Pulse Decay Method Research Articles

Simulation Analysis of the Characteristics of Layered Cores during Pulse Decay Tests

The permeability of low-permeability cores is generally measured using a pulse decay method. The core of low-permeability rocks, such as shale, often has a layered structure. The applicability of pulse decay testing for layered cores is not clear. In this study, the performance of the pulse decay method on layered cores was comprehensively investigated. Numerical simulations were conducted to investigate the influence of the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers on the pulse decay pressure and pressure derivative curves, as well as the permeability obtained from pulse decay testing. The results revealed that the pressure curves of layered cores exhibit distinct differences from those of homogeneous cores if the upstream permeability is larger than the downstream one. The pressure derivative curve shows more inclined or horizontal straight-line segments than in the homogeneous case. The shapes of the pressure and pressure derivative curves are affected by the upstream and downstream positions of the core, but the tested permeability is not affected. The tested permeability differs from the equivalent model permeability, with an error of up to 22%. If the number of layers is not less than 10, the permeability obtained from the pulse decay test is consistent with that of the equivalent model. These differences are influenced by the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers. To improve the accuracy of permeability analysis in pulse decay testing for layered cores, curve fitting using the characteristics of the pressure derivative curve can be employed.

Water Permeability Measurements by Steady-State and Pulse Decay Methods on the Callovo-Oxfordian Claystone and Impact on its Mechanical Properties

Water Permeability Measurements by Steady-State and Pulse Decay Methods on the Callovo-Oxfordian Claystone and Impact on its Mechanical Properties

The Submerged Nozzle Damping Characteristics in Solid Rocket Motor

In this paper, the effects of the geometry of a submerged nozzle on the nozzle damping characteristics are studied numerically. Firstly, the numerical method is verified by the previous experimental data. Then, the mesh sensitivity analysis and the monitor position independence analysis are carried out. Thirdly, the effects of nozzle geometry on nozzle damping are systematically studied, and focuses are placed on the cavity size, convergent angle and divergent angle. The pulse decay method is utilized to evaluate the nozzle decay coefficient. Several important results are obtained: the submerged cavity with large volume leads to low frequency acoustic oscillations in the combustion chamber and corresponds to a small nozzle decay coefficient; then, as the nozzle convergent angle is decreased, the nozzle decay coefficient is increased. In addition, the nozzle divergent angle has a trivial effect on the nozzle decay coefficient; and lastly, the effects of the temperature on the nozzle damping capability are conducted. The results show that an increase of the working temperature leads to an increase of the nozzle decay coefficient; therefore, the damping force is increased.

Modification of Pulse Decay Method for Determination of Permeability of Crystalline Rocks

An improvement of the pulse decay method of rock permeability measurement is presented. The technique is based on fitting experimental data to analytical and numerical solutions of the filtration equations derived with regard to the variation of flowing gas properties with temperature and pressure. A special apparatus and software for the implementation of this method were developed. A single experiment in which gas is used as a flowing medium enables determining both the permeability of a sample to water and the Klinkenberg constant. The permeability measurements on the samples of different types of rock with various reservoir properties were carried out and demonstrated satisfactory accuracy and efficiency of the method. An effective method for anisotropic permeability measurement is proposed as a development of this technique.

Experimental Study on Stress Sensitivity Evaluation and Permeability Anisotropy of Shales in Songliao Basin

Shale oil and gas resources are abundant in Songliao Basin, and shale reservoirs tend to have certain permeability anisotropy with different pore or laminar structures in different directions, and there is no experimental analysis of shale anisotropy and reservoir sensitivity. To solve this problem, this paper tests the shale permeability by pulse decay method, obtains the variation curve of permeability and effective stress, and analyzes the experimental data. The experimental results of permeability show that the permeability of shale in Songliao basin is basically 10-4mD, and the permeability parallel and perpendicular to the laminae shows strong anisotropy, and the permeability perpendicular to the laminae is about 3%-14% The permeability of different rock samples decreases exponentially with the increase of effective stress. It provides basic data support to ensure the development of shale oil in Songliao Basin.

A large pressure pulse decay method to simultaneously measure permeability and compressibility of tight rocks

Permeability and pore volume compressibility are two key parameters of rocks for the evaluation and exploitation of oil/gas reservoirs. This study presents a large pressure pulse decay method (LPPD) for simultaneously estimating rock permeability and compressibility. A numerical solution of the LPPD model is first developed using the finite difference method. A globally convergent least-squares method is proposed to determine permeability and pore volume compressibility. Then, a series of large pressure pulse decay tests are conducted on a coal sample by taking water as the testing fluid. The proposed method is applied to processing the experimental data obtained from large pressure decay experiments under different confining pressures. The results indicate that the fitting coefficients are all larger than 0.99, which shows that the LPPD can well match the experimental data. The estimated permeabilities are compared and verified with Brace's method and modified Brace's method. Since the pore volume and the pore volume compressibility of the sample are not considered in Brace's method, the calculated permeabilities of the new method are smaller than the other two methods. The estimated values of pore volume compressibility are also verified by experimental results, and the maximum error between them is −6.93%, which shows that the proposed method is accurate and reliable for estimating the two parameters. At last, a new simpler method is proposed to calculate the pore volume compressibility, which shows acceptable approximation results. Compared with other transient methods of measuring permeability, the LPPD method can simultaneously measure rock permeability and pore volume compressibility. With the obtained parameters, the permeability of rock under different effective stresses can be obtained. The results in this study can be beneficial to the evaluation and exploitation of oil/gas reservoirs.

Investigation of Shale Permeability Evolution considering Bivalued Effective Stress Coefficients for CO2 Injection

Because of the existence of multiscale pores from nano- to macroscale, a multimechanistic shale gas flow process involving the Darcy and Knudsen flows occurs during gas shale well depletion. The respective contribution of the Darcy and Knudsen flows to the permeability is constantly changing with pressure evolution. In this study, laboratory measurements of shale permeability with CO2 injections were carried out under hydrostatic conditions, using the transient pulse-decay method. The “U”-shape permeability curve resulted in both positive and negative effective stress coefficients (Biot’s coefficient) χ . A permeability turning point was thus created to partition permeability curves into the Darcy and Knudsen sections. The Knudsen effect was proven to be significant at low pressure/late time in the laboratory. Effective stress and sorption-induced deformation have been found to govern the Darcy permeability evolution under the tested experimental conditions. Thus, negative effective stress coefficients, together with the positive ones, should be applied to a nonmonotonic pressure-permeability evolution to explain the concurrent effect of the Darcy flow and Knudsen flow at different pore pressures.

Comparative Study on Applicability of Permeability Testing Methods in Shale Reservoirs.

Permeability is one of the important parameters for reservoir evaluation, development, and production prediction. Shale oil and gas being an important unconventional energy source, the characteristics of extremely low porosity and permeability bring great challenges to development. Therefore, it is crucial to accurately describe the permeability of shale reservoirs. Based on the steady-state method, pulse decay method, and nuclear magnetic resonance (NMR) method, this paper systematically analyzed the adaptability of various test methods in shale reservoir permeability characterization and optimized the best test method. On this basis, a new high-precision NMR single parameter Tw of shale reservoirs is established, and the compatibility between the model and the experimental results is verified. The results show that the new model with Tw as the main parameter is the most accurate one to calculate the permeability of shale reservoirs in the range of 10–3–100 mD. The correlation coefficient between the weighted average relaxation time and pulse decay method is as high as 96.31%, and the relative error between the permeability predicted by the new model and the pulse permeability is 19.43%. These studies have laid a theoretical foundation for the quantitative characterization of fluid seepage capacity in shale reservoirs.

Laboratory Measurement of Permeability Evolution Behaviors Induced by Non-Sorbing/Sorbing Gas Depletion in Coal Using Pulse-Decay Method

Laboratory Measurement of Permeability Evolution Behaviors Induced by Non-Sorbing/Sorbing Gas Depletion in Coal Using Pulse-Decay Method

Reassessment of transient permeability measurement for tight rocks: The role of boundary and initial conditions

The pulse-decay method is one of the most widely used transient methods for permeability measurements. Though many modified pulse-decay methods with various experimental designs have been proposed, the theoretical analysis is still insufficient, especially from the perspective of the boundary and initial conditions. In terms of boundary conditions, the tests can be conducted with a reservoir of finite volume on one side of the sample and a reservoir of “zero”, finite, or “infinite” volume on the other side. Common initial conditions differ in terms of the pore pressure within the sample at the start of the test, which can be either equal to the downstream or the upstream reservoir pressure. For the first time, the method of separation of variables is used to obtain the analytical solutions of the pulse-decay methods and assess the specific effects of boundary and initial conditions. The results indicate that if the pressure difference between two ends of the sample is less than 10 %, the slope of the semi-logarithmic plot of pressure versus time is solely determined by the boundary conditions (pore volume/reservoir volume ratios), and the intercept depends on both the boundary and initial conditions. We show that the requirement that a new pressure pulse cannot be applied before the previous pulse subsides is unnecessary and the restriction on the pulse size can be relaxed to some extent. The duration of the pulse-decay tests is mainly determined by the boundary conditions, and the influence of initial conditions decreases as the reservoir volumes increase. The error in the permeability evaluation caused by the inaccuracy of pore and reservoir volume measurements is also discussed.

Extension of the Gas Research Institute (GRI) method to measure the permeability of tight rocks

Different methods have been proposed to measure the permeability of tight rocks such as shales, mudstones, tight sandstones, and carbonates. The Gas Research Institute (GRI) method has been used to measure permeability and porosity of cuttings, crushed particles, or powders. The conventional pulse-decay method has been used to measure the permeability of bulk samples. The GRI method has a potential drawback in that measured permeability may not represent the original complex pore network properly. In this work, an innovative extension of the GRI method was applied to bulk samples with both regular and irregular shapes. A geocellular model was created, history matching was performed to evaluate permeability after constructing a numerical model based on the configuration of the apparatus and initial conditions. Permeability values measured under similar conditions vary from the order of 1E-5 to1E-2 mD for different samples, and the results were validated using permeability values from conventional pulse-decay tests as the benchmark. This approach highlights the simplicity of operation and applicability to irregularly shaped samples, as cylindrical samples are not always available for testing. In addition, this approach significantly shortens the test duration.

A simplified transient technique for porosity and permeability determination in tight formations: Numerical simulation and experimental validation

AbstractA simplified pulse decay method (PDM) with only a single downstream reservoir is proposed to replicate the in situ conditions for reservoir fluid flow, where the pore pressure at any location declines as production continues. The proposed PDM also allows determining the effective porosity and permeability for the core sample under replicated in situ conditions. A mathematical model is firstly established to closely represent the experimental design and verify the feasibility of the method. The analytical solutions of the model are derived to calculate the effective sample porosity and permeability. A series of experiments are then conducted under triaxial stress condition, and a detailed comparison is also made between the PDMs with a single upstream reservoir and a single downstream reservoir. The experimental results showed that accurate measurements on effective sample porosity and permeability can be achieved by the single downstream reservoir PDM due to its capability of better replicating the in situ fluid flow behavior, which extends the application of the transient technique. It is also found that the pore pressure along the sample changes linearly, and its gradient varies with time, indicating the applicability of the single‐reservoir PDMs in permeability determination. This method also lays a foundation for studying flow behavior when a second fluid phase evolves during pressure decline, which occurs in many reservoirs.

Anisotropic rock permeability evolution model based on wing crack propagation after dynamic load testing

The permeability evolution of rock is essential in geotechnical engineering, which is related to seepage. A permeability evolution model, which is based on the wing crack propagation model and Darcy’s law, is created for rock after dynamic load testing with confining pressures. It is assumed that permeability has two types: isotropic initial permeability and anisotropic microcrack-induced permeability. In this model, the wing crack length is associated with the absorption energy per unit volume of the rock specimen under dynamic loads, in accordance with the surface energy theory. Assuming that the initial crack families are evenly distributed, the contribution of each crack family to permeability in different directions is investigated. In this study, an expression of permeability, which is related to axial stress, confining pressure, and absorbed energy per unit volume, is obtained. Two groups of dynamic load testing with confining pressures of sandstone are conducted using a modified split Hopkinson pressure bar technique. In group A, the incident energy is a variable, whereas in group B, the confining pressure is a variable. After the dynamic load testing, the permeability of the sandstone specimens is measured using the pulse decay method on MTS 815. Owing to the limitations on the test equipment, only the permeability in the direction of the dynamic load is measured. The permeability obtained from the dynamic load testing is in good agreement with the permeability calculated by the model. In this model, the anisotropy of rock permeability is theoretically studied. The minimum microcrack-induced permeability in all directions is about 0.65 of the maximum permeability value. In summary, the model discussed here enables the prediction of the permeability of the rocks under dynamic impact and establishes the relationship between macro-mechanical parameters and micro-mechanical parameters. In addition, it provides a new idea for the research on the anisotropy of rock permeability.

Theoretical Comparison of Test Performance of Different Pulse Decay Methods for Unconventional Cores

Various pulse decay methods are proposed to test tight cores. These methods can be divided into three types. This study compares the performance of these methods to test the permeability of unconventional cores in terms of homogeneous cores, dual-medium cores, and gas adsorption, including the pressure equilibrium time, possible errors caused by conventional analysis methods, and reflections on the characteristics of dual-media. Studies shows that the two test methods with an antisymmetric relationship in the boundary conditions have basically identical test performance. When testing homogeneous cores, regardless of whether the gas is adsorptive or not, the pressure equilibrium time of the first type of method is approximately half of that of the second type of method. The dual-medium parameters seriously affect the pressure equilibrium time of different methods, which may cause the difference of order of magnitude. For homogeneous cores, the permeability errors of the first and second types of methods caused by porosity errors are similar and larger than that of the third type of method. For dual media, the fracture permeability obtained by the third type of method using the conventional analysis method may differ from the actual value by tens of times. No method can significantly eliminate the sorption effect. When the core is a dual-medium, only the pressure curves of the upstream positive-pulse method, downstream negative-pulse method and one-chamber method can reflect the characteristics of dual media. The pressure derivative of the one-chamber method cannot reflect the characteristics of dual media at the early time. The pressure derivative of the second type and the upstream positive-pulse downstream negative-pulse method can reflect the complete characteristics of dual media, but their pressure derivative of the constant-slope segment is small, and the interporosity flow parameter may not be identified.

A laboratory investigation of the impact of solvent treatment on the permeability of bituminous coal from Western Canada with a focus on microbial in-situ processing of coals

Coal biogasification via microbial metabolization has great potential to produce renewable methane and facilitate carbon dioxide sequestration while multiple challenges still remain to tackle especially the deficiency of direct permeability measurements. The pulse decay method has been performed on high-volatile bituminous coals from Western Canada to investigate permeability variations for raw, solvent soaked and solvent-extracted samples under variable confining and pore pressures. Coal permeability decreases with respect to increasing confining pressure while it increases tens of times with respect to increasing pore pressure. The vertical permeability is about one order of magnitude lower than horizontal one, indicating highly anisotropic nature of coal. Coal bioconversion stimulation by adding solvent may trigger a series of coal–solvent interactions due to matrix swelling. Coal permeability drops about one order of magnitude after soaked in toluene and dichloromethane but less dramatic in hexane. However, solvent-extraction and sorptive material removal can reduce the swelling strain and increase permeability about two orders of magnitude. Coal matrix swelling and shrinkage in solvent, coupled with the effects of external effective stress, make coal permeability relationships complicated and a deeper understanding of these processes is needed for coal bioconversion application in fields.

Experimental, algorithmic, and theoretical analyses for selecting an optimal laboratory method to evaluate working fluid damage in coal bed methane reservoirs

The existing laboratory methods have limitations that make it very difficult to select the most suitable method for obtaining precise permeability measurements for evaluating reservoir formation damage. To date, there has been no research critically addressing this issue. In this study, the permeabilities of core or cuttings samples taken from No.15 Reservoir in the Qinshui Basin before and after damage caused by drilling and fracturing fluids were randomly measured using six general laboratory methods. Their average permeability values, as well as the extent of absolute and relative formation damage, were calculated and analyzed using a simple ranking method, statistical screening algorithm, and theoretical method. The results show that, first, there is a regular distribution of absolute reservoir damage measured by the laboratory methods; and second, the application priority of permeability measurement methods for formation damage evaluation in coal bed methane reservoirs is as follows: cuttings pulse decay method > constant flow rate method > nuclear magnetic resonance method > plunger pulse decay method = pressure oscillation method = constant pressure method. The cuttings pulse decay method is therefore recommended for measuring core matrix damage, while the constant flow rate method is suggested for measuring overall damage to core samples.

A pulse-decay method for low permeability analyses of granular porous media: Mathematical solutions and experimental methodologies

A pulse-decay method for low permeability analyses of granular porous media: Mathematical solutions and experimental methodologies

Matrix permeability measurement from fractured unconventional source-rock samples: Method and application

Shale matrix permeability is one of the most important parameters for characterizing a source rock reservoir and for predicting hydrocarbon production. The low permeability value and the presence of induced fractures during core retrieval and transportation make the accurate measurement of the true permeability values for source rocks a significant challenge for the industry. The steady state flow method and the transient pressure pulse decay method on core plug samples mainly measure the permeability of fractures when fractures are present. While the Gas Research Institute (GRI) method that uses pressure decay on crushed rock samples was designed to overcome this difficulty associated with the induced fractures, its measurement results are reported to be sensitive to the particle size of crushed rock samples and also need correction of Knudsen diffusion effect. Moreover, the GRI method is limited to the unconfined stress condition.This work develops a practical method to measure the matrix permeability values from fractured source rock samples by extending the commonly used pressure pulse decay method. A source rock sample with fractures can be more accurately described by a dual-continuum system consisting of a fracture continuum and a matrix continuum. During the pulse decay test, the initial flow across the source rock sample is dominated by the fracture continuum because it has much higher permeability values than those for the rock matrix. Thus, the initial gas pressure signals from the test are used to estimate the fracture permeability. During the late-stage of a pulse decay test, the flow process within the rock sample is controlled by the rock matrix. The observed pressure signals at this stage are used for estimating matrix permeability. The method is based on the analytical solution to gas flow in the fractured rock sample and relatively simple to apply in practice. Both fracture and matrix permeability's dependence on the effective stress can be assessed with this method.

Effects of pore-fracture structure of ductile tectonically deformed coals on their permeability: An experimental study based on raw coal cores

The distribution area of ductile tectonically deformed coals (TDCs) usually coincides with the forbidden zones for coalbed methane (CBM) development. Permeability of coal reservoirs, an important indicator to evaluate the energy potential of CBM, is directly affected by the pore-fracture structures. To study the controlling mechanism of pore-fracture structures on permeability, we investigated the micropore - micro-fracture structures of various ductile TDCs by adopting mercury intrusion porosimetry (MIP) and low-pressure gas adsorption. The permeability and the pressure sensitivity of the standard TDC cores were tested by the pressure pulse decay method. The results showed that the total pore volume of ductile TDCs, especially the mesopores and macropores, significantly increased from that of primary structure coals (PSCs), while the volume of transitional pores only slightly increased in strongly crumpled and mylonitized coals, and thus, the dominant pores in coals gradually changed from micro-fractures to mesopores and macropores. The pore-fracture structure of ductile TDCs showed a poorer connectivity and a higher roughness than PSCs. The permeability of typical ductile TDCs obviously decreased, the permeability heterogeneity significantly increased, and the pressure sensitivity of permeability generally showed a pattern of “weakly crumpled - > PSCs > strongly crumpled - and mylonitized coals”. Correlation analysis showed that the weakly crumpled coals that contain well-developed and well-connected micro-fractures and fewer <10 μm coal particles usually display high permeability. In strongly crumpled – and mylonitized coals, the connected pore-fracture structures were damaged and many pore throats and flask-shaped pores formed, which is the main reason for the reduced permeability and the high permeability damage rate.

The rock-fabric/petrophysical characteristics and classification of the micropores hosted between the calcite and dolomite crystals

For the substantial hydrocarbon potential and academic significance, focus of interest has been directed towards the microporous carbonate. Compared with the documented shallow burial microporous carbonate, carbonate with a depth deeper than 6000 m present, of course, different characteristics due to the long-term influences of the strong cementation and compaction. With the deepening of exploration, it is therefore essential to improve the understanding about the deep burial microporous carbonate. In this paper, an integrated petrographic and petrophysical approach, which combines thin section, high-resolution field emission scanning electron microscopy (FESEM) observations, and nuclear magnetic resonance (NMR) measurements, is chosen to study the deep to ultradeep carbonate in the Shunnan area, Tarim Basin, NW China.Results show that all the studied carbonate samples consist entirely of micropores with a radius less than 10 μm, belonging to the strictly microporous carbonate. These micropores exist between the calcite and dolomite microcrystals. To reliably calculate the permeability based on NMR data, a newly introduced factor P aiming to adjust the T2 cut-off value derived from the relaxation curve is applied to enhance the Coates model. Values of P are found to correlate well with the FFI (free fluid index) of the bioclastic and bioclasts-free detrital limestones through different quantitative relationships, respectively. Permeabilities calculated from the modified Coates model are in good agreements with those measured by the pulse-decay method (R2 = 0.93, 0.67). Considering the existing classifications of pore systems are not applicable to the peculiar intercrystalline micropores within the deep burial microporous carbonate, a noval classification scheme is thus explored by integrating the rock-fabric and petrophysical properties. Micropores hosted within the subhedral to anhedral microcrystals with distinct boundaries are the main reserving space of the microbial lime-/dolostone, which lead to relatively higher porosities (averaging 3.41%) than the detrital limestone (1.99%) and dolostone (2.47%), and an identical right-skewed trimodal NMR T2 distribution. Micropores related with the coalescent polyhedral to anhedral microcrystals, that are always glued together to form fusing boundaries, are mainly located within the micrite matrix and allochem of the detrital limestone. Certain relationships among porosity, permeability and FFI/BVI also exist for the bioclastic and bioclasts-free detrital limestones, respectively. Micropores within the dolostone exist between the rhombic dolomite crystals. This proposed classification of micropores comprehensively reflects the depositional, diagenetic textures and physical properties of the deep burial microporous carbonate. The particularity of microbial lime-/dolostone is highlighted.