Oil-water Viscosity Ratio Research Articles

A computational study on transition mechanism of dripping to jetting flow in a flow‐focusing geometry

Abstract2D simulations have been performed to investigate flow regimes in a flow‐focusing geometry by changing the dispersed phase and continuous phase velocities. The dispersed phase is polydimethylsiloxane (PDMS), and the continuous phase is water. Simulations have been performed in a range of oil–water viscosity ratio from 3 to 50, and interfacial tension ranges from 0.0118 to 0.002 N/m. The walls of the microchannel are considered to be poly(methyl methacrylate) (PMMA) surfaces. The contact angle (θ) of an oil droplet in the presence of water wetting the PMMA surface is 140°. Our study observed two types of flow regimes, namely dripping and jetting, by changing the dispersed phase and continuous phase velocities. The sequential time steps of void fraction contour have been presented to explore the droplet formation mechanism. The droplet pinch‐off time and jet growth time have been calculated for the dripping and jetting regime, respectively. The outcomes are summarized in the form of a flow pattern map at a viscosity ratio of 12 and interfacial tension of 0.0118 N/m, which shows the transition boundary between dripping and jetting phenomena. The simulated transition boundary agrees well with the analytical solution available in the literature. The effect of oil–water viscosity ratio and interfacial tension on droplet size is also investigated. These findings will help understand different flow regimes and their transition in a flow focusing geometry and will directly apply to microfluidic platform‐based devices.

Two‐Phase Relative Permeability Curves of Bingham Heavy Oil Under Different Types of Wettability: A Theoretical Model

As an important and universal petrophysics of heavy oil reservoirs, the two‐phase flow ability inside porous medium is vital for heavy oil development. Utilizing the laminar flow theory and an ideal pore structure, especially cylinder model, the function of the relative permeability of heavy oil–water with water saturation is derived by incorporating the principles of momentum conservation and the characteristics of Bingham fluids, which was modified by validated experiment. Two‐phase relative permeability, considering heavy oil as non‐Newtonian fluid, is the function of water saturation, pore size, oil–water viscosity ratio, and yield stress. The results of the validated experiment show that the theoretical values calculated employing the modified equation exhibit better agreement with the experimental values, particularly when the viscosities of two‐phase fluid are great. The results of the modified two‐phase relative permeability show a decrease in water saturation interval corresponding to the two‐phase flow area and a smaller value of permeability at equal two‐phase relative permeability. The oil–water viscosity ratio in the hydrophobic pores affects the water‐phase relative permeability, although the magnitude of its influence diminishes as the viscosity ratio increases. The behavior of relative permeability in hydrophilic pores is the opposite of that in hydrophobic pores. This work can afford good application prospects for mobility control in multilayered reservoirs through the heterogeneous‐phase‐composite fluid. The saturations of the remaining oil and irreducible water also play a vital role in the prediction of permeability. The work can afford good application prospects for the flow behavior of Bingham heavy oil in pores with different types of wettability.

Fractal model of spontaneous imbibition in low-permeability reservoirs coupled with heterogeneity of pore seepage channels and threshold pressure

Spontaneous imbibition (SI) is an important mechanism for enhancing oil recovery in low-permeability reservoirs. Due to the strong heterogeneity, and the non-Darcy flow, the construction of SI model for low-permeability reservoirs is extremely challenging. Commonly, traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure (TP) on imbibition. Therefore, in this work, based on capillary model and fractal theory, a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established. On this basis, the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil. The proposed new SI model was verified by imbibition experimental data. The study shows that for weakly heterogeneous cores with permeability of 0–1 mD, the traditional SI model can characterize the imbibition process relatively accurately, and the new imbibition model can increase the coefficient of determination by 1.05 times. However, traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10–50 mD. The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem, and the determination coefficient is increased from 0.344 to 0.922, which is increased by 2.68 times. For low-permeability reservoirs, the production of the oil in transitional pores (0.01–0.1 μm) and mesopores (0.1–1 μm) significantly affects the imbibition recovery, as the research shows that when the heterogeneity of pore seepage channels is ignored, the oil recovery in transitional pores and mesopores decreases by 7.54% and 4.26%, respectively. Sensitivity analysis shows that increasing interfacial tension, decreasing contact angle, oil–water viscosity ratio and threshold pressure will increase imbibition recovery. In addition, there are critical values for the influence of these factors on the imbibition recovery, which provides theoretical support for surfactant optimization.

Numerical Simulation of Fracture Flow Interaction Based on Discrete Fracture Model

Hydraulic fracturing of horizontal wells is a common method for enhancing production in low-permeability and unconventional oil reservoirs. However, due to the interference between fractures, issues such as decreased production and water channeling often occur in hydraulic fracturing of horizontal wells. Therefore, studying how to mitigate the effects of fracture interference is of great significance for optimizing hydraulic fracturing design and improving oil and gas recovery rates. In this paper, an oil–water two-phase discrete fracture model was established, and the grid dissection was carried out by using the optimization method to obtain a triangular grid that can finely characterize the fracture in geometry. Then, typical discrete fracture models were designed, and the influences of the fracture permeability ratio, absolute fracture scale, oil–water viscosity ratio, and fracture length on the fracture flow interference were investigated separately. The degree of fracture interference was evaluated using the fracture fractional flow rate ratio, remaining oil saturation, and sweep efficiency. This study verified fracture interaction and identified that the threshold value of the fracture permeability ratio is 9 to classify the degree of interference. Sensitivity analysis shows that the absolute size of the fracture has a significant impact on fracture interference, while the impact of the oil–water viscosity ratio and fracture length on fracture interference is relatively small.

Study on effect of viscosity on thickness of boundary layer in tight reservoir

It has become a consensus that viscosity has an important impact on boundary layer of tight reservoirs. However, there are few quantitative studies on the effect of viscosity on boundary layer by core experiments. NMR analysis based on high-speed centrifugal gas-water and gas-oil displacement and low-temperature adsorption experiment were implemented in this study on typical tight reservoir parallel cores of Ordos and Bohai Bay basins. Total bound water/oil saturation, specific surface area and ratio of micro pore of the reservoir quantitatively were finally obtained, which were used for calculating irreducible water/oil film thickness of reservoir and analyzing influence of viscosity on movable oil and boundary layer. Research show that, movable oil saturation of core saturated high viscosity oil is 23.92% and 18.61% lower than that of core saturated low viscosity oil and water respectively, and effective seepage space is greatly reduced. The lower permeability reservoir has, the greater reduction movable space with high viscosity oil of reservoir owns. The average bound water film thickness of Ordos and Bohai Bay basin cores is 17.74 nm and 16.99 nm, respectively. The average bound oil film boundary of core in Ordos Basin is 20.72 nm. The average thickness of high viscous oil film of core in Bohai Bay basin is 38.10 nm, and the thickness of low viscosity oil film is 18.80 nm. The oil-water viscosity ratio in Ordos Basin is small, and oil-water film thickness is close, indicating that fluid viscosity has little influence on boundary layer thickness of target reservoir. The low viscosity oil-water viscosity ratio in Bohai Bay basin is small, and oil-water film thickness is close. The thickness of high viscosity oil film is more than twice that of low viscosity oil film and water film. When the oil viscosity is higher than 8.9 mPa s, thickness of boundary layer will be greatly affected, leading to a significant reduction of effective seepage throat, a significant increase of seepage resistance and development difficulty.

Research on the seepage mechanism and influencing law of shale oil fracturing

In order to clarify the characteristics of oil and water seepage during shale oil fracture, the tight reservoir in Jimsar Basin, Xinjiang Province was an example to get the characteristics of two-phase seepage between fracturing fluid and shale oil during fracture through the core experiment during injection. Effects of initial water saturation, viscosity ratio of oil to water, injection pressure, core permeability about imbibition displacement efficiency of fracturing fluid were systematically studied by using an improved one-dimensional core displacement device from Xinjiang tight sandstone artificial core under indoor conditions. The research results show that under constant pressure of 1 MPa, initial water saturation of the core is 43%, permeability is 0.12 md, and oil-water viscosity ratio between shale oil and fracturing fluid is 3:1, drive efficiency about fracturing fluid was about 23.5%. At the same time, results indicated at certain injection conditions, when initial water saturation increases, the permeability gradually decreases, and the viscosity ratio of oil to water gradually increases, the lower drive efficiency of fracturing fluid was, the worse its effect is. This conclusion could be used in the process of shale oil tight reservoirs.

The prediction of spontaneous oil-water imbibition in composite capillary

In view of the classical Lucas-Washburn equation, which can only describe the spontaneous imbibition of single wetted capillary, a tilted composite capillary model with circular cross section, composed of different wettability capillary wall was established. The model can describe the spontaneous oil-water imbibition of water-wet capillary, oil-wet capillary and mixed wetting capillary. Through numerical solution of the model equation, it is found that the component content of the capillary walls, the capillary radius and the oil-water viscosity ratio have great effects on the spontaneous oil-water imbibition. Effects of capillary inclination angle and inertia force on spontaneous oil-water imbibition are related to the capillary scale. Effects of capillary inclination angle and inertia force can be ignored in small radius capillary, while effects of inclination angle and inertia force can not be ignored in large radius capillary. • A composite capillary model composed of different wet walls was established. • Scale effects on spontaneous oil-water imbibition was considered. • The model is applicable to water-wet, oil-wet, mixed-wet pores.

Oil secondary migration simulation in tight reservoir and fingering factors analysis

In the tight reservoirs, the oil accumulation is characterized by ambiguous trap boundaries, complicated oil distribution and nano-scale pore-throat interconnection system. As one of significant process for understanding the oil trap in the tight reservoir, oil migration from source rocks to reservoirs is the key concern by geoscientist. Investigating the immiscible two-phase fluids displacement in porous media, especially the fingering problem during the hydrocarbon migration, has always been a challenge scientific topic. This study establishes PNMs (Pore Network Model) with multiple viable parameters. A fluid migration numerical program is built for the flow study by modifying Poiseuille equation. Sensitive studies have been conducted by several dimensionless numbers to investigate the control factors of the flow behavior. Five factors are identified as the key factors on the migration mode: 1) Fluid viscosity ratio; 2) Interface tension force; 3) Fluid density; 4) Pore structure of sediments; 5) Capillary number. Oil migration behavior is affected by pressure domain, buoyancy, and resistance forces, such as capillary resistance and viscous forces. As the distribution fractal dimension increases with a given viscosity ratio, the width of the front edge of oil-water interface gradually expands. Oil saturation increases in parallel with a rising capillary number. During the simulation, Haines Jump phenomenon is observed. When the capillary number increases, oil migration gravitates towards piston-like displacement. As the oil-water viscosity ratio increases, the front width reaches its maximum at a particular point in time, and plateaus.

A new computational approach to predict hot-water flooding (HWF) performance in unconsolidated heavy oil reservoirs

In this study, a new computational approach for predicting the performance of hot-water flooding in unconsolidated heavy oil reservoirs is presented. The proposed model predicts the changes in the oil–water viscosity ratio (μo/μw) by estimating the reservoir temperature distribution through porous media. Then, the dimensionless and normalized variables were redefined to forecast water fractional flow as a function of temperature and water saturation. Moreover, the proposed approach predicts the cumulative heavy oil production and recovery factor more accurately and with less required input data and runtime compared to commercial simulators such as CMG-STARS (computer modeling group), etc.Estimated results were validated using laboratory experimental data and numerical simulation outputs. A total of 4 core-flooding experiments were conducted at injection temperatures of 20–80 °C. Numerical simulation models based on the laboratory HWF tests were developed in CMG-STARS. The water–oil relative permeability curves were tuned to history match simulation results with those obtained from experiments.Finally, the predicted cumulative heavy oil productions, recovery factors (RF) and production rates by the proposed approach were compared to the results from the laboratory sandpacked tests and simulation runs for three scenarios. The relative errors between heavy oil recovery factors obtained from computational approach and experimental data were measured to be 11.01%, 14.51% and 13.69% for injection temperatures of 40, 60 and 80 °C, respectively.

Research of Microbial-gel Combined Flooding Technology of Ba19 Block in Baolige Oilfield

Bal9 fault block is a medium-high temperature (58°C) reservoir in Baolige Oilfield. The crude oil is characterized by poor physical properties which has high wax and high gum content. The oil-water viscosity ratio is high and this leads to a low water flooding efficiency. The reservoir heterogeneity is high and the contradictions between layers are prominent. According to the characteristics of the oilfield, a microbial-gel combined flooding technology with the microbial flooding as the main body and the gel flooding as the auxiliary is developed to improve the overall development effect of the oilfield water flooding. Microorganism can improve the physical properties of crude oil, and appropriate gel flooding should be carried out to enlarge the sweep volume of microorganism work and improve the effect of microbial-gel combined flooding. By continuous application of this technology in Baolige Oilfield, the concentration of microorganisms is maintained at about 106 a/ml, and the whole microbial field is formed. The average annual reduction rate of crude oil is 48.1%. The microbial-gel combined flooding technology is verified to increase the recovery factor by 9.5%. Since the combined flooding was carried out in 2010, the recoverable reserves of the Ba19 block increased by 630,600 tons.

On the Imbibition Model for Oil-Water Replacement of Tight Sandstone Oil Reservoirs

A model suitable for evaluating a tight sandstone reservoir is established. The model includes two oil-water replacement modes: capillary force mode and osmotic pressure mode. The relationship between oil-water displacement rate and dimensionless time under different parameters is drawn considering the influence of capillary force, osmotic pressure, production pressure difference, and starting pressure gradient. Results indicate that the higher the relative permeability of the water phase, the lower the relative permeability of the oil phase, the smaller the oil-water viscosity ratio, and the higher the oil-water replacement rate. The relative permeability of the water phase also affects the infiltration stabilization time. Low salinity fracturing fluid infiltration helps to improve the oil-water replacement rate.

Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change

Injection water temperature is often different from that of the reservoir during water injection development in the tight reservoir. Temperature change causes different fluid properties and oil-water interface properties, which further affects the imbibition process. In this paper, a matrix-fracture non-isothermal oil-water imbibition flow model in tight reservoirs is established and solved by the finite element method based on the phase-field method. The ideal inhomogeneous rock structure model was used to study the influence of a single factor on the imbibition. The actual rock structure model was used to study the influence of temperature. The mechanism of temperature influence in the process of imbibition is studied from the micro-level. It is found that the imbibition of matrix-fracture is a process in which the water enters the matrix along with the small pores, and the oil is driven into the macropores and then into the fractures. Temperature affects the imbibition process by changing the oil-water contact angle, oil-water interfacial tension, and oil-water viscosity ratio. Reducing oil-water contact angle and oil-water viscosity ratio and increasing oil-water interfacial tension are conducive to the imbibition process. The increase in injection water temperature is usually beneficial to the occurrence of the imbibition. Moreover, the actual core structure imbibition degree is often lower than that of the ideal core structure. The inhomogeneous distribution of rock particles has a significant influence on imbibition. This study provides microscale theoretical support for seeking reasonable injection velocity, pressure gradient, injection temperature, and well-shutting time in the field process. It provides a reference for the formulation of field process parameters.

A novel method to determine the thief zones in heavy oil reservoirs based on convolutional neural network

The tracer breakthrough curve tends to be unimodal in heavy oil reservoir due to high oil-water viscosity ratio, which makes it difficult to classify thief zone (TZ) in these reservoirs using tracer breakthrough curve. To solve the problem, the paper applies the convolutional neural network (CNN) to achieve fast and accurate classification of TZ in heavy oil reservoir. The tracer flow analytical model is established by equating TZ with the flow tubes that satisfy the Hagen-Poiseuille equation. Then, 3000 tracer breakthrough curves are generated by the model as sample. Additionally, one-hot encoding method is applied to deal with these sample curves. Through the orthogonal design, the optimal combination of hyperparameters are determined to establish an OD-CNN model. According to the results, the number of convolutional layers is the most significant influencing factor in the accuracy of OD-CNN. Besides, the optimal hyperparameter combination for OD-CNN is detailed as follows. The number of convolutional layers is 4, the dropout rate is 0.6, the initialization method is Xavier normal, the optimizer is Adam, and the activation function is ReLU. Compared with random forest (RF) and K-means, the accuracy of OD-CNN on the training set is 94.67%, which is higher than 82.30% of RF and 75.63% of k-means. Moreover, OD-CNN can correctly classify 89 of the 100 curves from the oilfield indicating the reliability of OD-CNN. Thus, applying orthogonal design to OD-CNN can avoid the blindness of hyperparameter combination optimization and significantly reduce computing time.

New Understanding of the Retention Mechanism of “Residual Oil in the Form of Oil Droplets (or Oil Column)”

Based on the oil-water two-phase liquid flow model, with equal-viscosity and water-wet unequal-diameter parallel channels, the previous researches on the retention mechanism of “residual oil in the form of oil droplets or oil column” during water flooding, and they stated that “residual oil in the form of oil droplets (or oil column)”can be retained in both large and small channels. Re-examination of the model shows that “residual oil in the form of oil droplets (or oil column)” cannot be retained in large channels, but only in small channels. By changing the wettability and oil-water viscosity (variable viscosity) of this model, the small channel retention characteristics of “residual oil in the form of oil droplets (or oil column)” remain unchanged. This research shows that: (1) When the oil-water phase flows in the unequal-diameter parallel channel model, the flow velocity of the large channel is always greater than the small channel, and the “residual oil in the form of oil droplets (or oil column)” is always retained in the small channel. (2) The retention of small channels of “residual oil in the form of oil droplets (or oil column)” is general, and is not affected by changes in factors such as pressure difference, capillary force, total flow, wettability, and oil-water viscosity ratio.

Hydrodynamics Study of Oil–Water Flow in Coiled Flow Inverter

The present numerical study is an effort to examine the hydrodynamics characteristics of two immiscible liquids (oil and water) flowing in different tubes. i.e., straight, coiled and Coiled Flow Inverter (CFI) tube of equal dimensions. CFI is a novel device in which fluid flow inversion takes place at uniform interval length of tube. The effect of oil-water viscosity ratio (µoil/µwater = 1.6 and 30) on velocity contours, phase distribution and pressure drop in the different tubes were investigated. The present work show that flow pattern of oil–water flows was changed from stratified to annular flows at higher water volume fraction for µoil/µwater = 1.6 in CFI. Phase inversion of oil–water flow was observed in CFI at higher viscosity ratio (µoil/µwater = 30). There was remarkable reduction in pressure drop with the increment in volume fraction of water flowing in coiled as well as CFI. CFI being more compact can be efficiently used in industries as chemical reactor, heat exchanger, mixer, etc.

Study on Water Ridge Variation of Horizontal Wells in Bottom Water Reservoir

X oilfield is a typical strong bottom water reservoir in Bohai Sea. It is developed by single sand body horizontal well. The edge and bottom water of the reservoir is active and natural energy development mode is adopted. At present, the comprehensive water cut of the oilfield is more than 96%, and has entered the stage of high water cut oil recovery. At present, fluid extraction from old wells and new adjustment wells are the main ways to increase oil production. With the deepening of development, the distribution of underground remaining oil is becoming more and more complex. In order to further improve the implementation effect of adjustment wells, the study of residual oil distribution law is increasingly important, and the study of water ridge morphology of horizontal wells in bottom water reservoir has an important guiding role in the study of remaining oil distribution. The main contents of this paper are as follows: the influence of horizontal well spacing, vertical and horizontal permeability ratio, single well liquid production, vertical position of horizontal well, oil-water viscosity ratio, water cut and interlayer on water ridge morphology. These understandings can effectively guide the deployment and optimization of adjustment wells. It provides technical support for the prediction of watered out thickness and optimization of adjustment well layout scheme in X oilfield, and guides the further development and production of the oilfield.

Mechanisms of water flooding characteristic curve upwarping at high water-cut stage and influencing factors

Water flooding is widely used in oilfield development as a secondary recovery method owning to its effectiveness and economic feasibility. When the injected water breaks through the production well, water is produced with oil. The water flooding characteristic curve is an important method for predicting recoverable reserves, recovery rates, and oilfield development dynamics. It reflects the oil-water composition of oilfield-produced fluids. The linear relationship between the relative permeability ratio ( K ro/ K rw) and water saturation ( S w) in semi-log coordinates is a theoretical basis for the water flooding characteristic curve. However, many mine practices and core experiments show that the relationship deviates from a straight line at a high water-cut stage, and the water flooding characteristic curve shows an upward trend. The upwarping phenomenon of the water flooding characteristic curve is related to the flow state of the oil/water phase. The continuum description, Darcy’s law, fails to predict and describe the transport of scattered residual oil in pore spaces. Many previous studies tried to obtain a non-linear relationship between ln( K ro/ K rw) and S w at the high water-cut stage by different methods, including fitting the experimental data. Though there are many studies on the upwarping phenomenon of water flooding characteristic curve, few studies focus on the mechanisms of this phenomenon. In addition, the effects of important development parameters, such as wettability and water-oil viscosity ratio, on the upwarping phenomenon are unclear. In this study, the Navier-Stokes equation is coupled with the phase field method to describe the water flooding processes in porous media and to track the two phase interface. The effects of wall wettability and oil-water viscosity ratio on the flow patterns were analyzed by numerical simulations. In addition, the critical water cut when the relationship between ln( K ro/ K rw) and S w deviates from the straight line was investigated. The results show that residual oil is mainly scattered at the high water-cut stage, and the flow capacity of oil rapidly decreases, which leads to the upwarping phenomenon of the water flooding characteristic curve. The critical water cut is different under different wetting conditions. Due to the effect of capillary force, the flow capacity of oil is stronger, and more oil can be displaced out through the imbibition process at the high water-cut stage in water-wet porous media, and the critical water cut increases when wettability changes from oil-wet to water-wet. The flow patterns of oil and water are different at different oil-water viscosity ratios. At the low viscosity ratio, the displacement front is more uniform, and the removal of oil by water mainly depends on expanding the sweeping area at the high water-cut stage. For the high viscosity ratio case, clear fingers of injected water can be observed during the flooding process, and it is difficult for the injected water to enter the areas which were not previously swept at the high water-cut stage. The viscous fingering phenomenon enhances the ineffective displacement of the injected water. The relationship between ln( K ro/ K rw) and S w deviates from a straight line at a lower water cut when the oil-water viscosity ration is high.

Multiphase flow in tight sandstone: An improved application for 3D intermingled fractal model

Abstract Multiphase displacement in tight sandstone is fundamental and critical for tight oil production. Micropores dominate the pore space in tight sandstone. Microscopic mineral components in micropores substantially influence the multiphase displacement behavior. Pore size distribution exhibits a self-similar or fractal property, similar to inorganic mineral grains. Utilizing fractal theory eases the rebuilding of the flowing space and calculation of relative permeability. As an improvement of previous work, we successfully extended the 3D intermingled fractal model (3D IFM). The extended 3D IFM can evaluate multiphase flow behavior in tight sandstone, considering fractal characteristics of pore size distribution and mineral grain distribution. The fractal information of pores and mineral properties are obtained by scalable scanning electron microscopy (SEM) and energy dispersive spectroscopy(EDS) images, respectively. This method is useful and reliable for calculating relative permeability and residual saturation. The method is also successfully used to evaluate the influence of oil-water viscosity ratio, mineral components and formation depth on multiphase displacement behavior, proving its convenience and potential in rapidly evaluating multiphase displacement behavior in tight sandstone.

Method of moderate water injection and its application in ultra-low permeability oil reservoirs of Yanchang Oilfield, NW China

Abstract To explore the method of improving development effect and solving the problem of water breakthrough and water out for ultralow permeability fractured reservoirs, an indoor evaluation method of dynamic imbibition for fracture-matrix system was established taking the Chang 8 reservoir in southern Yanchang Oilfield as a research target. Key factors for the imbibition effect were obtained, an imbibition's rate expression was obtained, a model considering the double effects of imbibition-displacement was built and optimal injection and production parameters for the research area were obtained as well. The results show that an optimum displacement rate that maximizes the oil displacement efficiency exists in the water displacing oil process, and the optimal displacing rate becomes smaller as the permeability decreases. The imbibition displacement efficiency increases as the reservoir quality index and water wettability index of rock become bigger. But the larger the initial water saturation or oil-water viscosity ratio is, the smaller the imbibition displacement efficiency is. The optimal injection-production ratio for the Chang 8 reservoir of southern Yanchang Oilfield is 0.95, and the predicted recovery is 17.2% when the water cut is 95%, it is 2.9% higher than the recovery of conventional injection-production ratio 1.2. By using the moderate water injection technique based on the double effects of imbibition-displacement mechanism, the water injection development effect for the ultra-low permeability fractured reservoirs can be improved significantly.

A further study on Welge equation

Buckley–Leverett theory and Welge equation is one of the most widely used methods for predicting fluid transport in porous media. However, the average water saturation in Welge equation is a function of both water saturation and water cut, which is inconvenient to be used. While the linear relationship (the slope is 2/3) of the average water saturation and outlet water saturation proposed by Зфрос provides a simple method the oil–water viscosity ratio greatly limits the application. In this paper, based on the analytical relative permeability model and Welge equation, a new average water saturation equation with a variable (the outlet water saturation) was derived and applied in some cases under different relative permeability parameters and oil–water viscosity. Moreover, a simplified equation was proposed through certain data regression. Thus, the coefficient calculation method of the linear function was introduced based on the actual production data. Results showed a nonlinear relationship between the average water saturation and outlet water saturation, which is mainly related to water and oil relative permeability, and oil–water viscosity ratio. For the outlet water saturation higher than frontal saturation, the equation can be simplified to a linear function, which is the derivation of Зфрос equation. However, it is a function of both relative permeability and oil–water viscosity ratio instead of a constant slope of 2/3. In view of the fact that oil–water viscosity is mostly bigger than 10 in most reservoirs, the new model is an important supplement to Buckley–Leverett theory and Welge equation.