Re-opening Pressure Research Articles

Geomechanical analysis of lost circulation control in tight formations

Unconventional oil and gas reservoirs, especially that in tight formations, contribute great parts to the global energy. During drilling in tight formations, lost circulation was one of the major problems, which can cause large amount of non operation time and millions of losses. In order to migrate the problem, lost circulation materials (LCMs) were used to prevent reopening of the fracture by isolating the fracture tip while the calculation of stress intensity factor (SIF) and fracture width is the key to LCMs design. In this paper, a dual porosity medium flow model suitable for tight formation is established to calculate the pressure distribution in fracture, and the fracture width and fracture reopening pressure (FROP) is then calculated by using the semi-analytical fracture mechanics model. Sensitivity analysis of critical parameters, for example, fracture length, wellbore radius, LCMs permeability, viscosity, wellbore pressure, and two rock-mechanics-related properties are implemented. The fracture width is larger in the formation with large horizontal principal stress anisotropy, low Young’s modulus and Poisson’s ratio. The increase in fracture length, wellbore radius and wellbore pressure also contributes to fracture opening. Meanwhile, we compared the situation before and after fracture plugging and the results emphasize that the fracture reopening is less likely to occur under the conditions of high viscosity and low permeability LCMs. The method proposed in this study can be used to calculate fracture width and FROP, which has potential significant application for lost circulation control in tight formation.

Evaluation of the Effects of Nano-SiO2 Microemulsion on Decompression and Augmented Injection in the Eunan Tight Reservoir

The residual oil saturation of the matrix near the well zone of a tight reservoir is high due to the tight reservoir’s complex conditions, such as the small pore throat radius and low permeability of the matrix and the development of microfractures, which can result in serious water channeling, even after long-term water injection development. The aim of this paper is to improve the effects of depressurization and augmented injection for tight reservoir waterflooding development by reducing the tight matrix’s residual oil saturation, increasing and maintaining its water phase permeability near the well zone using a nano-SiO2 microemulsion system with a small particle size and high interfacial activity. Therefore, four nano-microemulsion systems were evaluated and screened for their temperature resistance, salt resistance, interfacial tension, solubilization, and dilution resistance. A microemulsion system of 13% A + 4% B + 4% C + 4% n-butanol + 6% oil phase + 69% NaCl solution (10%) + 1% OP-5 + 0.5% anti-temperature agent + 0.3% nanosilica material was preferred. According to the core displacement experiment, the depressurization rate can reach 28~60% when the injection concentration of the system is 1~10% and the injection volume is 2~5 PV. The results of the on-site test show that the water injection pressure dropped to 17.5 MPa, which was lower than the reservoir fracture re-opening pressure. The pressure reduction rate was approximately 20%. The validity period of the depressurization and augmented injection has reached 23 months to date.

Wellbore strengthening evaluation with core fracturing apparatus: An experimental and field test study based on preventive approach

One of the most persistent and complicated challenges during drilling a well is lost circulation, which leads to more operational cost, time, and risk. Wellbore strengthening (WBS) with the addition of special solid particles, means lost control materials (LCMs), in drilling fluid is a major solution to control the fluid loss and improve the formation pressure-bearing capacity. The preventive approach of wellbore strengthening is based on the plastering effect of mud cake to inhibit the initiation of new induced fractures or the growth of pre-existing ones. The sealing capability of the mud cake can be affected by LCM properties which has been evaluated by some plugging apparatus with slotted disk in previous researches. However, in this paper, a self-designed core fracturing laboratory setup has been developed to simulate the fracturing process of a rock sample in a more realistic situation and study the effect of LCM particles on the creation of an efficient filter cake to improve the fracture gradient of the formation. Artificial cylindrical concrete cores with a central hole have been used to eliminate the heterogeneity effect of the rock and achieve the same experimental conditions. The fracture breakdown pressure (FBP) and fracture reopening pressure (FRP) have been considered as the objective parameters for evaluation of LCM performance. The experimental results on 18 core samples with two different types of LCM and different particle size distribution show that the addition of LCM particles into drilling fluid can improve FBP and FRP up to 33 % and 72 %, respectively. This indicates that the sealing/plastering effect of mud cake can be improved by LCM properties to achieve a higher fracture pressure. In addition, different fluid systems with different LCM types and LCM sizes have various effects on the preventive approach of wellbore strengthening. Finally, one of the drilling fluid formulations with a desirable performance during laboratory tests was selected to apply for drilling the 12–1/4” hole section in one of Iranian oil fields as a preventive approach where a history of severe lost circulations had been reported. The results of field test showed that using this approach was more successful than the remedial approach used in all previous wells of this field and resulted in a significant reduction in cost and material consumption.

A First Order Quantification of Effects of Uncertainties in Hydro-fracturing Parameters on Tunnel Ovalization Estimates

In-situ stresses are always present in rock-masses due to gravitational and tectonic forces. Excavation of a tunnel in such a pre-stressed media causes deformation of tunnel cross-section. Ovalization of tunnels due to in-situ stresses in rock-mass is an important design parameter. For estimation of tunnel ovalization, state of in-situ stresses needs to be determined first. In-situ stresses determined through hydro-fracturing technique (HFT) are dependent upon the three HFT parameters: (a) shut-in pressure, (b) re-opening pressure, and (c) fracture orientation. A critical review of previous studies indicates that HFT parameters are subjected to uncertainties due to (1) limitations of testing procedures and equipment, (2) assumptions and subjective engineering judgment associated with interpretation of test results, and (3) inherent variability of geological formations. Therefore, tunnel deformation estimates based on in-situ stresses determined through HFT would also be affected by these uncertainties. In this paper, a framework based on the first-order second moment method is developed to evaluate the effects of uncertainties in hydro-fracturing test data on tunnel deformation. The analysis indicates that uncertainty in tunnel deformation depends upon the uncertainty levels as well as magnitude of the three HFT parameters along with Poisson’s ratio, height of overburden, and the angular location of the point on the tunnel periphery where deformation is being estimated. It is also found that among the three parameters, the shut-in pressure has the maximum relative contribution in the resulting uncertainties in tunnel ovalization with an average of 68% (± 8% standard deviation). The proposed methodology is explained through an example case-study from Bukit Timah Granite rock-mass of Singapore. It is found that for a range of coefficient of variation of shut-in and re-opening pressure from 0 to 50%, the maximum coefficient of variation of tunnel deformation varies between 63 and 332%. In view of such high uncertainties, it is recommended that uncertainties of HFT parameters must be taken into account in the design procedure to avoid unsound engineering judgments.

An integrated fluid flow and fracture mechanics model for wellbore strengthening

Fracture-based wellbore strengthening techniques are preventive methods that can reduce the cost of lost circulation and non-productive time. The mud weight window can be extended by plugging fractures with wellbore strengthening materials (WSM) in the near-wellbore region. To maximize the strengthening effect, accurate fracture geometry prediction is of critical importance to the design of WSM. This paper presents a novel, coupled fluid flow and fracture mechanics model for wellbore strengthening applications that accounts for near-wellbore-induced fracture behavior. For fluid flow, mass conservation is considered and momentum conservation is examined; the latter shows that pressure loss with near-wellbore fracturing is low. Thus, we can neglect the pressure drop in the fractures and assume the fluid pressure inside the fractures is equal to the wellbore pressure. The pressure-width relationship (rock elastic deformation) and stress intensity factor are obtained by a dislocation-based approach. For the fracture propagation criterion, the calculated stress intensity factor is compared with fracture toughness at each time step.The stress intensity factor and fracture reopening pressure (FROP) are verified with Tada's model and Feng's model, respectively. Then, simulation results are compared with the large leak-off solutions of the Perkins-Kern-Nordgren (PKN) fracture model. The simulation results reveal that the PKN model overestimates the fracture mouth width, fracture length, and wellbore pressure. Furthermore, the simulation results of wellbore pressure show a different trend. Therefore, we cannot directly use the PKN model to design wellbore strengthening applications. The main reason is the presence of wellbore can generate near-wellbore effects that cannot be disregarded. Finally, we conduct a comprehensive parametric study (i.e., fracture toughness, Young's modulus, Poisson's ratio, horizontal stress ratio, and permeability) on wellbore strengthening fracturing.The proposed model is useful for wellbore strengthening applications using the intentionally induced fractures (i.e., near-wellbore fracturing). Particle size distribution (PSD) of WSM can be designed based on the simulated fracture geometry. No complex model mesh generation or assignment of boundary conditions are needed, which are commonly used in finite element simulation or other numerical methods. The proposed model can also be used to optimize wellbore strengthening operations by performing sensitivity analysis.

Critical pressure of closure fracture reopening and propagation: Modeling and applications

The reopening and propagation of natural closure fracture is one of the key causes of lost circulation in the fractured formation, which is directly related to safe and efficient drilling. In this paper, considering dip angle and dip direction of the fracture, the stress state on closed fracture surface near borehole is analyzed. Meanwhile, combining the critical mechanics condition of fracture reopening and propagation, a new model of the critical pressure for reopening and propagation of natural closure fracture is established based on rock mechanics theory and Linear Elastic Fracture Mechanics (LEFM), and the corresponding solution algorithm is proposed. Furthermore, the new model is utilized in investigating reopening and propagation of natural closure fracture, which intersects with the horizontal well along direction of the minimum horizontal principal stress σh, for R1 formation of HF oilfield in the Middle East. And the stress distribution on the fracture surface and critical pressure contour is presented. The result indicates that the normal stress and shear stress on the fracture surface near the wellbore are of central symmetry. Moreover, critical pressure distribution of reopening and propagation of closed fracture is symmetrical. The critical reopening pressure of natural closure fracture of R1 formation is consistent with the actual mud loss pressure, therefore the new model is reliable. This work provides a scientific foundation for drilling fluid density design for fractured formation. It can effectively avoid drilling and completion leakage, which eventually prevents drilling problems and dwindles drilling cost, as well as offer a theoretical support for fast, safe and efficient drilling.

Parametric study of controllable parameters in fracture-based wellbore strengthening

Fracture-based wellbore strengthening techniques have been widely used in the oil industry to reduce the cost of lost circulation, especially in depleted reservoirs. Accurate prediction of induced-fracture geometry is of critical importance for best particle size distribution (PSD) selection of wellbore strengthening materials (WSM). Conventional parametric analyses mainly focused on rock properties, well conditions and WSM plug location. Thus, the deficiency of ignoring time and fluid dynamics may result in erroneous operations. In this paper, a dynamic fracture model based on the dislocation method is employed to qualitatively characterize the influence of controllable parameters on fracture propagation and fracture reopening pressure (FROP). Fracture propagation length and profile are obtained for each parameter with different values. It is found that fluid injection rate, fluid viscosity, fluid injection time, wellbore inclination and wellbore radius have an inverse relationship with FROP. On the other hand, fracture plug width has a positive relationship with FROP. Finally, a procedure for determining optimal wellbore strengthening operations by manipulating the controllable parameters is developed based on the dynamic fracture model.

Re-Opening and Shut-in Behaviors under a Large Ratio of Principal Stresses in a Hydraulic Fracturing Test

In-situ stress measurements were carried out under a 290m overburden in the Kamaishi mine in Iwate Prefecture of Japan. The geology of the measurement site consists of granite. The Hydraulic Fracturing (HF) technique and the Compact Conical-ended Borehole Overcoring (CCBO) technique were applied in the same horizontal borehole. The three-dimensional stress state as measured by CCBO is explained below. The directions of the maximum principal stress (σ1) and the intermediate principal stress (σ2) are almost horizontal. The direction of σ1 is perpendicular to the borehole axis, and the direction of σ2 is parallel to the borehole axis. The direction of the minimum principal stress (σ3) is approximately vertical. In this case, σ1/σ3 ratio is about 5 which is considered to be beyond the scope of the application of the HF technique. To observe the behavior of re-opening and shut-in under a large principal stress ratio, we tried to apply the HF test under these conditions. While, the re-opening pressure could not be evaluated, the shut-in pressure was observed. The results confirmed that σ3 estimated by HF is substantially equal to the vertical stress evaluated by CCBO.

Interpreting Multistage Minifrac Tests using Discrete Element Modeling of Foliated Rock with Various Drilling Mud Properties

Multistage mini hydraulic fracturing tests were performed in a borehole located in central Hungary in order to determine in-situ stress. At depth of about 500 to 560 meters, observed pressure versus time curve in metamorphic rock (mica schist) show a typical results. After each pressurization cycle, the fracture breakdown pressure in the first fracturing cycle is lower than the reopening pressures in the subsequent reopening and step-rate phases. It is assumed that the composition of the drilling mud and observed foliation of the mica schist have a significant influence on the pressure values. In order to investigate this problem, numerical modeling was performed using the discrete element code (ITASCA Particle Flow Code, PFC), which has been proven as an effective tool to investigate rock engineering problems associated with hydraulic fracturing. The code presented in this study enables simulating hydro-mechanically coupled fluid flow in crystalline rock with low porosity and pre-existing fractures (represented by the smooth joint contact model in PFC) in two dimensions. In this study, the sensitivity of the effect of foliation angle and fluid viscosity on the peak pressure is tested. The anomalous characteristics of the pressure behavior are interpreted in that way that the drilling mud penetrates the sub-horizontal foliation plane, it clogs the plane of weakness and makes the opened fracture tight. Eventually, the process prevents leak-off from the opened fracture that might explain the increased fracture reopening pressure in subsequent cycles.

La revue dans le prisme de la réingénierie

Drilling fluid losses are challenging to prevent or mitigate during drilling. Lost circulation treatments are applied to stop losses using a corrective approach or to hinder losses using a preventive approach, also known as wellbore strengthening. The key factors that must be determined when treating losses are the fracture width and the required particle size. The fracture width is often estimated using analytical fracture models. In this paper, five different fracture width models were analyzed and compared to hydraulic fracturing experiments. The hydraulic experiments were conducted on impermeable concrete cores to investigate the effect of adding lost circulation materials (LCM) to enhance the fracture breakdown pressure and the fracture re-opening pressure. The results showed that adding LCM blends enhanced the breakdown pressure up to 18% and the re-opening pressure up to 210%. The cores that were fractured with fluid-containing solids had a larger fracture width compared to the fractured cores using base fluid. Comparing the measured fracture widths from experiments with analytical models showed a discrepancy in the fracture width estimation for all of the models and the experiments, except for one model.

Analysis of analytical fracture models for wellbore strengthening applications: An experimental approach

Drilling fluid losses are challenging to prevent or mitigate during drilling. Lost circulation treatments are applied to stop losses using a corrective approach or to hinder losses using a preventive approach, also known as wellbore strengthening. The key factors that must be determined when treating losses are the fracture width and the required particle size. The fracture width is often estimated using analytical fracture models. In this paper, five different fracture width models were analyzed and compared to hydraulic fracturing experiments. The hydraulic experiments were conducted on impermeable concrete cores to investigate the effect of adding lost circulation materials (LCM) to enhance the fracture breakdown pressure and the fracture re-opening pressure. The results showed that adding LCM blends enhanced the breakdown pressure up to 18% and the re-opening pressure up to 210%. The cores that were fractured with fluid-containing solids had a larger fracture width compared to the fractured cores using base fluid. Comparing the measured fracture widths from experiments with analytical models showed a discrepancy in the fracture width estimation for all of the models and the experiments, except for one model.

Effect on Fracture Pressure by Adding Iron-Based and Calcium-Based Nanoparticles to a Nonaqueous Drilling Fluid for Permeable Formations

This paper presents a comprehensive experimental evaluation to investigate the effects of adding iron-based and calcium-based nanoparticles (NPs) to nonaqueous drilling fluids (NAFs) as a fluid loss additive and for wellbore strengthening applications in permeable formations. API standard high-pressure-high-temperature (HPHT) filter press in conjunction with ceramic disks is used to quantify fluid loss reduction. Hydraulic fracturing experiments are carried out to measure fracturing and re-opening pressures. A significant enhancement in both filtration and strengthening was achieved by means of in situ prepared NPs. Our results demonstrate that filtration reduction is essential for successful wellbore strengthening; however, excessive reduction could affect the strengthening negatively.

Intraoperative testing of opening and closing pressure predicts risk of low intraocular pressure after Ahmed glaucoma valve implantation.

The aim of this study was to assess whether intraoperative testing of silicone Ahmed glaucoma valves (AGVs) would identify valves with an increased risk of low postoperative intraocular pressure (IOP). In 30 consecutive cases of glaucoma surgery with AGV implantation, after priming the AGV, we intraoperatively measured the opening pressure A, closing pressure B, and re-opening pressure C using the active infusion pump of a phako-machine. IOP was checked postoperatively on the same day. Low IOP was defined as <5 mm Hg. Intraoperatively measured pressure characteristics of the valve function were analysed for their ability to predict postoperative IOP outcomes. Opening A, closing B, and re-opening C pressures (mean, (SD)) were 18.4 (5.1), 8.3 (4.7), and 11.7 (4.8)mm Hg, respectively. Ten patients (33.3%) had low IOP. An opening pressure of ≤18 mm Hg predicted low postoperative IOP with a sensitivity (10/10) of 100% (95% CI, 69.2-100) and a specificity (13/20) of 65.0% (95% CI, 40.8-84.6). AGVs have a high variability of opening, closing, and re-opening pressures. An opening pressure of ≤18 mm Hg, a closing pressure of ≤10 mm Hg, or a re-opening pressure of ≤11 mm Hg identified all patients with low postoperative IOP.

Development of borehole-jack fracturing technique for in situ stress measurement

In order to measure crustal stresses at great depths of more than 1000m from the ground surface, we have been promoting research and development of borehole-jack fracturing technique. When a borehole wall is loaded by a borehole-jack, a pair of new fractures will be induced oppositely in parallel to the borehole axis. After unloading, if the same place on the borehole wall is loaded again by the jack, the pair of fractures will be opened again. Two principal stresses and the orientation of crustal stress in the plane perpendicular to the borehole axis are determined by the re-opening pressures and the orientation of the fractures respectively. This technique is similar to a hydraulic fracturing from the viewpoint of analysis. The features of this technique are that it is possible to produce a pair of axial fractures in an arbitrary direction, possible to measure a displacement of the fracture opening, and, as a result, it is possible to determine the re-opening pressure accurately. This paper describes our results of numerical analyses, laboratory experiments, and field tests.

Physicochemical Effects Enhance Surfactant Transport in Pulsatile Motion of a Semi-Infinite Bubble

In this study, we investigate the sorption of pulmonary surfactant (Infasurf, Ony, Buffalo, NY) occurring at the air-liquid interface of a semi-infinite finger of air as it oscillates and progresses along a small rigid tube ( 1 mm inner diameter ) occluded with a surfactant-doped solution of concentrations C = 0.1 , 0.05 , or 0.01 mg/mL . This simple experimental model of pulmonary airway reopening is designed to examine how altering the fluid flow field may lower reopening pressures and lead to a reduction in airway wall damage that is associated with the mechanical ventilation of an obstructed pulmonary system in airways of the deep lung with depleted endogenous and little exogenous surfactant. We analyzed a range of pulsatile flow scenarios by varying the oscillation frequency ( 0 ≤ f ≤ 1 Hz ), the oscillation flow waveform, and the steady flow rate ( Q steady = 0.1 or 0.01 mL / min ). These experimental studies indicate that a high frequency (1 Hz, amplitude = 5 mm), fast-forward oscillation waveform superimposed onto a fast steady flow ( 0.1 mL / min ) substantially reduces mean reopening pressures (31%) as a consequence of the modified flow field and the commensurate increase in surfactant transport and adsorption. This result suggests that imposing high frequency, low amplitude oscillations during airway reopening will help to diminish ventilator-induced lung injury.

Crucial effect of system compliance on the maximum stress estimation in the hydrofracturing method: Theoretical considerations and field-test verification

Abstract Why do the currently available data sets from field hydrofracturing tests indicate that the measured re-opening pressure lies close to the shut-in pressure far more often than can reasonably be expected? In order to explain such a strange phenomenon, it is necessary to take into consideration two additional factors, those of (1) a residual aperture of fracture and (2) hydraulic compliance of the test equipment, both of which are ignored in the conventional theory of hydraulic fracturing. The residual aperture causes pressure penetration into the fracture prior to opening, and its effect is to reduce the re-opening pressure by a factor of two from the value expected when the conventional theory is used. The conventional theory implies that the fracture always begins to open at a borehole pressure less than the shut-in pressure. However, due to the effect of large hydraulic compliance, the reopening pressure measured in the conventional manner becomes larger than the true reopening pressure and approaches the shut-in pressure. Contrary to this, the reopening pressure measured using the test equipment with sufficiently small compliance represents a good estimate of the true reopening pressure. This pressure is related to the maximum horizontal stress S H, and its measured value allows us to estimate the value of S H.

The use of leak-off tests as means of predicting minimum in-situ stress

Leak-off tests (LOTs) or, preferably, extended leak-off tests (XLOTs), can be successfully used in minimum in-situ stress, S 3 , estimations. Selecting a point on the leak-off graph that represents the best proxy for S 3 can reduce inaccuracies in the use of LOTs as a means of determining S 3 . If the testing procedure is well conducted and recorded, picking the leak-off pressure (LOP) or instantaneous shut-in pressure (ISIP) gives equally valid estimates of S 3 . During testing, most of the pressure applied in the deduction of S 3 is exerted by the static mud column, particularly in overpressured settings where higher drilling mud weights are used. Since the mud column contributes such a large proportion of the applied pressure, estimating S 3 from tests conducted at greater depth means the observed small difference between LOP and ISIP has even less of an effect on the deduced S 3 value. The data used in this study show that LOP closely matches ISIP when considering multiple cycle XLOTs. It can therefore be inferred that the LOP is the fracture re-opening pressure and hence S h given that the assumptions made by the Kirsch equation for wellbore failure are upheld. This study also considers the implications for calculating the magnitude of S H .

水圧破砕ブレークダウンの確率論的検討と地圧測定への応用

Hydrofracturing is widely used for stress measurement because of its simplicity and high applicability to great depth. In the conventional hydrofracturing, supposing axi-parallel fracture plane in intact rock, the minimum stress σh in the plane normal to hole axis is calculated from the shut-in pressure Ps , and the maximum stress σH from breakdown pressure Pb or re-opening pressure Pr. But it has been pointed out that σH is less reliable because breakdown criterion depends on water permeation, and reopening is difficult to detect and vague in its mechanism. So it would be helpful if one could get information about σH from other than Pb or Pr. In this paper, the effect of stress difference (σH-σh ) on the probability distribution of the azimuth of vertical fractures is regarded as a new source of information about σH. Though the azimuth of fracture has been thought to coincide with that of maximum stress σH, one can easily expect that the fractures' azimuths would randomly scatter in direction when stress difference (σH-σh ) is small. The distribution of fracture azimuth, therefore, possibly provides the information about σH. In order to deal with such azimuth distribution caused by strength variation from location to location, this paper adopts the weakest link theory to investigate the breakdown phenomenon probabilistically. Based on the theory, the probability of breakdown and p. d. f of fracture azimuth are deduced, and the mean and 90 % confidence interval of Pb (or tensile strength T) and 90 % confidence interval of fracture azimuth are numerically calculated. From the results it was found that those calculated values are closely related to the stress difference or anisotropy providing new information about σH. This approach of stress estimation has been applied to in-situ test at a granitic rock mass with scarce joints.

Analysis of high-pressure fluid flow in fractures with application to Yucca Mountain, Nevada, slug test data

Increases in water pressure, if large enough, can be sufficient to open existing fractures in a fractured rock-water system. Such large water pressure increases are expected during earthquake activity and are also produced artificially in high-pressure hydraulic fracturing and slug injection tests. In an in-situ slug injection test, the slug of water is initially released into a packed-off interval of the borehole where the contained fluid is at ambient pressures. We recognize three separate stages in the behaviour of the fracture as the water pressure decreases due to drainage, namely opening, closing and, finally, completely closed. In the first stage, the water will initially drain out along conduits between the faces of the opening fracture. As the fracture opens and grows, it can become long enough to intersect any pre-existing network of open joints and fractures. If this connection occurs, the opened fracture will stop growing and there will be further rapid flow of fluid out along these open conduits. Even if connection to an open conduit does not occur, as the pressure drops the fracture will stop growing and eventually halt. At the pressure where the fracture tip begins to close, drainage into any open conduits will cease and drainage during fracture closing will thus be by flow into the porous walls of the fracture and borehole. This effect of the conduit being shut off may manifest as a kink in the observed height decay of the slug at this pressure due to the effect of the different drainage terms. As the water pressure decreases, the fracture will continue to close until the water pressure drops below the critical pressure and the fracture becomes completely closed. This total closure occurs at the same pressure as that necessary to re-open the fracture, and has been taken equal to the minimum principal stress. This total closure of the fracture also may manifest as a kink in the observed height decay of the slug, as below this closure pressure is the third, and final, stage where drainage is at the usual low pressures controlled by the permeability of the rock just around the packed-off interval of the borehole. We develop the most general mathematical model for this phenomenon using conservation of mass of the water in the borehole-fracture system for each separate pressure stage. This model of fracture behaviour, with separate flow stages and pressure regimes, explains the physical basis for the increasingly used technique in high-pressure injection tests of measuring the so-called re-opening pressure at the sharp change in slope of the rate of change of water height vs. height. Analytic and numerical solutions yield the rate at which the water height drops during the slug test and comparison with high-pressure test data confirms the accuracy of the model. Analysis of data from Yucca Mountain, Nevada, gives values for the fracture opening pressures that indicate the presence of extensional stresses of significant magnitude and of zones of pre-existing open fracture networks in the vicinity of the proposed repository site.

Airway reopening pressure in isolated rat lungs

In a previous modeling study, we predicted that the yield pressure for airway reopening (Pyield) should depend on airway fluid surface tension (gamma) and airway radius (R), according to the relationship Pyield = 8.3 gamma/R. To test this prediction, we studied tantalum bronchograms of isolated perfused rat lungs from three rats by using microfocal X-ray imaging. Thirty-two airways with diameters ranging from 300 to 2,400 microns were recorded as the airways were collapsed and reinflated. Airway pressure was reduced transiently to -40 cmH2O to produce airway closure. Airway pressure was then slowly increased from 0 to 25 cmH2O. In each airway, the observed diameter remained constant until a Pyield was reached; at this pressure, airways were seen to "pop" open, allowing clear identification of airway reopening pressure. When Pyield was plotted against diameter at maximum inflation, the experimental data were in approximate agreement with predictions of Pyield made assuming a gamma of 35 dyn/cm. The close correspondence of the measured values with these predictions suggests that surfactant is present in these airways and facilitates airway reopening.