Academic literature on the topic 'Pressure pulse-decay method'

The pulse decay test is the main method employed to determine permeability for tight rocks, and is widely used. The testing gas can be strongly adsorbed on the pore surface of unconventional reservoir cores, such as shale and coal rock. However, gas adsorption has not been well considered in analysis pulse decay tests. In this study, the conventional flow model of adsorbed gas in porous media was modified by considering the volume of the adsorbed phase. Then, pulse decay tests of equilibrium sorption, unsteady state and pseudo-steady-state non-equilibrium sorption models, were analyzed by simulations. For equilibrium sorption, it is found that the Cui-correction method is excessive when the adsorbed phase volume is considered. This method is good at very low pressure, and is worse than the non-correction method at high pressure. When the testing pressure and Langmuir volume are large and the vessel volumes are small, a non-negligible error exists when using the Cui-correction method. If the vessel volumes are very large, gas adsorption can be ignored. For non-equilibrium sorption, the pulse decay characteristics of unsteady state and pseudo-steady-state non-equilibrium sorption models are similar to those of unsteady state and pseudo-steady-state dual-porosity models, respectively. When the upstream and downstream pressures become equal, they continue to decay until all of the pressures reach equilibrium. The Langmuir volume and pressure, the testing pressure and the porosity, affect the pseudo-storativity ratio and the pseudo-interporosity flow coefficient. Their impacts on non-equilibrium sorption models are similar to those of the storativity ratio and the interporosity flow coefficient in dual-porosity models. Like dual-porosity models, the pseudo-pressure derivative can be used to identify equilibrium and non-equilibrium sorption models at the early stage, and also the unsteady state and pseudo-steady-state non-equilibrium sorption models at the late stage. To identify models using the pseudo-pressure derivative at the early stage, the suitable vessel volumes should be chosen according to the core adsorption property, porosity and the testing pressure. Finally, experimental data are analyzed using the method proposed in this study, and the results are sufficient.

The pressure-pulse decay is a preferred technique for determining permeability of unconventional gas reservoir rocks. The pressure-pulse decay often shows quite different characteristics during the early time and the later time. Most approaches for estimating the permeability proposed in the literature are required to use the later-time pressure-pulse decay measurements. However, the later-time data are often selected subjectively, lacking a universal criterion. In this paper, a method of differentiating the early-time and late-time behavior for pressure-pulse decay test is proposed. The analytical results show that the critical time (dimensionless time) of early-/late-time decay characteristics mainly depends on the volume ratios, and it increases first and then decreases with the volume ratios. The critical time for cases with same chamber sizes is much less than that for cases with unequal chamber sizes. Applicability of the proposed methods is examined using a numerical simulator, TOUGH+REALGASBRINE. The numerical results show that the pressure gradient along the sample varies nonlinearly at the early time and becomes a constant at the late time. Then, the proposed method is applied to real data for permeability estimation. It is found that the early-time behavior is negligible as the volume ratio takes on small values. As the volume ratios increase, the deviation becomes significant and considerable permeability errors will be produced if these early-time data are used.

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.

The permeability of coal is an indispensable parameter for predicting the coalbed methane (CBM) and enhanced CBM (ECBM) production. Considering the low permeability characteristics of coal, the permeability is usually measured by the transient technique in the laboratory. Normally, it is assumed that the calculated permeability will not greatly vary if the pulse pressure applied in the experiment is small (less than 10% of pore pressure) and previous studies have not focused on the effect of the pulse pressure on the measurement permeability. However, for sorptive rock, such as coals and shales, the sorption effect may cause different measurement results under different pulse pressures. In this study, both nonadsorbing gas (helium) and adsorbing gas (carbon dioxide) were used to investigate the adsorption effect on the gas permeability of coal measurement with the pulse-decay technique. A series of experiments under different pore pressures and pulse pressures was performed, and the carbon dioxide permeability was calculated by both Cui et al.’s and Jones’ methods. The results show that the carbon dioxide permeability calculated by Jones’ method was underestimated because the adsorption effect was not considered. In addition, by comparing the helium and carbon dioxide permeabilities under different pulse pressures, we found that the carbon dioxide permeability of coal was more sensitive to the pulse pressure due to the adsorption effect. Thus, to obtain the accurate permeability of coal, the effect of adsorption should be considered when measuring the permeability of adsorptive media with adsorbing gas by the transient technique, and more effort is required to eliminate the effect of the pulse pressure on the measured permeability.

We determined total arterial compliance from pressure and flow in the ascending aorta of seven anesthetized dogs using the pulse pressure method (PPM) and the decay time method (DTM). Compliance was determined under control and during occlusion of the aorta at four different locations (iliac, renal, diaphragm, and proximal descending thoracic aorta). Compliance of PPM gave consistently lower values (0.893 ± 0.015) compared with the compliance of DTM (means ± SE; r = 0.989). The lower compliance estimates by the PPM can be attributed to the difference in mean pressures at which compliance is determined (mean pressure, 81.0 ± 3.6 mmHg; mean diastolic pressure, over which the DTM applies, 67.0 ± 3.6 mmHg). Total arterial compliance under control conditions was 0.169 ± 0.007 ml/mmHg. Compliance of the proximal aorta, obtained during occlusion of the proximal descending aorta, was 0.100 ± 0.007 ml/mmHg. Mean aortic pressure was 80.4 ± 3.6 mmHg during control and 102 ± 7.7 mmHg during proximal descending aortic occlusion. From these results and assuming that upper limbs and the head contribute as little as the lower limbs, we conclude that 60% of total arterial compliance resides in the proximal aorta. When we take into account the inverse relationship between pressure and compliance, the contribution of the proximal aorta to the total arterial compliance is even more significant.

Arterial compliance (C) is related to the elasticity, size, and geometrical distribution of arteries. Compliance is a determinant of the load that impedes ventricular ejection. Measuring compliance is difficult, particularly in the pulmonary circulation in which resistive and compliant vessels overlap. Comparing different methods for quantification of compliance to a method that involves a continuous flow might help to identify the optimal method. Pulmonary arterial compliance was computed in six pigs based on the stroke volume to pulse pressure ratio, diastolic decay exponential fitting, area method, and the pulse pressure method (PPM). Compliance measurements were compared to those obtained under continuous flow conditions through a right ventricular bypass (Heartware Inc., Miami Lakes, FL, USA). Compliance was computed for various flows using diastolic decay exponential fitting after an abrupt interruption of the pump. Under the continuous flow conditions, resistance (R) was a decreasing function of the flow, and the fitting to P = e-t/RC yielded a pulmonary time constant (RC) of 2.06 s ( ± 0.48). Compliance was an increasing function of flow. Steady flow inter-method comparisons of compliance under pulsatile flow conditions showed large discrepancies and values (7.23 ± 4.47 mL/mmHg) which were lower than those obtained under continuous flow conditions (10.19 ± 1 0.31 mL/mmHg). Best agreement with steady flow measurements is obtained with the diastolic decay method. Resistance and compliance are both flow-dependent and are inversely related in the pulmonary circulation. The dynamic nature of the pulsatile flow may induce a non-uniformly distributed compliance, with an influence on the methods of measurement.

A Pulse Detonation Engine (PDE) is a new invented propulsion device that takes advantage of the pressure rise inherent to the efficient burning of fuel-air mixtures via detonations. Detonation initiation is a critical process that occurs in the cycle of a PDE. A practical method of detonation initiation is Deflagration-to-Detonation Transition (DDT), which describes the acceleration of a subsonic deflagration created using low initiation energies to a supersonic detonation. The DDT process is not well understood due to a wide range of time and length scales involving complex chemistry, turbulence and unsteady pressure waves. This paper discuss about the effects of blocking ratio in the augmentation of detonation pressure and velocity inside a cylindrical tube of diameter 0.0254m and a length of 1 m. The blockages are rectangular in shape placed at 2/3rd distances of the length of the tube and the heights of the blockages are varied in terms of the diameter of the tube as 1/4th, 1/3rd, ½, 2/3rd and 3/4th the diameter of the tube. The setup is then analyzed in MATLAB using the physics of Friedlander’s equation, which formulate the decay time duration of pressure across the tube length, with and without the blockage. Further, a 2D CFD analysis through ANSYS Workbench is conducted which gave the effective blocking ratio in a rectangular type of blockage placed at the 2/3rd position of the length of the tube and the results are compared. For variable pressures ranging from 1 MPa to 100 MPa input, the effective pulse length is around 0.25 seconds after which the decay of pressure and temperature attain the critical limit. Also it is found that the maximum feasible velocity occurs for an inlet pressure of 10 MPa and 2/3rd height of the blockage where the corresponding outlet velocity is 4692m/s and outlet total pressure being 10.542 MPa.

The steady flow method (SFM), most commonly used for permeability measurement in the laboratory, is not applicable for tight rocks, higher rank coals and coals under highly stressed condition because of the difficulty in measuring steady-state gas flowrates resulting from the tight rock structure of. However, accurate estimation of permeability of highly stressed coals is pivotal in coalbed methane (CBM) operations in order to precisely and effectively model and project long-term gas production. A fast and accurate permeability measurement technique is, therefore, required to investigate gas flow behavior of CBM reservoirs. The pulse-decay method (PDM) of permeability measurement is believed to be better suited for low-permeability rocks. In this study, application of the currently used pulse-decay laboratory permeability measurement techniques for highly stressed coals were evaluated. Considering the limitations of these techniques in permeability measurement of unconventional gas reservoirs, such as coal and gas shales, the conventional PDM was optimized by adjusting the experimental apparatus and procedures. Furthermore, the applicability of an optimized PDM was verified numerically and experimentally. This dissertation is composed of five chapters. To complete the research objectives as discussed above, it is necessary to have a profound understanding of the basic theories, such as, gas storage mechanism, gas migration, and permeability evolution during gas depletion in coalbed reservoirs. In Chapter 1, a brief discussion regarding the basic knowledge of reservoir properties and transport mechanisms is presented. The chapter also provides the appropriate background and rationale for the theoretical and experimental work conducted in this study. Chapter 2 presents the transient pressure-decay technique in permeability measurement of highly stressed coals and verifies the validity of Brace et al.’s solution (1968) by comparing it with Dicker and Smits’s solution (1988) and Cui et al.’s solution. The differences between these three solutions are discussed in detail. Based on the established permeability trends from these different solutions, a persuasive suggestion is presented for selection of the best alternative when testing coal permeability. Furthermore, permeability is regarded as a coupled parameter, resulting from the combined effects of mechanical compression and “matrix shrinkage” caused by desorption of gas. To isolate the role of gas desorption from the coupled result, a series of experiments were carried out under constant effective stress condition and a stress-dependent permeability trend was established. Chapter 3 proposes an optimized experimental design in order to improve the accuracy of the calculated permeability for sorptive rocks. In order to verify the optimized design theoretically, a modified mathematical model is presented and describes the one-dimensional fluid flow in porous media by a partial differential equation. The numerical solutions of the model are presented graphically to evaluate the fluid flow behavior in porous media. Finally, the validity of Brace et al.’s solution when testing sorptive rocks, without the need of consideration on the compressive storage and sorption effect, is elucidated. Chapter 4 demonstrates the efficiency and applicability of the optimized PDM through its direct application to experimental work designed to establish the permeability trend under best replicated in situ conditions. In this chapter, CO2 was used as the test fluid to profile and characterize the pulse decay plots due to its higher affinity towards coal than methane, and then establish the stress-dependent-permeability trend for highly-stressed CBM reservoirs. In this chapter, Brace et al.’s solution was also verified by comparing the laboratory data and computer simulated results obtained from the optimized mathematical model proposed in Chapter 3. The experimental work demonstrates that the optimized technique can be used for permeability tests of sorptive rocks without the need to carry out additional experimental work required to measure rock porosities and sorption isotherms. Finally, a summary and future research perspectives are presented in Chapter 5.

“Any chemical species, which under ambient conditions (i.e., a temperature around 25°C, and a pressure close to 1 atm) will, for a combination of kinetic and thermodynamic reasons, decay on a timescale ranging from microseconds, or even nanoseconds, to a few minutes” can be classified as a short-lived compound. According to this definition, suggested by Almond, it is clear that the experimental methods described in previous chapters can only be used to study the thermochemistry of long-lived substances. The technique that we address here, known as photoacoustic calorimetry (PAC) or laser-induced optoacoustic calorimetry (LIOAC), is suitable for investigating the energetics of molecules with lifetimes smaller than about 1μs. It relies on the photoacoustic effect, which was discovered by Bell more than 100 years ago. With the assistance of Tainter, he was able to “devise a method of producing sounds by the action of an intermittent beam of light” and conclude that the method “can be adapted to solids, liquids, and gases”. Figure 13.1 shows a photophone, “an apparatus for the production of sound by light,” used by Bell to investigate the photoacoustic effect. The controversy around the origin of this phenomenon was settled by Bell himself and by Lord Rayleigh; their views were rather close to our present understanding: When a light pulse is absorbed by a substance, a given amount of heat is deposited, producing a local thermal expansion; this thermal expansion propagates through the medium, generating sound waves. The basic theory of the photoacoustic effect was described by Tam and Patel and some of its applications were presented in a review by Braslavsky and Heibel. The first use of PAC to determine enthalpies of chemical reactions was reported by the groups of Peters and Braslavsky. The same groups have also played an important role in developing the methodologies to extract those thermodynamic data from the experimentally measured quantities. In the ensuing discussion, we closely follow a publication where the use of the photoacoustic calorimety technique as a thermochemical tool was examined. Consider the elementary design of a photoacoustic calorimeter, shown in figure 13.3. The cell contains the sample, which is, for instance, a dilute solution of a photoreactive species.

In this work, we address the issue of sealing performance of ring-shape valves compression packings. Our analysis is focused on the characterization of the permeabilty of the rings made of die-formed exfoliated graphite. Because of the tight character of the material, significant Klinkenberg effects are expected. In addition, due to the manufacturing process, permeabilities kz and kr as well as Klinkenberg coefficients bz and br in the respective axial and radial directions are markedly different and strongly dependent upon the applied stress. A specific experimental device, based on pressure pulse relaxation of nitrogen through the material, was designed for the measurement in each direction under a controlled axial compression. Determination of kz, kr and bz, br is performed on the basis of a non-stationary gas-flow model in the radial and axial directions using an inverse procedure applied to the pressure decay signal. Our results confirm the efficiency of the method developed here. They clearly show the anisotropic character of the material (kz is roughly one order of magnitude larger than kr) and the dependence upon axial compression. The present analysis is the key step before further quantification of the leak rate which may result from the permeation through the material as envisaged here as well as through interfaces between the housing, the packings and the stem.

Abstract Water hammer is oscillatory pressure behavior in a wellbore resulting from the inertial effect of flowing fluid being subjected to an abrupt change in velocity. It is commonly observed at the end of large-scale hydraulic fracturing treatments after fluid injection rate is rapidly reduced or terminated. In this paper, factors affecting treatment-related water hammer behavior are disclosed, and field studies are introduced correlating water hammer characteristics to fracture intensity and well productivity. A simulator based on fundamental fluid-mechanics concepts was developed to model water hammer responses for various wellbore configurations and treatment characteristics. Insight from the modeling work was used to develop an optimal process of terminating fluid injection to obtain a consistent, identifiable oscillatory response for evaluating water hammer periodicity, decay rate, and oscillatory patterns. A completion database was engaged in a semi-automated process to evaluate numerous treatments. A data screening method was developed and implemented for enhancing interpretation reliability. Derived water hammer components were correlated to fracture intensity, well productivity and in certain cases, loss of treatment confinement to the intended treatment interval. Using the above process, thousands of hydraulic fracturing treatments were evaluated, and the results of that work are included in this study. The treatments were performed in wells based in Texas, South America, and Canada and completed in low permeability and unconventional reservoirs. The water hammer decay rate was determined to be a reliable indication of the system friction (friction in the wellbore and hydraulic fracture network) that drains energy from the water hammer pulse. In unconventional reservoirs characterized by small differences in the minimum and maximum horizontal stresses, high system friction correlated positively with fracture intensity/complexity and well performance. Results were constrained with instantaneous shut-in pressure (ISIP) and pressure falloff measurements to identify instances of direct communication with previously treated offset wellbores. The resulting analyses provided: – identification of enhanced-permeability intervals – indications of hydraulic fracture geometry – assessment of treatment modifications intended to enhance fracture complexity – identification of loss of treatment confinement to the intended interval – location of associated points of failure in the wellbore Topics covered in the paper include: Introduction Joukowsky Equation Period and Boundary Conditions Review of Prior Work on Water Hammer Analysis Shut-In Pressure Data, Analysis, and Model Data collection frequency Data issues and requirements Water Hammer Analytical Method Water Hammer Model Effects on Water hammer signature Fluid properties Step-down rate change and duration Perforation friction Applications Identification of Boundary Condition Identification of Treatment Stage Isolation Identification of Casing Failure Depth Identification of Excess Period (Excess Length) Case Study – Water Hammer Data in an Unconventional Reservoir Interpretation of frac geometry and friction in the fracture Relationship to well productivity