Pre-Darcy Flow Research Articles

A dynamic Pre-Darcy model and its application in the numerical simulation of enhanced geothermal system

Numerical simulations of Enhanced Geothermal Systems (EGS) currently primarily depend on the Darcy model, neglecting pre-Darcy flow in the matrix rock and the impact of temperature on pre-Darcy flow. This paper introduces a dynamic pre-Darcy model that accounts for the influence of temperature, deriving from the capillary flow model and boundary layer theory. This model is able to consider how temperature variations affect both the thickness of the boundary layer and the yield stress of the fluid. The reliability of the dynamic pre-Darcy model is validated through experimental data, and comparison with both static pre-Darcy and Darcy models demonstrates its superior ability to accurately capture the influence of temperature on pre-Darcy flow. Subsequently, a thermal-hydraulic simulation methodology incorporating the dynamic pre-Darcy model is developed to characterize mass and heat transfer between the matrix and fracture based on the framework of the embedded discrete fracture model (EDFM), which is further validated with analytical and numerical solutions. In the simulation of single-fracture case, we explore the impact of the dynamic pre-Darcy flow on mass and heat transfer between the matrix and fracture. Field-scale numerical simulations for EGS further demonstrate that the Darcy model tends to overestimate both production temperature and total extracted energy. In contrast, the static pre-Darcy model generally underestimates these metrics. The dynamic pre-Darcy model, however, provides more accurate and reasonable predictions.

Effect of movability of water on the low-velocity pre-Darcy flow in clay soil

Water seepage in soil is a fundamental problem involving various scientific and engineering fields. According to the literature, low-velocity water seepage in low-permeability porous media, such as clay, does not follow Darcy's law, also known as pre-Darcy flow. The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow. However, this view lacks direct solid evidence. To investigate the pre-Darcy water flow in clay, head permeability experiments are conducted on six clay samples with different densities. The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law. A clear nonlinear relationship between flow velocity and hydraulic gradient is observed. Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient, which is 10–12 for the Albic soil with dry density between 1.3 g/cm3 and 1.8 g/cm3. According to the disjoining pressure theory, immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay. The results indicate that the percentage of movable water ranges from 39.7% to 59.3% for the six samples at a hydraulic gradient of 1. As the hydraulic gradient increases, the percentage of moveable water also increases. Additionally, there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient. Furthermore, a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established. The results of this study suggest that water adsorption on the pore wall not only affects the water movability, but is also closely related to the pre-Darcy flow phenomenon in clay.

The roles of microstructure and water mobility in pre-Darcy flow formation in saturated clay soil

Water flow in saturated clay soil at low hydraulic gradients usually occurs via pre-Darcy flow. The occurrence of the pre-Darcy flow phenomenon is attributed to the adsorption of water on pore walls via surface forces. However, a clear understanding of the amount of water that is movable in saturated clay soil and the distribution of movable/immovable in the microstructure of clay soil is lacking. Furthermore, it is difficult to accurately evaluate the effect of water mobility on the seepage characteristics of clay soil. To investigate the effects of water mobility and pore microstructure on pre-Darcy flow in clay soil, nine clay samples were used to conduct constant head permeability experiments. The results showed that the seepage of water in clay deviated from that predicted by Darcy's law, and with increasing hydraulic gradient, the apparent water permeability first increased and then tended to remain constant. The porosity ϕ, average pore radius rp, sorting coefficient Sp, mean pore radius Dm, dry density ρ and tortuosity τ had major influences on the stable apparent water permeability ks. In contrast, the influences of maximum pore radius and median pore radius on ks were relatively weak. Macropores (>1.0 μm) and mesopores (100–1000 nm) were the dominant pore types in the clay and accounted for almost 80 % of the overall porosity. The water in saturated clay can be divided into four types according to interfacial forces. The results showed that weakly bound water (in the outer layer) was the main type of water in the clay. Among the four types of water, ks had the strongest correlation with the proportion of free water. The mobility of water was affected by coupling between interfacial forces and hydraulic gradients. The movable water content was closely related to the permeability of the clay.

A mathematical model for pre-Darcy flow in low permeability porous media with stress sensitivity and the boundary-layer effect

Pre-Darcy flow is widely found in many naturally porous media, such as low-permeability clay. Nonflowing liquid boundary layers strongly influence fluid flow in low-permeability porous media. There is evidence in the literature that the porosity and permeability of low-permeability porous media change with variations in the effective stress, which is called stress sensitivity. In this paper, a new mathematical model for pre-Darcy flow in low-permeability porous media is developed and validated with experimental data from the literature. The nonflowing boundary layer thickness can be obtained from the proposed model instead of the empirical equation. First, an equation for calculating the pore radius with stress sensitivity is derived. Two parameters εp and εr are defined to calculate the nonflowing boundary layer thickness. Second, based on the capillary bundle model, the apparent flow velocity and apparent liquid permeability of the porous media are determined. Finally, the stress sensitivity and boundary-layer effects on the apparent flow velocity and apparent liquid permeability are analyzed. The research results show that the effect of stress sensitivity on apparent flow velocity increases with increasing pore compressibility. When the pore compressibility Cp>0 MPa−1, the apparent liquid permeability increases continuously with increasing pressure gradient. When the pore compressibility Cp=0 MPa−1, the apparent liquid permeability continues to increase with increasing pressure gradient. The apparent liquid permeability eventually tends to a constant value. The apparent flow velocity decreases with εp, and εr decreases at a given pressure gradient. The larger εp and εr are, the faster the rate of increase in the apparent liquid permeability with increasing pressure gradient. The proposed model can estimate the apparent flow velocity at different pressure gradients with a high accuracy. This work is important for understanding flow phenomena in low permeability porous media, such as landslides caused by seepage of water in clay.

Effects of Centrifugal Force on Performance of Heat Pipe

The effects of rotation (centrifugal force) and inclination on the performance of a 6.0-mm-diameter heat pipe are experimentally examined. Both static and dynamic tests are performed. The capillary structure is sintered copper powder, and the fluid is deionized water. The static test ranges from 1.0 to , and the thermal resistance and maximum heat transfer rate are affected by the inclination angle. The dynamic test spans from 1.75 to . The maximum value of gravity is provided by the centrifugal force generated by a rotating platform. The test results indicate no appreciable difference amid static and dynamic tests when the centrifugal force is below . The departure starts to increase for a further increase of centrifugal force. For static operation, the existing correlation can reasonably predict the maximum heat transfer rate of the heat pipe under various inclination angles. Still, they cannot provide a good prediction when the maximum value of gravity of the dynamic test exceeds . By considering the second-order effect of the Darcy equation and combining with the accurate measurement of permeability of the pre-Darcy flow of the sintered structure. The prediction after correcting the modified correlation can predict the dynamic test results well.

The coupling effects of pore structure and rock mineralogy on the pre-Darcy behaviors in tight sandstone and shale

The pore structure and mineral composition play a crucial role in controlling the water flow behaviors of low-permeability media, which is characterized by threshold pressure gradient (TPG) and nonlinear flow curve. To figure out the coupling effects of these two factors on pre-Darcy flow regimes, water flow experiments were conducted on four tight sandstones, three shales and one fractured shale. The results indicate that both the TPG and pseudo threshold pressure gradient (PTPG) decrease with an increase in total porosity and macropores porosity. The variation of the nonlinear exponent (n) with total porosity and macropore porosity can be described by an exponential function with three parameters. The clay minerals and brittle minerals exert completely opposite influence on the variation of pre-Darcy flow parameters (PTPG, TPG and n). Both TPG/PTPG and n increase with increasing clay content while reduce with increase in the brittle minerals content. Theoretical analyses based on the disjoining pressure demonstrate that immovable water and electro-viscous effect are mainly responsible for water flow deviating from Darcy's law in tight sandstone and shale. Calculation results show that the proportion of immovable water of intact samples ranges from 23.46% to 89.73%, the movable water content ranges from 10.27%–76.54%. The pre-Darcy flow parameters exponentially increase with increase in immovable water content while exponentially decrease with increasing proportion of movable water. For the shale sample used in this work, the immovable water and electro-viscous effect contributing to the pre-Darcy flow account for 81.11%–90.35% and 9.58%–18.51%, respectively. The different flow regimes are controlled by the pore diameter and the thickness of water with shear fluidity. If the diameter of interconnected pores is larger than 10 μm, the Darcy flow regime dominates. When the diameter of minor pore throat of the flow channels are less than 33.82 nm for sandstones and 37.68 nm for shales, the movement of water in this flow channel would generate the TPG.

Experimental study of non-Darcy flow characteristics in permeable stones

Abstract. This study provides experimental evidence of Forchheimer flow and the transition between different flow regimes from the perspective of the pore size of permeable stone. We first carry out seepage experiments on four kinds of permeable stones with mesh sizes of 24, 46, 60 and 80, corresponding to mean particle sizes (50 % by weight) of 0.71, 0.36, 0.25 and 0.18 mm, respectively. The seepage experiments show that an obvious deviation from Darcy flow regime is visible. In addition, the critical specific discharge corresponding to the transition between flow regimes (from pre-Darcy to post-Darcy) increases with increasing particle size. When the “pseudo” hydraulic conductivity (K, which is computed as the ratio of the specific discharge q and the hydraulic gradient) increases with increasing q, the flow regime is denoted pre-Darcy flow. After q increases to a certain value, the pseudo hydraulic conductivity begins to decrease; this regime is called post-Darcy flow. In addition, we use the mercury injection technique to measure the pore size distributions of four permeable stones with different particle sizes. The mercury injection curve is divided into three stages. The beginning and end segments of the mercury injection curve are very gentle, with relatively small slopes, while the intermediate mercury injection curve is steep, indicating that the pore size in permeable stones is relatively uniform. The porosity decreases as the mean particle sizes increases. The mean pore faithfully reflects the influences of the particle diameter, sorting degree and arrangement mode of the porous medium on seepage parameters. This study shows that the size of pores is an essential factor for determining the flow regime. In addition, the Forchheimer coefficients are discussed. The coefficient A (which is related to the linear term of the Forchheimer equation) is linearly related to 1/d2: A=0.00251/d2+0.003. The coefficient B (which is related to the quadratic term of the Forchheimer equation) is a quadratic function of 1/d: B=1.14×10-61/d2-1.26×10-61/d. The porosity (n) can be used to reveal the effects of the sorting degree and arrangement on the seepage coefficients. A larger porosity leads to smaller coefficients A and B for the same particle size.

Numerical modeling of fluid flow in tight oil reservoirs considering complex fracturing networks and Pre-Darcy flow

Multistage hydraulic fracturing for horizontal wells is extensively applied in the exploitation of tight oil reservoirs. Complex fracture networks with different scales are created and hydrocarbon flowing in the matrix demonstrates a Pre-Darcy characteristic due to a strong interaction of rock and fluids in nanoscale pores. The modeling of complex fracture networks and a Pre-Darcy effect is required in numerical simulation of tight oil reservoirs. In this paper, stochastic fracture networks are employed to mimic actual fracturing networks according to the corresponding probability density functions (PDFs), and microseismic events are used to constrain the locations of fractures. The numerical simulation for tight oil reservoirs is developed by considering complex fracture networks and the Pre-Darcy effect based on an embedded discrete fracture model (EDFM) framework. Finally, the influences of fracture network properties including isolated fractures, connected fracture networks and the Pre-Darcy effect on well production are investigated via integrating the developed fracture network generation and tight oil numerical simulator. The results indicate that for isolated fractures with no direct connection with a wellbore, there is little influence on well performance. The influence becomes more obvious when isolated fractures connect to a wellbore, and an increase in fracture length and conductivity can enhance well performance especially when fractures lie off streamline lines. Similarly, for a connected fracture network, an increase in fracture network properties (number, length and conductivity) can promote well performance and fractures perpendicular to a horizontal wellbore can generate a maximal flow rate compared with other fracture orientations. The fracture network connectivity plays an important role in the fluid flow, and there are good relationships between well production and two proposed parameters, which can be treated as candidates to characterize the flow characteristics in fractured reservoirs.

Numerical simulation for hydrocarbon production analysis considering Pre-Darcy flow in fractured porous media

Fracture has significant effect on the production of hydrogen–carbon compound reservoirs. Underground fluid always flows through different spaces which involves different flow patterns. In this study, the embedded discrete fracture method (EDFM) to couple the flow in matrix and fracture is introduced. The Darcy flow is considered in fracture while the Pre-Darcy flow is employed in matrix. The model of two phase flow problem is established. The governing equations are coupled through multiple spatial scales. The structured mesh is applied to discrete the whole matrix domain. The fracture grids are embedded to the matrix meshes. The verification shows good accuracy of the fully implicit method for solving the model. Based on the numerical simulation, the results of 1D, 2D flow problems considering Pre-Darcy flow are presented. The characteristic of pressure and saturation is analyzed. Some numerical experiment examples are conducted to demonstrate the capability of the method including multiple wells system, complex fracture problem, and hydraulic fractured horizontal well system. Furthermore, we extend the model to 3D transport problem. The newly developed numerical simulation method improves the limitations of EDFM in Pre-Darcy flow. The newly developed simulation method can be taken as an effective tool for hydrocarbon production analysis when Pre-Darcy flow happens in fractured porous media.

The effect of the viscosity-dependent boundary layer on tight oil flow behavior in CO2 Huff-Puff processes: A unified dimensional Pre-Darcy flow model

There are numerous percolation studies of unconventional reservoirs showing that in tight or low-permeability formations, the oil flow behavior could be described by the Pre-Darcy mechanism. However, for the CO 2 Huff-n-Puff operations, the most presented low-velocity Pre-Darcy flow models may result in an erroneous evaluation due to the intensive boundary layer thickness changes caused by the CO 2 extraction and dissolution. In this paper, with multiple parameters fitting the seepage experimental results of the studied area, a unified dimensional Pre-Darcy flow model for CO 2 enhanced oil recovery (EOR) is derived from the classic Poiseuille model. Then, the proposed flow model is applied in the compositional simulator for analyzing the viscosity-dependent boundary layer (VDBL) effect, applicability evaluation in Huff-Puff EOR, and field history matching. The results indicate that the VDBL effect improves the oil mobility in injection periods and lowers the residual oil saturation at the front of the CO 2 convection-diffusion area in reproduction periods. Additionally, the nonlinear parameter α and the shape parameter β enhance the proposed model's applicability for the Huff process and the Puff process respectively. Finally, by adjusting the parameters α and β for different permeability intervals of the geological model, the flow model is successfully applied in the oil production matching of the Y6 well, which exhibits its reliability in the history matching. • A unified dimensional flow model is derived from the classic Poiseuille model to characterize the oil seepage behavior. • The proposed flow model is applied in the compositional simulator for analyzing the VDBL effect. • The flow model is successfully applied in history matching of the Songliao tight field in China to exhibit its reliability.

The dynamic convection-diffusion effect of CO2 Huff-n-Puff on Pre-Darcy flow behavior

Many reports have presented that in tight matrix, oil phase obeys Pre-Darcy flow. However, for the CO2 Huff-n-Puff development, it is an outstanding challenge to understand the changing oil properties could influence the nonlinear degree in the Pre-Darcy percolation process. As the dynamic Pre-Darcy flow model has been presented for describing the nonlinear degree variation, the dynamic convection-diffusion effect of the injected gas on the percolation behavior has become a key issue. In this paper, based on the fluid-rock experiments of the studied area, the near miscible system of CO2-injected mixtures in nanopores is firstly investigated. Then, the dynamic Pre-Darcy flow numerical simulation is launched for gas diffusion coefficient evaluation, convection-diffusion effect on Pre-Darcy flow behavior and field development program optimization. The results indicate that considering the dynamic change of the nonlinear degree in CO2 injection process, the diffusion coefficient for the studied area is set as 0.00093 cm2/s by fitting the experiment and field data. Additionally, based on the detailed discussion on the DDPC, pore pressure, and oil saturation, it could be seen the simulation prediction accuracy will reduce without linking this gas convection-diffusion effect. Finally, for maximizing the field oil recovery in two Huff-Puff cycles, the optimal re-opened time with this effect is when the near-well pressure drops to 14.7 MPa. This investigation could provide further insight into the gas enhanced oil recovery of the Pre-Darcy flow.

Pre-Darcy flow behavior of CO2 Huff-n-Puff development in Fuyu tight formation: Experiment and numerical evaluation

There is growing evidence showing that the oil phase seepage in tight matrix obeys the low-velocity Pre-Darcy flow because of the boundary effect between pore wall and fluid. However, most Pre-Darcy flow model may cause inaccuracy in simulating the reduction of non-linear degree, because of oil properties improvement caused by CO2 injection. In this paper, we propose a newly Pre-Darcy model with dynamic non-Darcy parameter c1 to characterize the tight-oil non-linear flow behavior in CO2 Huff-n-Puff process. Firstly, based on the high accurate experimental data in flow velocity testing with representative cores in Fuyu reservoir, non-linear parameter c1 is modified as a two-parameter function of tight oil flow capability. Then, the validated self-developed compositional simulator with embedded-discrete-fracture model (EDFM) and unstructured perpendicular bisection (PEBI) grid system is applied in field-scale cases to compare this proposed newly Pre-Darcy flow model with other previously presented flow models. Based on the comprehensive simulation comparison, the results show when the oil properties improvement occurs in injected-CO2 swept and diffusion area, the proposed Pre-Darcy flow model can properly describe the reduction of non-linear degree, leading to additional 0.45% oil recovery in three-cycle Huff-Puff operation. Additionally, in this newly dynamic flow model, capillary pressure in nanopores could degrade the non-linear degree of oil phase, which exhibits typical advantages on production well performance. Finally, this Pre-Darcy flow model is successfully applied in history matching of Fuyu Oilfield to validate its reliability.

Pre-Darcy flow in shales: Effects of the rate-dependent slip

The pre-Darcy flow phenomena in porous media is still not well understood, and the liquid slip mechanism in shales is controversial. Both issues need more exploration. In the field of microfluidic research, the concept of the slip length is widely employed to characterize the deviation from the no-slip flow, and it is recognized that the slip is rate-dependent. For the first time, the rate-dependent slip is proposed as an explanation for the pre-Darcy flow phenomena in porous media and the compromise between existing controversial views with regard to the liquid slip flow in shales based on careful analysis, and then such slip is incorporated in the one-dimension unsteady diffusion equation for liquids. The finite difference method is employed to numerically solve the equation, and detailed sensitivity analysis is conducted for the critical shear stress, the pore radius and the slip length. The results are summarized, and suggestions for future research are provided. This work can provide new insight into the pre-Darcy flow phenomena in the nanoporous media, and can compromise between existing controversial views regarding the liquid slip mechanism in shales. More importantly, this subject is also significant to research and develop EOR methods in shale reservoirs.

Pre-Darcy Flow and Klinkenberg effect in Dense, Consolidated Carbonate Formations

Experimental studies on pre-Darcy flow generally focus on unconsolidated porous media with high permeability. In this work, pre-Darcy flow is studied in consolidated carbonate rocks from different formations of Zagros basin. The core samples are calcite, dolomite and chalk-salt characterized by low-porosity (12.33–28.21%) and low permeability (0.011–18.53 md). Digital rock images were obtained using dental CT-scan with a resolution of 200 pixels per μm. A series of single-phase flooding experiments were conducted to evaluate the onset of pre-Darcy flow in different cores using N2 as gas phase. Superficial velocity versus pressure gradient was measured and different onset values were reported. Results indicate the presence of pre-Darcy flow in single phase gas experiments. The minimum observed Darcy velocity was 0.445 × 10−05 m/s, below which pre-Darcy flow prevails. In addition, different flow regimes such as pre-Darcy, Darcy and non-Darcy flow regimes were determined using reduced pressure drop analysis and Reynolds number analysis. The range of Reynolds number were reported for different flow regimes and different core permeabilities. The pre-Darcy regime was observed at velocities in the range of (0.445–5.88) × 10−05 m/s for all cores. For a carbonate core with k = 0.01 md, pre-Darcy flow was observed in the range of $$Re_{\sqrt k }$$ < 2.1 × 10−07, Red < 0.168 and Rep < 0.025. It was also found that pre-Darcy flow arises due to Klinkenberg effect at low gas pressure in different core samples which show different behavior depending on their permeability.

Flow behavior of hydraulic fractured tight formations considering Pre-Darcy flow using EDFM

For tight reservoirs/formations, flow in fracture and matrix obey different flow patterns. Pre-Darcy flow always exists in low permeability subsurface porous media while Darcy flow can be applied in fracture. It is an outstanding challenge to understand the flow behavior coupling different flow mechanisms. As numerical simulation can predict field-scale performance so the development of efficient simulation method becomes a key issue to evaluate the flow behavior. In this paper, we develop an improved discrete fracture model based on the widely used embedded discrete facture model (EDFM) to simulate the transport both in homogenous and heterogeneous porous media in the presence of Pre-Darcy flow. The conservation equations are derived for fracture and matrix firstly and then discretized by fully implicit method. The transmissibility of different connection types is defined and the detailed calculation workflow is presented as well. The proposed model is verified through the comparison with the model using local grid refined (LGR) method. It is discovered that our simulation method exhibits good accuracy when analyzing the effect of Pre-Darcy flow. Some examples are shown including 1D scalar transport, 2D heterogeneous, 3D flow, complex fracture system and multiple well system problems with fully-coupled flow in fracture and matrix. The pressure distribution and well flux are demonstrated to analyze the Pre-Darcy flow characteristics. Results indicate that the new model works robustly for different flow problems which provide further insight into the Pre-Darcy flow in low permeability media.

Analysis of Pre-Darcy flow for different liquids and gases

Fluid flow in porous media is extensively associated with Darcy's law. Deviations from Darcy's law and its limitations result in modifications known as non-Darcy flow at high velocity and Pre-Darcy flow at low velocity. In this paper, experiments were conducted to explore significance of departure from linearity at low fluid velocity (Pre-Darcy flow) in porous media. Effect of different liquid and gas types on the onset of Pre-Darcy flow were studied for water, condensate, n-hexane and n-heptane as liquid phase and CH4, CO2 and N2 as gas phase. Superficial velocity versus pressure gradient was measured and different onset values were reported. The minimum observed Darcy velocity was 0.189 × 10−05 m/s, below which Pre-Darcy flow prevails. Analysis was performed in terms of friction factor and Reynolds number for different particle size of 0.15, 0.25 and 0.3 mm. Pre-Darcy, Darcy and Non-Darcy flow regimes were observed and characterized in terms of Re√k, Red and Rep. The range of Reynolds number were reported for different flow regimes, different particle sizes and different types of liquids. For the case of condensate in 0.15 mm sand pack, Pre-Darcy flow was observed in the range of Re√k < 2.81 × 10−06, Red < 0.0014 and Rep < 0.0005. In addition to new liquids and gases that are investigated in this study, one of the differences between this study and previous ones, is investigation the relevance of Pre-Darcy flow to fluid properties in addition to rock properties for wide ranges of liquids and gases. The existence of Pre-Darcy flow means that, there is unknown opportunities for improved oil recovery in petroleum reservoirs. Also, accurate emission velocity is effective for reduction of soil pollution by hydrocarbon leakage. This velocity can be corrected by considering Pre-Darcy flow.

Effects of particle diameter on flow characteristics in sand columns

This work aims to investigate the effects of particle size on flow regimes and validation of Darcy law. Experiments were conducted in sand columns with five different particle sizes of silica sand in mean diameter 1.075mm, 1.475mm, 1.85mm, 2.5mm and 3.17mm. Both pre-Darcy flow and post Darcy flow were identified but no obvious linear flow was observed, the Reynolds number of two flow regime are different with different grain sizes. Relative error was used to evaluate the experimental data and obtain that the values of Reynolds number at the demarcation point are 3.90, 7.08, 9.1 and 10.78. The values of Reynolds number of two flow regime increased gradually as the particle diameter increased. A new Reynolds number defined as ratio of inertia term and viscous term in Forchheimer equation can lead to a single criterion for determining the limit of validity of Darcy law. The recommended critical Reynolds number for non-Darcy flow is equal to 0.1, where the error of neglecting inertial effects in the hydraulic gradient will be less than 10%.

Pre-Darcy flow revisited under experimental investigation

Sufficient literature has been published about Pre-Darcy flow in non-petroleum disciplines. Investigators dissent about the significance of deviation of Darcy’s law at very low fluid velocities. Most of their investigations are based on coarse, unconsolidated porous media with an aqueous fluid. However little has been published regarding the same for consolidated oil and gas reservoirs. If a significant departure from Darcy’s law is observed, then this could have multiple implications on: reservoir limit tests, under prediction of reserves, unrecognized prospecting opportunities etc. This study performs a comprehensive review of the literature. Experiments were conducted to confirm the presence and the significance of Pre-Darcy flow effect in petroleum rocks. The review of literature and experiments indicate the presence of Pre-Darcy effect. Contributing factors to Pre-Darcy effect are discussed and some reasons causing this effect are postulated. The experiments also show that this effect is significant. Pre-Darcy effect is significant because it is the dominant flow regime in typical petroleum reservoirs.

Pre-Darcy Flow Revisited under Experimental Investigation

Sufficient literature has been published about Pre-Darcy flow in non-petroleum disciplines. Investigators dissent about the significance of deviation of Darcy’s Law at very low fluid velocities. Most of their investigations are based on coarse, unconsolidated porous media with an aqueous fluid. However little has been published regarding the same for consolidated oil and gas reservoirs. If a significant departure from Darcy’s Law is observed, then this could have multiple implications on: reservoir limit tests, under prediction of reserves, unrecognized prospecting opportunities etc. This study aims to perform a comprehensive review of the literature; and to experimentally demonstrate that the Pre-Darcy flow effect is significant in petroleum rocks.

SINGLE FLUID FLOW IN POROUS MEDIA

A comprehensive study on single fluid flow in porous media is carried out. The volume averaging technique is applied to derive the governing flow equations. Additional terms appear in the averaged governed equations related to porosity ε, tortuosity τ, shear factor F and hydraulic dispersivity D h. These four parameters are uniquely contained in the volume averaged Navier-Stokes equation and not all of them are independent. The tortuosity can be related to porosity through the Brudgemann equation, for example, for unconsolidated porous media. The shear factor models are reviewed and some new results are obtained concerning high porosity cases and for turbulent flows. It is known that there are four regions of flow in porous media: pre-Darcy's flow, Darcy's flow, Forchheimer flow and turbulent flow. The transitions between these regions arc smooth. The first region, the pre-Darcy's flow region represents the surface-interactive flows and hence is strongly dependent on the porous media and the flowing fluid. The other flow regions are governed by the flow strength of inertia. For Darcy's flow, the pressure gradient is found to be proportional to the flow rate. The Forchheimer flow, however, is identified by a strong inertia! effects and the pressure gradient is a parabolic function of flow rate. Turbulent flow is unstable and unsteady flow characterized by chaotic flow patterns. The pressure drop is slightly lower than that predicted using the laminar flow equation. The hydraulic dispersivity is a property of the porous media. It may be considered as the connectivity of the pores in a porous medium. It characterizes the dispersion of mementum, heat and mass transfer. In this paper, only the dispersion of momentum is studied. Single fluid flow through cylindrical beds of fibrous mats and spherical particles has been used to show how to solve the single fluid flow problems in porous media utilizing the knowledge developed in this communication. Both the pressure drop and axial flow velocity profiles are computed using the developed shear factor and hydraulic dispersion models. Both the predicted velocity profile and pressure drop compare fairly well with the published experimental data.