A Technique for the Determination of Capillary Pressure Curves Using a Constantly Accelerated Centrifuge

1963 ◽  
Vol 3 (03) ◽  
pp. 227-235 ◽  
Author(s):  
Robert N. Hoffman
Keyword(s):  
Capillary Pressure ◽  
Pressure Curve ◽  
Barrier Method ◽  
Centrifuge Method ◽  
Permeable Barrier ◽  
The Core ◽  
Capillary Pressure Curve ◽  
Fluid Saturation ◽  
Time Required ◽  
Capillary Pressure Curves

HOFFMAN, ROBERT N., MISSOURI SCHOOL OF MINES, ROLLA, MO. JUNIOR MEMBER AIME Abstract A new technique for determining capillary pressure curves has been developed and tested. The technique differs from previously reported centrifuge techniques in that the centrifuge is slowly accelerated from zero to the maximum desired speed rather than being held constant at particular, progressively higher speeds. An important advantage of this technique over other methods of determining capillary pressure curves is the short time required to obtain the desired amount of data over the chosen pressure range. For example, to obtain 30 data points between 1.2 and 104 psig with a 1.55-in. long, 3/4-in, diameter core using a brine-air system, 6. 6 hours were required with this technique. An equally important development of this paper is an analytic method for the conversion of the data from the centrifuge experiment to capillary pressure curve data. Previously there has been only an approximate conversion available.Although the capillary pressure curves determined by this technique appear to be as accurate as those determined by other techniques, the accuracy could be improved if certain variables, not treated in this experiment, were investigated. Among these are the dynamic distortion of the centrifuge equipment and imperfect initial saturation of the cores. Introduction Pirson defines capillary pressure in a porous medium as "the differential pressure that exists between two fluid phases at their interfaces when they are distributed under static equilibrium within a porous material". Capillary pressure in rocks is known to be a function of fluid saturation, among other things, and a capillary pressure curve is defined for the purposes of this paper as a plot of the capillary pressure-wetting phase saturation relationship for a particular rock sample.Several methods are used for determining capillary pressure curves for small rock cores. Prominent among these are the semi-permeable barrier, mercury injection, and, to a lesser extent, centrifuge methods. The semi-permeable barrier method is currently the most popular. It features simplicity in both execution and the mathematical conversion of the experimental data into a capillary pressure curve. The main disadvantages of the semi-permeable barrier method are the time required - as long as two months - to obtain several points for the curve, and a fairly low maximum pressure before breakthrough of the non- wetting phase into the barrier occurs, for example, about 32 psig for a brine-air system.It is for these reasons that other methods such as the centrifuge method have been introduced. High accelerations and the absence of a barrier result in quicker attainment of saturation equilibrium at a given pressure. However, the centrifuge method involves much more expensive equipment and more difficult procedures and calculations than does the barrier method. The purpose of this investigation has been to improve the equipment and procedures of the centrifuge method and to develop an analytic method for the conversion of the experimental data into a capillary pressure curve.Hassler and Brunner did the original work in the determination of capillary pressure using a centrifuge. In their work the centrifuge speed was increased in a step-wise manner, each speed being held constant until saturation equilibrium was reached in each core. Saturation equilibrium was indicated when the volume of liquid collected in the graduated pipette of the core holder remained constant. According to Hassler and Brunner, equilibrium was reached in "a few minutes to one-half hour or more".In the centrifuge method, as opposed to the barrier method, the fluid saturation of the core is not a constant throughout the length of the core, but varies with the radius of centrifugation. Also, the capillary pressure cannot be read directly but must be calculated from a knowledge of the centrifuge speed and other parameters. SPEJ P. 227^

Capillary-Pressure Curves for Low-Permeability Chalk Obtained by Nuclear Magnetic Resonance Imaging of Core-Saturation Profiles

1999 ◽  
Vol 2 (02) ◽  
pp. 141-148 ◽  
Author(s):  
J.V. Nørgaard ◽  
Dan Olsen ◽  
Jan Reffstrup ◽  
Niels Springer
Keyword(s):  
Steady State ◽  
Capillary Pressure ◽  
Porous Plate ◽  
Low Permeability ◽  
Pressure Curve ◽  
Centrifuge Method ◽  
The Core ◽  
Fluid Saturation ◽  
Capillary Pressure Curves ◽  
Saturation Profile

Summary A new technique for obtaining water-oil capillary pressure curves, based on nuclear magnetic resonance (NMR) imaging of the saturation distribution in flooded cores is presented. In this technique, a steady-state fluid saturation profile is developed by flooding the core at a constant flow rate. At the steady-state situation where the saturation distribution no longer changes, the local pressure difference between the wetting and nonwetting phases represents the capillary pressure. The saturation profile is measured using an NMR technique and for a drainage case, the pressure in the nonwetting phase is calculated numerically. This paper presents the NMR technique and the procedure for calculating the pressure distribution in the sample. Inhomogeneous samples produce irregular saturation profiles, which may be interpreted in terms of variation in permeability, porosity, and capillary pressure. Capillary pressure curves for North Sea chalk obtained by the new technique show good agreement with capillary pressure curves obtained by traditional techniques. Introduction Accurate petrophysical properties of reservoir rock such as capillary pressure, permeability, and relative permeability functions are essential as input for reliable oil in place estimations and for the prediction of the reservoir performance. Traditional methods for capillary pressure measurements are the mercury injection method, the diaphragm method, and the centrifuge method. In the mercury injection method,1 the nonwetting phase is mercury which displaces a gas. The samples are usually evacuated to a low pressure and Hg is then injected in steps allowing for pressure equilibrium at each step, or alternatively Hg is continuously injected. Corresponding data on injected volume of Hg and the injection pressure are recorded. This technique is widely used for measuring capillary pressure functions for low permeability rocks. This is primarily because it is generally believed that pressure equilibrium in each pressure step is readily obtained, while this is normally a problem for other methods where a liquid is the wetting phase. The disadvantage of this technique is the uncertainty in the scaling of the measured data to reservoir fluid data and conditions. In the diaphragm method or porous plate method, the problem concerning the scaling of the measured data is avoided, since this technique allows for the direct use of reservoir fluids. A water saturated sample is placed on a water-wet diaphragm to impose a boundary condition pc=0 to the wetting phase, i.e., the wetting phase is allowed to drain through the outlet end of the sample, at the same time as the nonwetting phase (oil or gas) is impeded. Pressure is added to the nonwetting phase and through a limited number of pressure steps, the capillary pressure curve is recorded. However, an important requirement is that equilibrium is obtained at each pressure step. This is the major problem when the diaphragm method is used on microporous materials. The drainage time may be considerable for each step, e.g., several weeks. In recent studies, thin micropore membranes have been used in an attempt to reduce the experimental time.2 Such a reduction will be less pronounced for low permeability rocks such as chalk since the flow resistance in the core is relatively more important. In the centrifuge method, the amount of liquid produced from the outlet end of the plug sample at a certain spin rate is read directly from a measuring tube during rotation. From the geometry of the centrifuge, the spin rate and the average fluid saturation in the plug, it is possible to calculate the capillary pressure relative to the inlet end of the sample.3 However, a number of assumptions must be made3,4: the sample must be homogeneous and have a well-defined outlet pressure boundary condition, i.e., condition pc=0, and drainage equilibrium must be established at each spin rate. Most of these conditions can only be approximated in practice. For the centrifuge method, the condition of drainage equilibrium may be questionable even for sandstone samples.5 Slobod6 reported that equilibrium had not been attained for a 2 mD sample after 20 hr of spinning. King7 concluded that low permeability rock samples may suffer from very long equilibrium times. After 10 days of spinning in the centrifuge, a Berea sandstone sample of 200 mD had just reached equilibrium. The objective of the development of the method presented here has been to avoid some of the disadvantages of the conventional methods described above. In this method a capillary pressure curve is obtained from a measured saturation profile after flooding the core. A similar experimental procedure was used by Richardson et al.8 to study end effects associated with flooding processes. The technique described here can be used with reservoir fluids. There is no porous plate to increase the flow resistance and the measurement of the capillary pressure function can be an integrated part of traditional flooding processes as performed with, e.g., unsteady-state relative permeability measurements. Only a very limited number of steps are needed, in principle only one step is required, therefore the time requirement for obtaining drainage equilibrium has not proved to be a problem. The technique utilizes the unavoidable end effect present in experiments with low permeability rocks. The capillary pressure function is obtained from the steady-state saturation profile in the core at drainage equilibrium.

Experimental Validation of a Pore-Scale-Derived Dimensionless Capillary Pressure Function for Imbibition Under Mixed-Wet Conditions

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1338-1348 ◽  
Author(s):  
Y.. Zhou ◽  
J. O. Helland ◽  
D. G. Hatzignatiou ◽  
R.. Ahsan ◽  
A.. Hiorth
Keyword(s):  
Capillary Pressure ◽  
Reservoir Simulation ◽  
Simulation Models ◽  
Pressure Curve ◽  
Pore Scale ◽  
Pressure Function ◽  
Capillary Pressure Curve ◽  
Mixed Wettability ◽  
Dimensionless Function ◽  
Capillary Pressure Curves

Summary We validate experimentally a dimensionless capillary pressure function for imbibition at mixed-wet conditions that we developed recently on the basis of pore-scale modeling in rock images. The difference from Leverett's traditional J-function is that our dimensionless function accounts for wettability and initial water saturation after primary drainage through area-averaged, effective contact angles that depend on the wetting property and distribution of oil- and water-wet grain surfaces. In the present work, we adopt the dimensionless function to scale imbibition capillary pressure data measured on mixed-wet sandstone and chalk cores. The measured data practically collapse to a unique curve when subjected to the dimensionless capillary pressure function. For each rock material, we use the average dimensionless curve to reproduce the measured capillary pressure curves and obtain excellent agreement. We also demonstrate two approaches to generate different capillary pressure curves at other mixed-wettability states than that available from the data used to generate the dimensionless curve. The first approach changes the shape of the spontaneous- and forced-imbibition segments of the capillary pressure curve whereas the saturation at zero capillary pressure is constant. The second approach shifts the vertical level of the entire capillary pressure curve, such that the Amott wetting index (and the saturation at zero capillary pressure) changes accordingly. Thus, integrating these two approaches with the dimensionless function yields increased flexibility to account for different mixed-wettability states. The validated dimensionless function scales mixed-wet capillary pressure curves from core samples accurately, which demonstrates its applicability to describe variations of wettability and permeability with capillary pressure in reservoir-simulation models. This allows for improved use of core experiments in predicting reservoir performance. Reservoir-simulation models can also use the dimensionless function together with existing capillary pressure correlations.

Using Parameter Estimation Techniques To Convert Centrifuge Data Into a Capillary-Pressure Curve

1977 ◽  
Vol 17 (01) ◽  
pp. 57-64 ◽  
Author(s):  
R.G. Bentsen ◽  
J. Anli
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Capillary Pressure ◽  
Estimation Methods ◽  
Pressure Curve ◽  
Estimation Techniques ◽  
The Core ◽  
Capillary Pressure Curve ◽  
Irreducible Water Saturation ◽  
Parameter Estimation Techniques

Abstract Previously reported techniques for converting basic centrifuge data into a capillary-pressure curve have one serious drawback: they all involve the graphical or numerical differentiation of experimental data. The problems associated with the differentiation of experimental data can be avoided by using the parameter estimation techniques proposed here. The parameter estimation techniques proposed here. The purpose of this paper is to demonstrate The advantages purpose of this paper is to demonstrate The advantages of using parameter estimation techniques for obtaining a capillary-pressure curve from centrifuge data. Two parameter estimation methods for handling centrifuge data were investigated and compared with a modified form of Hassler's technique for interpreting such data. This investigation indicates that, while Hassler's method and the parameter estimation techniques were equally able parameter estimation techniques were equally able to generate the capillary-pressure curve from centrifuge data, the latter procedures are preferable since they use various integration preferable since they use various integration schemes and, hence, avoid the differentiation problems associated with previously reported problems associated with previously reported methods of data interpretation. Moreover, if the parameter estimation techniques are used, the data can be smoothed and the irreducible water saturation, displacement pressure, and capillary-pressure normalizing parameter can be estimated. Introduction The theory for converting experimental data obtained with a centrifuge into a capillary-pressure curve was developed by Hassler and Brunner. The basic equation used in the conversion is P2 a ci Sn(x) dxP S = cos ---- .....(1)ci n 2 × 21 - ----- sin aPci wherep 2P = ----- w (re2 − ri2), ci 2 p 2x = ------ w (re2 − r2), 2 and ricos a = ----- .re Hassler and Branner were unable to find an analytical solution to Eq. 1, but they demonstrated bow it could be solved by the method of successive approximations. Since this method is very tedious in application, Hassler and Brunner preferred using a simplifying assumption that amounts to setting ri equal to re. This assumption, which the authors considered to be reasonable provided the ratio ri/re was greater than 0.7, resulted in the equation P ciPci Sn = Sn(x)dx, 0 from which it follows that d Sn (Pci) = ------ (Pci Sn)................(2)dP Setting ri equal to re assumes that the length of the core is negligible compared with the radius of rotation of the core. Hoffman has shown that this assumption is unnecessary, and that Eq. 3 should be used to solve for the saturation at each speed level. 2 cos adSnS (P) = -------- (S + P ------)....(3)n ci 1+cos a n ci dPci Eqs. 2 and 3 can be solved by taking slopes of graphs of Sn and Pci Sn vs Pci. SPEJ P. 57

scholarly journals Revisiting the applications of drainage capillary pressure curves in water-wet hydrocarbon systems

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
István Nemes
Keyword(s):  
Capillary Pressure ◽  
Water Saturation ◽  
Pressure Curve ◽  
Initial Water ◽  
New Approach ◽  
Capillary Pressure Curve ◽  
Side Track ◽  
Relationship Of ◽  
Capillary Pressure Curves ◽  
The Relationship

AbstractThe main focus of the paper is to introduce a new approach at studying and modelling the relationship of initial water saturation profile and capillarity in water-wet hydrocarbon reservoirs, and describe the available measurement methods and possible applications. As a side track it aims to highlight a set of derivable parameters of mercury capillary curves using the Thomeer-method. Since the widely used mercury capillary pressure curves themselves can lead to over-, or underestimations regarding in-place and technical volumes and misinterpreted reservoir behaviour, the need for a proper capillary curve is reasonable. Combining the results of mercury and centrifuge capillary curves could yield a capillary curve preserving the strengths of both methods, while overcoming their weaknesses. Mercury injection capillary curves were normalized by using the irreducible water saturations derived from centrifuge capillary pressure measurements of the same core plug, and this new, combined capillary curve was applied for engineering calculations in order to make comparisons with other approaches. The most significant benefit of this approach is, that all of the measured data needed for a valid drainage capillary pressure curve represents the very same sample piece.

The Role of Gravity in Capillary Pressure Measurements

1972 ◽  
Vol 12 (02) ◽  
pp. 85-88 ◽  
Author(s):  
Miklos T. Szabo
Keyword(s):  
Capillary Pressure ◽  
Gravitational Effect ◽  
Test Sample ◽  
Gravity Drainage ◽  
Pressure Curve ◽  
High Permeability ◽  
Technical Literature ◽  
Capillary Pressure Curve ◽  
Capillary Pressures ◽  
Capillary Pressure Curves

Abstract This paper shows on a theoretical basis how saturation profiles are influenced by gravity during the measurement of profiles are influenced by gravity during the measurement of capillary pressures in porous samples. A precise method is suggested for calculating the realistic capillary pressure curves from the data obtained in either the "diaphragm" or the "gravity drainage of long vertical core" method. A capillary pressure curve, free of the influence of gravity, can be determined by the equations developed in this paper from measurement of the pressures applied in the nonwetting phase and from the average saturations corresponding to capillary equilibria. The same equations may also be used for the evaluation of centrifuge data, provided the increase in capillary pressures is achieved by gradual lengthening of end-effect absorbers set up under the test sample, using the same constant speed of rotation at each run. Introduction The disc method is usually referred to in the technical literature as a standard method for determining capillary pressure curves. This study shows that using this method a certain pressure curves. This study shows that using this method a certain saturation distribution can be observed in the samples when the viscous fluid flow has ceased. The description of this phenomenon led to equations that offer a more precise formulation of the results obtained by the disc method. In addition, this formulation simplifies the "gravity drainage of long vertical cores" method because it is now sufficient merely to determine average saturations. Thus, it is unnecessary to determine saturations by electric methods or by the weighing of sectors of the drainage column. EXAMINATION OF SATURATION DISTRIBUTIONS IN POROUS MEDIA In order to study deviations that appear in the capillary pressure curve of high permeability porous samples due to gravity, pressure curve of high permeability porous samples due to gravity, a study of saturation distributions in a test sample is necessary. The horizontal pipet arrangement shown in Fig. 1 is the most suitable to study this effect because there is no need to correct the pressures with the rising meniscus in the pipet. Curve 1 in Fig. 2 represents a capillary pressure curve of a very thin porous disc. This curve can be considered a true capillary pressure curve of a porous material because of its short length; no gravitational effect is involved in that curve. Curve 1 in Fig. 2 will be used throughout for determining saturation distributions in a longer sample. In the example, a 30-mm long sample will be studied. SPEJ P. 85

Capillary Equilibrium in Porous Materials

1965 ◽  
Vol 5 (01) ◽  
pp. 15-24 ◽  
Author(s):  
Norman R. Morrow ◽  
Colin C. Harris
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Porous Materials ◽  
Capillary Pressure ◽  
Chemical Engineering ◽  
Fluid Distribution ◽  
Bulk Fluid ◽  
Fluid Saturation ◽  
Capillary Pressure Curves ◽  
The Relationship

Abstract The experimental points which describe capillary pressure curves are determined at apparent equilibria which are observed after hydrodynamic flow has ceased. For most systems, the time required to obtain equalization of pressure throughout the discontinuous part of a phase is prohibitive. To permit experimental points to be described as equilibria, a model of capillary behavior is proposed where mass transfer is restricted to bulk fluid flow. Model capillary pressure curves follow if the path described by such points is independent of the rate at which the saturation was changed to attain a capillary pressure point. A modified suction potential technique is used to study cyclic relationships between capillary pressure and moisture content for a porous mass. The time taken to complete an experiment was greatly reduced by using small samples. Introduction Capillary retention of liquid by porous materials has been investigated in the fields of hydrology, soil science, oil reservoir engineering, chemical engineering, soil mechanics, textiles, paper making and building materials. In studies of the immiscible displacement of one fluid by another within a porous bed, drainage columns and suction potential techniques have been used to obtain relationships between pressure deficiency and saturation (Fig. 1). Except where there is no hysteresis of contact angle and the solid is of simple geometry, such as a tube of uniform cross section, there is hysteresis in the relationship between capillary pressure and saturation. The relationship which has received most attention is displacement of fluid from an initially saturated bed (Fig. 1, Curve Ro), the final condition being an irreducible minimum fluid saturation Swr. Imbibition (Fig. 1, Curve A), further desaturation (Fig. 1, Curve R), and intermediate scanning curves have been studied to a lesser but increasing extent. This paper first considers the nature of the experimental points tracing the capillary pressure curves with respect to the modes and rates of mass transfer which are operative during the course of measurement. There are clear indications that the experimental points which describe these curves are obtained at apparent equilibria which are observed when viscous fluid flow has ceased; and any further changes in the fluid distribution are the result of much slower mass transfer processes, such as diffusion. Unless stated otherwise, this discussion applies to a stable packing of equal, smooth, hydrophilic spheres supported by a suction plate with water as the wetting phase and air as the nonwetting phase. SPEJ P. 15ˆ

Fractal Capillary Pressure Curve Models

Fractals ◽  
2017 ◽  
pp. 29-54
Author(s):  
Behzad Ghanbarian ◽  
Humberto Millán
Keyword(s):  
Capillary Pressure ◽  
Pressure Curve ◽  
Capillary Pressure Curve

Characterization of Fluid Drainage Mechanism at Core and Pore Scales: an NMR Capillary Pressure–Based Saturation Exponent Prediction

2021 ◽  
Author(s):  
Abubakar Isah ◽  
Abdulrauf Rasheed Adebayo ◽  
Mohamed Mahmoud ◽  
Lamidi O. Babalola ◽  
Ammar El-Husseiny
Keyword(s):  
Electrical Resistivity ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Gas Storage ◽  
Pressure Curve ◽  
Pore Scale ◽  
Resistivity Index ◽  
Capillary Pressure Curve ◽  
In Series ◽  
Saturation Exponent

Abstract Capillary pressure (Pc) and electrical resistivity index (RI) curves are used in many reservoir engineering applications. Drainage capillary pressure curve represents a scenario where a non-wetting phase displaces a wetting phase such as (i) during gas injection (ii) gas storage in reservoirs (e.g. aquifer or depleted hydrocarbon reservoirs). The gas used for injection is typically natural gas, N2, or CO2. Gas storage principally used to meet requirement variations, and water injection into oil-wet reservoirs are drainage processes. Resistivity index (RI) curve which is used to evaluate the potential of oil recovery from a reservoir, is also an important tool used in log calibration and reservoir fluid typing. The pore drainage mechanism in a multimodal pore system is important for effective recovery of hydrocarbon reserves; enhance oil recovery (EOR) planning and underground gas storage. The understanding of pore structure and drainage mechanism within a multimodal pore system during petrophysical analysis is of paramount importance to reservoir engineers. Therefore, it becomes inherent to study and establish a way to relate these special core analyses laboratory (SCAL) methods with quick measurements such as the nuclear magnetic resonance (NMR) to reduce the time requirement for analysis. This research employed the use of nuclear magnetic resonance (NMR) to estimate saturation exponent (n) of rocks using nitrogen as the displacing fluid. Different rock types were used in this study that cover carbonates, sandstones, and dolomites. We developed an analytical workflow to separate the capillary pressure curve into capillary pressure curve for macropores and a capillary pressure curve for the micropores, and then used these pore scale Pc curves to estimate an NMR - capillary pressure - based electrical resistivity index - saturation (NMR-RI-Sw) curve for the rocks. We predicted the saturation exponent (n) for the rock samples from the NMR-RI-Sw curve. The NMR-based saturation exponent estimation method requires the transverse (T2) relaxation distribution of the rock - fluid system at various saturations. To verify the reliability of the new workflow, we performed porous plate capillary pressure and electrical resistivity measurements on the rock samples. The reliability of the results for the resistivity index curve and the saturation exponent was verified using the experimental data obtained from the SCAL method. The pore scale Pc curve was used to ascertain the drainage pattern and fluid contribution of the different pore subsystems. For bimodal rock system, the drainage mechanism can be in series, in parallel, or in series - parallel depending on the rock pore structure.

Investigation of the Factors Influencing the Flowback Ratio in Shale Gas Reservoirs: A Study Based on Experimental Observations and Numerical Simulations

2021 ◽  
Vol 143 (11) ◽  
Author(s):  
Lin Hun ◽  
Zhou Xiang ◽  
Chen Yulong ◽  
Yang Bing ◽  
Song Xixiang ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Capillary Pressure ◽  
Influencing Factors ◽  
Shale Gas ◽  
Water Distribution ◽  
Pressure Curve ◽  
Gas Reservoirs ◽  
Desorption Process ◽  
Fluid Saturation ◽  
Shale Gas Reservoirs

Abstract The flowback behavior of hydraulic fractured horizontal well in shale gas reservoir is relatively different from that of conventional reservoirs. Therefore, it is necessary to investigate the relationship between the potential influencing factors and the flowback behavior in shale gas reservoirs. This study is based on experimental observations and numerical simulations. In the experiments, the flowback process was simulated through a gas displacement experiment, and the cores were scanned simultaneously to obtain the water distribution. Then, the water migration and retention mechanisms were investigated to determine the flowback behavior. For the numerical simulations, a multi-porosity model was established. The mathematical model accounted for the capillary pressure term. By matching the fluid saturation-front curves of the experimental and simulation results, a fitted capillary pressure curve, which reflects the multiple mechanisms controlling flowback, was obtained. Based on the established model and fitted capillary pressure, the flowback behavior and relevant influencing factors of the shale gas were investigated. The results show that the flowback ratio is inversely proportional to the clay content of the shale. A high salinity fracturing fluid or a surfactant solution can increase the flowback ratio. In addition, the injection pressure is proportional to the flowback ratio, while the matrix permeability and the flowback ratio have an inverse relationship. The adsorption–desorption process of gas has no significant effect on the flowback ratio. This study aims to provide a new method for analyzing the flowback performance of shale gas using a combination of experimental and numerical simulation methods.

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