudi Arabia. The measurement showed that its membrane efficiency was 4.2%. This result proves that osmosis cannot be neglected in shale formations. Schlemmer et al. [100] discussed factors that can improve membrane efficiency and hence increase osmosis. These factors are clay type of high cation exchange capacity, shale pore structure with more compacted clay, formation fluid with lower salt concentration, and compositions of drilling fluid that can affect the interface of clay.

However, those studies argued about the actual role of osmosis in fluid movement because it is difficult to distinguish osmotic flow from capillary flow in the imbibition process in tight formations. Zhou et al. [9] indicated this combinational mechanism during fracturing fluid flow in shale gas formation rocks.

In Zhou et al.'s experiments, it was found that the weight of rocks increased and decreased alternately when they were immerged into high salinity fluid, which can cause osmotic extraction [9]. Weight increase indicated that fluid invaded into rocks because capillary-driven imbibition was the dominant force. With the continuous fluid invasion, capillary pressure was decreased so that fluid was imbibed into rocks less and less. When osmotic extraction was stronger than capillary imbibition, the rock weight decreased because fluid flowed out of the tight pores more than it flowed in. However, capillary imbibition became stronger again when fluid saturation was declined, so that the weight of rock increased again after a certain point of time. Hence, it is difficult to distinguish

the capillary pressure and osmotic forces in the fluid movement processes, as they are dynamically changing and interacting with each other.

The osmotic effect can also contribute to the enhanced oil recovery (EOR) mechanism of unconventional shale formations. Recent studies show that low-salinity waterflooding EOR is can significantly improve oil production from shale formations, especially in highsalinity tight shale formations [8,101–104]. The concept is to enhance osmotic flow through a smaller salinity of waterflooding fluid than that of formation fluid. Figure 4 shows osmosis effect in clay-rich rocks. The application also depends on membrane efficiency. Fakcharoenphol et al. [8] and Teklu et al. [102] proved in clay-rich tight formations that osmosis can improve oil displacement under low-salinity fluid. Figure 5 shows experimental results of osmosis effect on oil displacements based on authors' work. However, it is challenging to quantify the osmosis effects on oil recovery, since fluid chemical equilibrium and rock–fluid interactions all change dynamically with salinity change in this extremely complicated process. Thus, direct measurement of osmosis during oil recovery experiments may reveal new important insights.

**Figure 4.** The schematic showing osmosis effect on fluid flow in clay-rich rocks.

**Figure 5.** A preserved one-inch diameter Bakken shale core sample submersed in high-salinity brine (240,000 ppm KCl) (**top**) and low-salinity brine (20,000 ppm KCl) (**bottom**) showing oil expulsion vs.

imbibition period. At imbibition Day 5 (**top**), the core was removed from a high-salinity brine beaker and produced/expelled oil was wiped and immersed in low-salinity brine from Day 5 until Day 10 (**bottom**). This shows that more oil is expelled due to osmosis during a low-salinity brine imbibition period.

A study by Padin et al. [103] performed high-pressure high-temperature chemical osmosis-driven fluid flow experiments in carbonate-rich mud rocks (shales). Their experiment showed a gradual, slow (within 120 days of experiment) increase of pressure within the samples. Based on their experiments, they concluded that chemical osmosis in organic-rich carbonate rocks could create a significant amount of driving force for oil mobilization or EOR; also, they stated that water imbibition in their experiment cannot be explained by only capillary forces.

#### **4. Simulation for Osmosis-Associated Imbibition**

The model that simulates spontaneous imbibition has been predominately attributed to capillary action [71,105–117]. Osmosis has been overlooked for a long time, as it is not as significant as other mechanisms, such as capillarity and gravity, because the membrane efficiency in a conventional reservoir is too low to make a real impact. However, shale and other unconventional formations present a significant osmosis effect due to their mineralogy and pore size structure [9]. Recently, several modeling efforts have been made to investigate the osmosis effect in unconventional reservoir development.

Fakcharoenphol et al. [118] proposed a triple-porosity fracture-matrix model and incorporated the effects of matrix wettability, capillary pressure, relative permeability, and osmotic pressure to investigate the impact of shut-in time on well productivity. In the model, the fracture forms a continuum of an interconnected network created during the hydraulic fracturing, while the organic and non-organic matrices are embedded in the fracture continuum. Fakcharoenphol et al. [8] used a numerical model to calculate osmotic pressure by tracking the salinity concentration. The simulation results indicated that osmotic pressure can be a viable mechanism by promoting water–oil counter-current flow. Wang and Rahman [119] proposed a numerical model to investigate both capillary pressure and osmosis effects on fluid leak-off during shale gas reservoir stimulation. The results showed that rock composition greatly affects the leak-off rate, and the invaded water due to capillary and osmotic pressures significantly increases the pore pressure. There is a strong non-linear relationship between imbibition volume and square root of time. Li et al. [60] developed a multi-component matrix imbibition model to investigate the effects of low-salinity water and surfactant on unconventional recovery. Simulation results matched with experimental data and revealed some important insights on the effects of water salinity and surfactant that the combination effects of contact angle and interfacial tension determine capillary pressure imbibition and that the concentration of charged ions and surfactant molecules affect the osmosis imbibition. All these processes are associated with different rock components and mineralogy, and there exists an optimum water salinity for maximum imbibition. Different from previous simulation studies, Li et al. [90] proposed a multi-mechanistic numerical shale matrix imbibition model by dividing the rock into nonmembrane and membrane components. Figure 6 introduces the coupling in the model. The model considered capillary pressure and osmotic pressure as a function of water saturation, could track the dynamic water and salt movement, and was validated by matching with experimental measurements. The principles associated with the imbibition and osmosis behind each model of these reviewed works are summarized in Table 1.


**Figure 6.** Numerical model with imbibition and osmosis coupling.

**Table 1.** Imbibition mechanisms for different models that considered imbibition and osmosis.

