Low Permeability Porous Media Research Articles

Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect.

Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.

Difference Schemes for Three Kinds of Nonlinear Flow Model in Low Permeability Porous Media

This paper discusses three kinds of typical one-dimensional nonlinear equations coming from low permeability reservoir seepage models with different boundary conditions. The several finite difference methods including forward difference method and second central order difference quotient method are used for the respective discrete process of three models. With these difference methods, the discrete schemes of models are obtained. Then the corresponding nonlinear discrete equations are deduced. While dealing with the boundary condition, the mid-rectangle formula is used. Finally, integrated discrete equations of three nonlinear equations are formed. The results should be meaningful for the numerical simulation of non-Darcy flow model of the low-permeability oil wells.

Gas Flow Property in Microtube and Its Effect on Gaseous Seepage

The flow characteristics of nitrogen in microtubes with the diameters of 2.05, 5.03, and 10.1 μm are investigated experimentally. The results indicate that all the flow characteristics of nitrogen in microtubes depart from the classical Poiseuille's theory, and microscale effect appears apparently in gaseous flow. The experimental flow values are higher than the theoretical values calculated by Poiseuille's equation, and the deviations between experimental flow values and calculated values increase with the decrease of the inner diameter of microtube. However, the first-order slip boundary theory considered, the experimental flow values are in accordance with the theoretical predictions. Microscale effect can be characterized by the size of kn, and the larger kn, the stronger microscale effect. When Knudsen number is smaller than 0.002, the experimental microscale effect becomes negligible. Based on capillary bundle model, the influence of microscale effect on the gas seepage law in low-permeability porous media is researched. The results show that gas percolation has an obvious characteristic of non-Darcy flow, which is in accordance with the Klinkenberg effect.

Light reflection visualization to determine solute diffusion into clays

Light reflection visualization (LRV) experiments were performed to investigate solute diffusion in low-permeability porous media using a well-controlled two-dimensional flow chamber with a domain composed of two layers (one sand and one clay). Two different dye tracers (Brilliant Blue FCF and Ponceau 4R) and clay domains (kaolinite and montmorillonite) were used. The images obtained through the LRV technique were processed to monitor two-dimensional concentration distributions in the low-permeability zone by applying calibration curves that related light intensity to equilibrium concentrations for each dye tracer in the clay. One dimensional experimentally-measured LRV concentration profiles in the clay were found to be in very good agreement with those predicted from a one-dimensional analytical solution, with coefficient of efficiency values that exceeded 0.97. The retardation factors (R) for both dyes were relatively large, leading to slow diffusive penetration into the clays. At a relative concentration C/C0=0.1, Brilliant Blue FCF in kaolinite (R=11) diffused approximately 10mm after 21days of source loading, and Ponceau 4R in montmorillonite (R=7) diffused approximately 12mm after 23days of source loading. The LRV experimentally-measured two-dimensional concentration profiles in the clay were also well described by a simple analytical solution. The results from this study demonstrate that the LRV approach is an attractive non-invasive tool to investigate the concentration distribution of dye tracers in clays in laboratory experiments.

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained. It is notable that the TPG (J) and permeability (K) of the porous medium analytically exhibit the scaling behavior J ∼ K−DT/(1=DT), where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.

Enhanced Transport and Transformation of Zerovalent Nanoiron in Clay Using Direct Electric Current

One of the major obstacles to zerovalent iron nanoparticles (nZVI) application in soil and groundwater remediation is the limited transport, especially in low-permeability soils. In this study, direct current (constant potential of 5.0 V) was used to enhance polymer-coated nZVI mobility in different porous media, including a bed of glass beads and kaolin clay. The tests were conducted using a modified electrophoretic cell and with nZVI concentrations typical of field applications (4 g L−1). Experimental results indicate that the use of direct current can enhance the transport of the polymer-modified nanoparticles when compared with natural diffusion in low permeability or surface neutral porous medium. The applied electric field appeared to enhance the oxidation–reduction potential, creating a synergistic effect of nZVI usage with electrokinetics. Aggregation of the nanoparticles, observed near the injection point, remained unresolved.

Principles of Unsaturated Flow in Tight Gas Reservoirs

The future of the energy sector in the coming years is expected to be significantly affected by unconventional gas resources. Flow through porous media has many applications in the chemical, petroleum, gas, and pulp and paper industries, as well as in soil remediation and material characterization. In petroleum and natural gas production, flow through porous media has significance in the production of gas and/or oil. There are many characteristics of tight reservoir rock resulting in high and complex water saturation such as tiny pore throat, poor sorting, high displacement pressure, and so on. The one hand, the gas seepage is affected by the slippage effect, resulting in the abnormal gas relative permeability. On the other hand, the residual water of the tight core is controlled by displacement pressure. This study is directly related to gas reservoir engineering and is specifically focused to obtain fundamental information for two phase flow through low permeability porous media (Tight Sand Gas).

Sealing efficiency of caprocks: Experimental investigation of entry pressure measurement methods

Caprocks play a key role in hydrocarbon entrapment and in the geological storage of gas. Top seals inhibit vertical migration due to their low permeability and high entry pressure (PE). This study investigated four different techniques for measuring PE: (1) step by step method; (2) dynamic approach; (3) racking method; (4) residual pressure method. This article reports results on two samples: a carbonate (1.5 μDarcy (1.5 10−18 m2)) and a claystone (15 nDarcy (1.5 10−20 m2)). On the carbonate sample, methods 1, 2 and 3 gave a PE value of 1.1 MPa, whilst method 4 gave a PE of 0.4 MPa. On the claystone sample, methods 1 and 2 gave a PE value around 12 MPa. The data allow us to consider best practices for PE measurements on caprocks. Methods 2 and 3 are the quickest and most accurate methods but show limitations in very low permeability porous media. Method 2 required three days to measure PE in the 15 nD claystone and experiments on 1 nD (10−21 m2) materials would take longer. Additional issues on mechanical stresses impact the result reliability since in methods 2 and 3 effective stress can significantly change during the experiment. Method 4 measures a snap-off pressure that is lower than the entry pressure value. Method 1 is a long experiment but is the most representative of in situ hydrocarbon migration though caprocks.

Coupled thermo-hydro-mechanical model with consideration of thermal-osmosis based on modified mixture theory

A coupled formulation based on non-equilibrium thermodynamics, Biot’s elasticity is derived to model thermal-osmotic flow in very low permeability rock. Darcy’s law has been modified by incorporating thermal effects from the dissipation process by using standard arguments of non-equilibrium thermodynamics. The relationship of chemical potential of water and pore water pressure has been analysed. Helmholtz free energy is used to construct the structure of the mechanics model. The derived coupled equations can be validated by comparing with those from Mechanics approach. Finally, finite elements are used to solve the governing equations. The numerical results show the thermal-osmosis has an important effect on water transport in very low permeability porous media.

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.

The Boundary Negative Slippage of Fluid Flowing in Hydrophilic Micro-Channels

In order to analyze the characteristics of the liquid flow in hydrophilic micro-channels, the negative slippage in the hydrophilic micro-channels were studied by molecular dynamics simulation and experimental research in this paper. The simulation results indicate that there exists negative slippage in the small shear rate. The absolute value of slip length decreases with the augment of shear rate and keeps constant when the shear rate increases to a certain extent. In the condition of same wettability, the slip length is only relative to shear rate of fluids near the wall rather than channel widths. At last, a experiment of deionized water flow in the micro-channel of 10 diameter was carried out. The experimental results have a good agreement with the simulation, and there exists Pseudo Threshold Pressure Gradient(PTPG) under low flow velocity. The negative slippage as the reason of existence of PTPG is analyzed in low permeability porous media

Overcoming Permanganate Stalling during Electromigration

AbstractElectrokinetic experiments were undertaken to transport permanganate (MnO4−) through a low permeability porous media. The experiments employed a one-dimensional apparatus in which MnO4− was electromigrated through a central porous media core. Two outer porous media cores separated the electrode reservoirs from the inner permanganate source and permanganate target reservoirs. By utilizing a pH-isolation technique, whereby electrolysis reactions occurring at electrodes were isolated, uniform and repeatable MnO4− electromigration was achieved. This result was compared with non-pH-isolated experiments (normal mode), which resulted in a stalled MnO4− electromigration front. The research also investigated potential stalling mechanisms, including voltage gradient nonlinearity through the central porous media core and the reduction of MnO4− to Mn2+. It was observed that the voltage gradient decreased as a result of MnO4− stalling; however, it was not considered a stalling mechanism. Results from Mn2+ anal...

Fluid filtration in a porous medium with wells with vertical hydraulic fracture of the formation

Consideration is given to the problem on propagation of a pressure field in a low-permeability porous medium with two wells that are connected by a technogenic hydraulic fracture. The approximate numerical solution of this problem is obtained; an analysis of the influence of the above fracture on the system’s parameters is made; responses of the pressure in a well are modeled. The inverse problem is solved with the numerical model developed, and the system’s parameters are evaluated from the field data measured in the process of hydrodynamic investigation by the method of pressure interference testing.

A Fuzzy Method to Classify Low Permeability Reservoirs

Cluster analysis is a multivariate statistical method of the study of sample (or variables) classification, gradually classified by the analysis of the sample or the similarity between the variables. In this paper, taking the case of Daqing low permeability reservoir, according to the movable fluid saturation, the average throat radius and the starting pressure gradient, we used cluster analysis method to conduct the multi-parameter classification of low permeability porous media, and achieved good results. The results showed that: The method in low permeability porous media category is feasible and has strong rationality.

Contribution of the Steady State Method to Water Permeability Measurement in Very Low Permeability Porous Media

Very low permeability geomaterials (order of nanoDarcy (10-21 m2 )), such as clay rocks, are of interest for many industrial applications including production from unconventional reserves of oil and gas, CO2 geological storage and deep geological disposal of high-level long-lived radioactive waste. In these last two applications, the efficiency of clay, as a barrier, relies on their very low permeability. Yet, laboratory measurement of low permeability to water (below 100 nD (10-19 m2 )) remains a technical challenge. Some authors (Hsieh et al. , 1981, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 18 , 245-252) argue that steady state methods are irrelevant due to the time required to stabilize water fluxes in such low permeability media and prefer a transient technique called pulse decay. This study aims to perform and compare transient and steady state techniques on three samples. Regarding the steady state method, a high precision pump was used to measure water flow rate through the sample. We show that with a suitable set-up, the steady state method enables us to measure a very low permeability of 0.8 nD (8 × 10-22 m2 ) over a period of three days and 2.6 nD (2.6 × 10-21 m2 ) over a period of one day. While the pulse decay test provides only an average estimate of the permeability for a comparable duration. Many issues are raised in pulse decay tests: determination of the reservoirs storage factor, micro leakage effects, determination of the initial pulse pressure, 2D mechanical effect. Contrary to the widespread belief that transient techniques are required to measure very low permeability, we show that direct steady state measurement of water permeability, with suitable equipments, can be much faster and more accurate than measurement by pulse decay. In fact, low water and rock compressibilities result in fast propagation of pressure wave and it cannot be argued that steady state conditions are not reachable in a reasonable amount of time. Still, pulse decay remains an interesting alternative to steady state methods when permeability is higher than 50 nD (5 × 10-20 m2 ).

A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses

The transient stress, displacement, pore pressure and temperature fields around a wellbore in a thermo-poro-elastic (THM) medium subject to non-hydrostatic remote stresses are analyzed under non-isothermal plane-strain conditions. The linear THM model proposed by Coussy (1989) is adopted in the analysis with a focus on thermal effects in low-permeability saturated rocks, characterized by a latent heat associated with local changes of fluid mass content. Non-dimensionalized parameters are identified by reformulating the fully-coupled governing equations and boundary conditions. The wellbore problem is simplified by decomposing it into axisymmetric and deviatoric loading cases. The corresponding analytical solutions are obtained in Laplace space. The inverse Laplace transforms are performed numerically to find the time-dependent distributions of field variables in the rock mass around the wellbore. These numerical results show that although the pore pressure diffusion has little influence on temperature and stress, temperature changes can strongly affect the pore pressure and stress around the wellbore. The temperature change can lead to changes in near-well stresses and the resulting significant change in wellbore breakdown pressure illustrates the importance of considering the THM coupling.

Electrophoresis enhanced transport of nano-scale zero valent iron

Electrokinetics (EK) has been used extensively to remove heavy metals from low permeability porous media. Electrokinetics (EK) or more specifically electrophoresis (EP) has also been proposed to enhance transport of nanoscale zero valent iron (NZVI) in fine grained porous media in the subsurface. However, increased dissolved oxygen and lower pH, due to electrolysis of water at the anode oxidizes NZVI particles and thus affects the remediation potential of EP with NZVI. This study focuses on minimization of NZVI oxidation and quantification of NZVI migration enhancement through the application of EP. Application of 50 and 100mA currents under constant current conditions with an oxygen scavenger enhanced NZVI transport from the cathode to the anode. The enhancement in transport compared to diffusion was proportional to the applied current. Predictions of a numerical model, based on traditional colloidal filtration theory (CFT), were consistent with experimental results. In developing the model, the traditional CFT based mass balance equation was modified for the case of no advection. This study suggests that EP has the potential to deliver NZVI in low permeability porous media and that the numerical simulator can be used to predict NZVI mobility with EP.

Permeabilities of tight reservoir cores determined for gaseous and liquid CO2 and C2H6 using minimum backpressure method

Permeability is the most important parameter for characterizing fluid flow though porous media and determined experimentally using a gas or liquid. For most porous materials the values of permeability determined with gas and liquid are the same. For tight rocks, however, the permeability obtained with liquid is much lower than that with gas. Such difference has been ascribed to uncertainties involved in the measurement, including the inaccuracy of the gas permeability extrapolated from Klinkenberg correlation, or the effects of liquid polarity and fine particle movements on liquid permeability when the liquid is present. In this paper, we report a noticeable difference between the gas and liquid permeability determined after all the above uncertainties are excluded by using a novel-designed experiment. The results show that the permeability of the same fluid varies as its state changes from gas to liquid in low-permeability porous media. This indicates that the gas behaves differently from liquid of the same fluid in low-permeability porous media.

Study on the Performance of Hydrophobic Association Water-Soluble Polymer with Strong Association Ability

In this article, the viscosifying abilities, rheological properties, and flow characteristics of hydrophobic association water-soluble polymer with high association ability were studied using technical methods of viscosity measurement, rheological and core flow experiments. The results illustrate that hydrophobic associated polymers with low molecular weight rely on a strong hydrophobic interaction, the intermolecular and intramolecular micellar structure formed in solution with a strong ability to increase viscosity. Hydrophobic association water-soluble polymer, comparing with partially hydrolyzed polyacrylamides polymer with low molecular weight, presents a better ability of shear stability under the condition of shearing and the solution structure strengthens gradually so as to increase viscoelasticity remarkably. The hydrophobic association water-soluble polymer with high association ability take on greater injectivity and mobility control ability in low permeability porous media solving the problem of low injectivity and poor control ability in mid-low permeability reservoirs, which improves polymers flooding effect in such reservoirs and underlie the reasonable design of polymer molecular structure.

Effect of absorption boundary layer on nonlinear flow in low permeability porous media

Taking low permeability cores of Daqing oilfield for example, the flow characteristics at low velocity were studied with the self-designed micro-flux measuring instrument. Considering the throat distribution and capillary model, the thickness of fluid boundary layer under different pressure gradients was calculated, and the mechanism and influencing factors of nonlinear percolation were discussed. The results show that the percolation curve of ultra-low rocks is nonlinear, and apparent permeability is not a constant which increases with pressure gradient. The absorption boundary layer decreases with the increase of pressure gradient, and changes significantly especially in low pressure gradient, which is the essence of nonlinear percolation. The absorption boundary layer is also found to be impacted by the surface property of rocks.