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Obtainable recovery vs. water accessible pore volumes. Comparative test where ω = αβ∆s is constant for 5 values: ω i =0.025, 0.06, 0.15 (base), 0.4 and 1 (i=1,..,5). O and W denote POW and PWW sets. Parameters α, β, ∆s are varied in 20 tests. ω seems to characterize the flow regime of the fracture-matrix system. Unspecified parameters are given by reference case.
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The flow of oil and water in naturally fractured reservoirs (NFR) can be highly complex and a simplified model is presented to illustrate some main features of this flow system. NFRs typically consist of low-permeable matrix rock containing a high-permeable fracture network. The effect of this network is that the advective flow bypasses the main po...
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... We make a number of variations of the base case to obtain 5 different values of omega: ω 1 , ω 2 , ..., ω 5 . For each fixed ω i we vary parameters like α, β, and saturation flow functions (POW, PWW) to take into account different flow scenarios. The values of ω differ roughly by a factor of 2.5 between adjacent groups. The results are shown in Fig. 13. For comparison the results are plotted as fraction of obtainable recovery, R/R ∞ (where obtainable recovery is R ∞ = 1+β∆s 1+β(1−s m 0 ) ) vs injected water-accessible reservoir pore volumes (WARPVs) (τ f /(1 + β∆s)). The reason for this visualization is that if no water leaves until all possible imbibition has occurred and the ...
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Citations
... The imbibition of conventional reservoirs has been studied extensively in recent years. A large number of studies have shown that imbibition in tight oil reservoirs is one of the important driving forces for crude oil recovery [4][5][6]. The spontaneous imbibition induced by capillary force is especially remarkable because the pore size is in micron or even nanometer range [7]. ...
This study utilizes nuclear magnetic resonance (NMR) techniques to monitor complex microstructures and fluid transport, systematically examining fluid distribution and migration during pressure imbibition. The results indicate that increased applied pressure primarily affects micropores and small pores during the initial imbibition stage, enhancing the overall imbibition rate and oil recovery. Higher capillary pressure in the pores strengthens the imbibition ability, with water initially displacing oil from smaller pores. Natural microfractures allow water to preferentially enter and displace oil, thereby reducing oil recovery from these pores. Additionally, clay minerals may induce fracture expansion, facilitating oil flow into the expanding space. This study provides new insights into fluid distribution and migration during pressure imbibition, offering implications for improved oil production in tight reservoirs.
... with a non-negative constant P * c1 representing interfacial tension between the two immiscible phases. The functional form of capillary pressure is for simplicity set to be as given by (5) where the main feature is that it can have a decreasing trend as a function of water saturation with suitable choices of parameters, similar to other functions commonly used (Andersen et al. 2014;Qiao et al. 2018). Finally, the following initial and boundary conditions complete the model definition. ...
Gas migration behind casings can occur in wells where the annular cement barrier fails to provide adequate zonal isolation. A direct consequence of gas migration is annular pressure build-up at wellhead, referred to as sustained casing pressure (SCP). Current mathematical models for analyzing SCP normally assume gas migration along the cemented interval to be single-phase steady-state Darcy flow in the absence of gravity, and use a drift-flux model for two-phase transport through the mud column above the cement. By design, such models do not account for the possible simultaneous flow of gas and liquid along the annulus cement, or the impact of liquid saturation within the cemented intervals on the surface pressure build-up. We introduce a general compressible two-fluid model which is solved over the entire well using a newly developed numerical scheme. The model is firstly validated against field observations and used for a parametric study. Next, detailed studies are performed and the results demonstrate that the surface pressure build-up depends on the location of cement intervals with low permeability, and the significance of two-phase co-current or counter-current flow of liquid and gas occurs along cement barriers that have an initial liquid saturation. As the magnitude of the frictional pressure gradient associated with counter-current of liquid and gas can be comparable to the relevant hydrostatic pressure gradient, two-phase flow effects can significantly impact the interpretation of the wellhead pressure build-up.
... It has been extensively studied in the enhanced oil recovery (EOR) topic. 2,9,10 To recover this type of residual oil, either the pressure gradient should be increased or the negative capillary pressure should be reduced. By applying EOR materials with better mobility control, such as polymers, 11 viscoelastic surfactants, 12,13 and foam, 14 the pressure gradient exerted on the rock matrix can be increased, thus increasing the macro sweep efficiency. ...
Interfacial tension (IFT) reduction and wettability alteration (WA) are both important enhanced oil recovery (EOR) mechanisms. In oil-wet formations, IFT reduction reduces the magnitude of negative capillary pressure, releasing trapped oil. WA changes the negative capillary pressure to positive conditions, helping the entrance of the aqueous phase, and the displacement of the oil phase. In most cases, IFT reduction and WA happen at the same time. However, studies regarding the coupled effect provided different, sometimes conflicting observations. It requires further study and better understanding. In our study, oil-aged Indiana limestone samples were chosen to represent oil-wet carbonate rocks. Static contact angle and spinning drop method were adopted for wettability assessment and IFT measurement, respectively. Spontaneous imbibition was adopted to reflect on the oil recovery mechanisms in different cases. The impact of IFT reduction, WA, and permeability on the coupled effect was discussed by choosing four pairs of comparison tests. Results showed that when the coupled effect took place, both a higher IFT value and a stronger WA performance resulted in faster and higher oil recoveries. The importance of IFT reduction was enhanced in the higher-permeability condition, while the importance of WA was enhanced in the lower-permeability condition.
... The wettability alteration aids in residual oil mobilization, which creates the spontaneous imbibition process. In general, carbonate and fractured reservoirs are considered as oil-wet or mixed-wet; therefore, the process of water imbibition is either deprived or unable to occur owing to the negative capillary pressure (Andersen et al., 2014). Consequently, for increasing the oil recovery from such reservoirs, the reservoir matrix's wettability needs to be altered to more beneficent ranges so that it enables imbibition of water into the rock matrix and drive the oil out of the matrix into the fracture (Zhang et al., 2006a). ...
Most oil fields today are mature, and the majority of the reservoirs in the Middle East are carbonate rocks characterized by high temperature high salinity (HTHS), heterogeneous mineral composition, and natural fractures. Enhanced oil recovery (EOR) methods are used for boosting oil recovery from the aged reservoirs beyond primary and secondary recovery stages. Nevertheless, it can be a challenging task to employ EOR techniques in these aged carbonate reservoirs. This is because carbonate reservoirs have mixed-to-oil-wet wettability with temperatures exceeding 85 °C and salinity of over 100,000 ppm, which renders secondary EOR-methods such as waterflooding ineffective. Therefore, even though carbonate reservoirs contain 60–65% of world's remaining oil, with immense intrinsic economic prospects, the oil recovery process from carbonate reservoirs remains a considerable challenge. Chemical-EOR (cEOR) techniques, like SP based cEOR, have shown marked promise in improved oil recovery, mainly from clastic reservoirs with medium temperature and salinity, unlike carbonate reservoirs. During SP-floodings, the surfactants get adsorbed due to the mineral composition of the carbonate rocks, and polymer degradation occurs due to HTHS conditions. Consequently, new surfactants and polymers have been structurally conformed and tested to improve their robustness and related recovery efficacy. For instance, Guerbet alkoxy-carboxylate surfactants demonstrated good stability at temperatures over 100 °C and salinities up-to 275,000 ppm, yielding tertiary recovery of 94.5% and low adsorption of 0.086 mg/g of rock. The cationic Gemini surfactants, zwitterionic or amphoteric class of surfactants are also suitable for HTHS carbonates. Besides, effective biosurfactants sourced from plant such as, soy, corn, etc., are non-toxic and readily biodegradable. The hydrophobically associating polyacrylamide (HAPAM) and its modified nanocomposite derivative can act as replacement surfactants, due to their wettability altering and robust characteristics. Novel polymers viz., NVP-based, novel smart thermoviscosifying polymers (TVP), soft microgel, and sulfonated polymers, are also relevant to HTHS carbonate applications. Xanthan gum, scleroglucan, and schizophyllan biopolymers have been noted to resist HTHS and low permeability conditions, requiring lower concentration and having low adsorption. Recent surfactant-polymer (SP) formulations also can be applicable for HTHS carbonates with excellent ternary recoveries (93.6%) and minimal retention (0.083 μg/g of rock). Such low retention values suggest low surfactants cost with minimal environmental impact. Moreover, several successful field applications in carbonates were conducted in preceding years; however, the performance of some novel surfactants under HTHS carbonates is yet to be fully understood. Hence, this comprehensive review aims to provide renewed perspectives on surfactant and polymer optimizations for field applications in HTHS carbonates. A list of recommendations is presented as guidelines for efficient SP-flooding designs. This critical literature appraisal furnishes an array of potential manifestations for successful field application of SP-flooding in HTHS carbonates, which holds both economic and environmental feasibility.
... The capillary pressure function is a key parameter in the modeling of multiphase flow phenomena in porous media. Especially, it controls fluid distributions established over geological time due to the balance between gravity and capillary forces, but also plays a key role in the recovery of hydrocarbons in naturally fractured reservoirs where spontaneous imbibition is perhaps the most important recovery mechanism (Andersen et al., 2014;Mason and Morrow, 2013). Capillary pressure can also affect the measurement and interpretation of relative permeability from core flooding experiments (Andersen, 2021;Moghaddam and Jamiolahmady, 2019;Rapoport and Leas, 1953;Richardson et al., 1952). ...
There are several approaches for the calculation of capillary pressure curves in porous media including the centrifuge method. In this work, a new installation of centrifuge test is introduced and compared with the traditional setup. In the first setup, which is a standard approach in labs, the core face closest to the rotational axis is open to the non-wetting phase, while the farthest face is open to the wetting phase where strictly co-current flow is generated in rotations; labeled Two-Ends-Open (TEO). In the second setup, which is proposed as a new approach, only the outer radius surface is open and is exposed to the light non-wetting phase; labeled One-End-Open (OEO). This setup strictly induces counter-current flow. The two systems and their corresponding boundary conditions are formulated mathematically and solved by a fully implicit numerical solver. The TEO setup is validated by comparison with commercial software. Experimental data from the literature are used to parameterize the models. It is mathematically, and with examples, demonstrated that the same equilibrium is obtained in both systems with the same rotational speed, and changing the installation does not influence the measured capillary pressure. This equilibrium state is only dependent on the rotational speed, rock capillary pressure properties, and fluid densities, not the installation geometry, relative permeabilities, or fluid viscosities. However, the dynamic transition trend and saturation profiles were found to be dependent on the applied installation. It was observed that the OEO setup takes almost identical equilibration time as the TEO setup for mixed-wet states, although it needed much longer time in water-wet states. The presence of threshold capillary pressure significantly increased the time scale of the OEO setup. Also, it was found that in contradiction to the TEO setup, the dynamic saturation profile in OEO was rarely influenced by viscosity ratio. To conclude, the performed history matching analysis demonstrated that the OEO setup can be applied for the calculation of counter-current relative permeability from the production data with reasonable accuracy.
... These alterations can only be achieved by injecting suitable surfactants. 108,109 The modification of wettability in carbonates by surfactant injection takes place via two major mechanisms: the coating process, which is related to the use of anionic surfactants, and the cleaning mechanism for cationic surfactants. The molecules of anionic surfactants form a monolayer on the carbonate rock surface (coats the rock surface), where the hydrophobic surfactant tails interact with the adsorbed oil. ...
... This helps to mobilise residual oil and produce it through the spontaneous imbibition process. Generally, carbonate reservoirs and fractured reservoirs are characterised as oil-wet or mixed-wet; thus, the imbibition process of water is either poor or cannot occur due to the negative capillary pressure (Andersen et al., 2014). Accordingly, to increase the oil recovery from these types of reservoirs, the wettability of the reservoir matrix must be made more favourable in order to allow water to imbibe into the rock matrix and push the oil out of the matrix into the fracture (Standnes and Austad, 2000a;Zhang et al., 2006a). ...
Surfactant-based oil recovery processes are employed to lower the interfacial tension in immiscible displacement processes, change the wettability of rock to a more water-wet system and emulsify the oil to displace it in subsurface porous media. Furthermore, these phenomena can reduce the capillary pressure and enhance spontaneous imbibition. The key influencing factors affecting such immiscible displacement process are temperature, salinity and pH of the fluids, surfactant concentration and adsorption. Therefore, before any surfactant flooding process is applied, extensive studies on fluid-fluid and rock-fluid
interactions are needed. The use of other chemicals along with surfactants in chemical enhanced oil recovery (cEOR) processes have been widely considered to exploit the synergy of individual chemicals and complement the weakness arises from each of them during immiscible displacement of fluids in porous media. Therefore, such combinations of chemicals lead to alkaline-surfactant (AS), surfactant- polymer (SP), alkaline-surfactant19 polymer (ASP), and nanoparticles- surfactant (NS) flooding processes, among others. In this review study, we categorised the role and displacement mechanisms of surfactants and discussed the key factors to be considered for analysing the fluid displacement in porous media.
... If wetting and non-wetting phases cover different parts of the matrix, the non-wetting phase will be produced predominantly out of the sides covered by non-wetting phase, while wetting phase enters at the sides open to wetting phase (Bourbiaux and Kalaydjian 1990;Andersen et al. 2019a, b). Spontaneous imbibition is regarded as a crucial driving mechanism for oil recovery from naturally fractured reservoirs (Morrow and Mason 2001;Andersen et al. 2014;Abd et al. 2019). Numerous works have modeled this phenomenon with analytical and numerical approaches (Mattax and Kyte 1962;Ma et al. 1997;Mason et al. 2012;Schmid and Geiger 2012). ...
A numerical model is investigated representing counter-current spontaneous imbibition of water to displace oil or gas from a core plug. The model is based on mass and momentum conservation equations in the framework of the theory of mixtures. We extend a previous imbibition model that included fluid–rock friction and fluid–fluid drag interaction (viscous coupling) by including fluid compressibility and Brinkman viscous terms. Gas compressibility accelerated recovery due to gas expansion from high initial non-wetting pressure to ambient pressure at typical lab conditions. Gas compressibility gave a recovery profile with two characteristic linear sections against square root of time which could match tight rock literature experiments. Brinkman terms decelerated recovery and delayed onset of imbibition. Experiments where this was prominent were successfully matched. Both compressibility and Brinkman terms caused recovery deviation from classical linearity with the square root of time. Scaling yielded dimensionless numbers when Brinkman term effects were significant.
Article HighlightsSpontaneous imbibition with viscous coupling, compressibility and Brinkman terms.
Viscous coupling reduces spontaneous imbibition rate by fluid–fluid friction.
Brinkman terms delay early recovery and explain seen delayed onset of imbibition.
Gas compressibility accelerates recovery and can be significant at lab conditions.
Gas compressibility gives recovery with two root of time lines as seen for shale.
... The arithmetic mean (83) was suggested to scale nonlinear capillary diffusion coefficients for COUSI in Andersen et al. (2014). The use of a harmonic mean (84) better reflects the presence of small values. ...
The aim of this work is to present semi-analytical solutions for shale gas production from a 1D porous medium, where constant pressure is assumed at one side and a no-flow boundary at the other. Adsorbed gas is modeled by a Langmuir isotherm, the gas and rock are compressible, porosity reduction reduces intrinsic permeability and apparent permeability further depends on the Knudsen number.
The partial differential equation describing this system can be formulated as a nonlinear diffusion equation in terms bulk gas density M. This system is comparable to a form described for spontaneous imbibition with semi-analytical solutions regardless of the shape of the diffusion coefficient as function of the conserved property, in that case fluid saturation. Semi-analytical solutions are thus obtained that can give spatial profiles, at given times, of pressure, adsorption, porosity and apparent permeability, in addition to time profiles of gas recovery. These solutions are valid until the no-flow boundary is encountered (the critical time). Late time behavior is investigated using numerical solutions. The roles of system length, adsorption isotherm, rock compressibility, porosity-permeability relations and non-Darcy effects are examined.
It is shown that gas recovery follows a square root of time profile before the critical time. Scaling yields full overlap of recovery curves until their critical time. The square root of time solution is valid for recoveries around 12–22%, but is a good approximation until obtainable recoveries of 35–50% for typical shale cases. Cases where the diffusion coefficient increases more steeply with M leave the square root profile at lower recovery values and obtain slower recovery with time systematically according to the steepness of the coefficient.
... x(t) actual imbibition length, m N r cumulative number of pores D f fractal parameter of pore size, dimensionless A d total pore area, m 2 β comparison of d min /d max , dimensionless P i imbibition pressures, MPa P f displacement pressure, MPa P c capillary pressure, MPa P π osmotic pressure in clay, MPa P g gas pressure of free gas, MPa P g0 initial gas pressure, MPa P a increased gas pressure from the desorption of adsorbed gas, MPa V im , V c fluid loss in shale gas well, shale sample, m 3 x f fracture half-length, m h reservoir thickness, m η m , η o , η c area ratio of fragile mineral, organic matter and clay mineral, per unit area, % φ, φ m , φ o , φ c total porosity and the surface porosity in fragile mineral, organic matter, clay mineral, % 2020; Zarringhalam et al., 2019;Rostami et al., 2020), the lattice Boltzmann method (LBM) (Arabjamaloei and Ruth, 2014;Warda et al., 2017;Zheng et al., 2018), pore network models (PNMs) (Øren et al., 1998;Øren and Bakke, 2003;Sorbie and Skauge, 2012;Zhou et al., 2012;Sun et al., 2016;Li et al., 2017;Qin and Brummelen, 2019;Qin et al., 2021a), and continuum models (Schmid and Geiger, 2012;Andersen et al., 2014;Jabbari et al., 2019). However, MD and LBM cannot be applied on a large scale and longtime interval (Wang and Zhao, 2019); PNM is complex with enormous amounts of data and is difficult to use in the descriptive combination of pore structures and hydrodynamic processes (Li and Zhao, 2012), and current continuum models lack the analysis of spontaneous imbibition mechanisms in shale gas wells (Wang and Zhao, 2019). ...
Spontaneous imbibition is the main factor that reduces the fracturing efficiency and damages gas production in shale gas wells, which is regulated by the gas–water interaction. Water (fracturing fluid) is imbibed spontaneously due to the characteristics of the water–rock interface, especially in shale with micro–nano–scale pores, while imbibition is not impeded but prevented by the pore structure resistance and original free gas compression as well as the increased fraction from the desorption of adsorbed gas. To accurately predict the fluid loss in a shale gas reservoir during fracturing, the imbibition pressures of the gas–water phase were comprehensively analyzed in this study, and the increased gas pressure from the desorption of adsorbed gas was first considered with other imbibition pressures, such as gas pressure from free gas compression, displacement pressure, capillary pressure, and osmotic pressure. By substituting the gas–water phase pressures into the Lucas–Washburn equation with the fractal characteristic of the capillary bundle, an imbibition model for micro–nano-scale pores in shale gas reservoirs considering gas–water interaction is established. The proposed model is compared with the traditional imbibition models and verified through imbibition experiments, and a case application to a shale gas well in the Sichuan Basin is undertaken. The results prove that the new fractal imbibition model performs better than the other models for imbibition estimation in reservoir shale, and it can accurately predict the fluid loss during the hydraulic fracturing process for shale gas wells.
