Fluid Loss Coefficient Research Articles

Development of a novel heat- and shear-resistant nano-silica gelling agent

Abstract The efficient and sustainable development of deep marine carbonate rock reservoirs in the Sichuan Basin has higher technical requirements for reservoir acidizing alteration technology. However, the acidification effect of deep marine carbonate rock reservoirs was hampered by the drawbacks such as uncontrollable acidification rate of the reservoir, the large friction resistance, and the great acid filtration. A novel heat- and shear-resistant nano-silica gelling agent CTG-1 is prepared based on nano-silica and combined with amide compounds. The influence of different factors on the acid filtration performance and heat- and shear-resistant capacity of carbonate rock reservoirs were analyzed, and then the mechanism of nano-silica gelling agent for acid filtration reduction in carbonate rock reservoirs is revealed. The research results showed that the filtration resistance of acid solution decreases slightly with the increase in the content of nano-silica gelling agent and reservoir pressure. The viscosity, fluid loss coefficient, and friction-reducing rate are as high as 25 mPa s, 2.4 × 10−2 m3 min1/2, and 71%, respectively, showing significantly better result than that of commonly used commercial gelling agents. The development of nano-silica gelling agent provides a reliable reference for effectively improving the acidification and stimulation effect of deep marine carbonate rock reservoirs.

Numerical Simulation Investigation on Fracture Propagation of Fracturing for Crossing Coal Seam Roof

The fracturing crossing coal seam roof is a technology that fulfills the fracturing of a coal seam through the vertical propagation of fractures. Geological conditions are the key factors determining the effect of this kind of fracturing, but there is hardly any research on this aspect. To determine the favorable geological conditions for through-roof fracturing, based on a 3D fracture propagation model, and considering the interlayer vertical fracture toughness and leak-off heterogeneity, a mathematical model of fracturing through a horizontal well in a coal seam roof was established, and the calculation method of fractures crossing layer propagation was determined. In this method, the effect of fracture communication with the coal seam is evaluated by taking the area and the area ratio of fractures in the coal seam as the objective functions. The effects of parameters such as in situ stress combination profile, coal seam fracture toughness, and fluid loss coefficient on fracturing results were evaluated. The reasonable distance from the horizontal well to the coal seam’s top surface was determined in this work. The study results show that: (i) the fracturing effect is better when the coal seam is lower in in situ stress; (ii) the distance between the horizontal well and the top surface of the coal seam is recommended to be less than 4 m to obtain the ideal fracturing effect; and (iii) the combination of the in situ stress profile is the key factor, and the fracture toughness and fluid loss coefficient of the coal seam, fluid viscosity, and the number of perforations in one cluster are the secondary factors affecting the fracturing effect.

Study on fracturing fluid filtration fracturing technology

The filtration of fracturing fluid is one of the important factors that affect the effect of fracturing construction. Therefore, it is of great significance to study fracturing fluid loss for fracturing technology. Based on the fracturing fluid filtration theory, the fluid loss coefficient is used to describe the loss of the fracturing fluid in the formation. At the same time, according to the different formation conditions, the corresponding pressure drop analysis model is used to describe the pressure falling process. According to a target area, the filter loss parameter is calculated by combining the filtration mechanism and the pressure drop pressure drop analysis model. It is necessary to study the fracturing fluid technology and optimize the fracturing fluid with the concentration of 4% of the filtrate reducer, which is compared with the original formula with the concentration of 1% of the original filtrate loss agent. The loss coefficient is reduced by 44.13% on average, which can better meet the actual demand.

Mathematical modeling of the process of water-soline transport in soils

A problem related to the actual problem of the process of water and salt transport in soil is solved in the paper; the review of scientific papers devoted to various aspects and mathematical support of the object under research is given. A mathematical model is proposed in the paper to carry out a complex study, taking into account: the colmatage of soil pores with finely dispersed particles with time; the changes in soil permeability coefficient, fluid loss and filtration coefficient; the changes in the initial porosity and settled mass porosity and an effective numerical algorithm based on the Samarsky-Fryazinov vector scheme with the second order approximation where the differential operators in equations are substituted by finite-difference ones. For the derivation of mathematical model of salt transport it is assumed in the paper that the pressure gradient in the canal is constant and equal to atmospheric pressure. The results of calculations on the proposed algorithms are presented in the form of graphs; a detailed analysis of these results is given. At the end of the paper, conclusions are drawn related to the analysis of numerical computer calculations. It is established that with scarce irrigation, the maximum absorption of water and the accumulated salt transport occurs in the upper layers of soil. Numerical calculations have established that changes in the rate of water transport in soil depend on: porosity, soil permeability, filtration coefficient, composition and structure of soil, and the porosity of settled mass. The process of salinity has reached equilibrium after the use in irrigation of salt water for several years.

Novel Nozzle Shapes for Synthetic Jet Actuators Intended to Enhance Jet Momentum Flux

An axisymmetric synthetic jet actuator based on a loudspeaker and five types of flanged nozzles were experimentally tested and compared. The first (reference) type of nozzle was a common sharp-edged circular hole. The second type had a rounded lip on the inside. The third nozzle type was assembled from these two types of nozzles—it had a rounded lip on the inside and straight section on the outside. The fourth nozzle was assembled using orifice plates such that the rounded lips were at both inner and outer nozzle ends. The last nozzle was equipped with an auxiliary nozzle plate placed at a small distance downstream of the main nozzle. The actuators with particular nozzles were tested by direct measurement of the synthetic jet (SJ) time-mean thrust using precision scales. Velocity profiles at the actuator nozzle exit were measured by a hot-wire anemometer. Experiments were performed at eight power levels and at the actuator resonance frequency. The highest momentum flux was achieved by the nozzle equipped with an auxiliary nozzle plate. Namely, an enhancement was approximately 31% in comparison with an effect of the reference nozzle at the same input power. Furthermore, based on the cavity pressure and the experimental velocity profiles, parameters for a lumped element model (mass of moving fluid and pressure loss coefficient) were evaluated. These values were studied as functions of the dimensionless stroke length.

Analysis of Design Parameters Effects on Vibration Characteristics of Fluidlastic Isolators

The control of vibration in helicopters which consists of reducing vibration levels below the acceptable limit is one of the key problems. The fluidlastic isolators become more and more widely used because the fluids are non-toxic, non-corrosive, nonflammable, and compatible with most elastomers and adhesives. In the field of the fluidlastic isolators design, the selection of design parameters is very important to obtain efficient vibration-suppressed. Aiming at getting the effect of design parameters on the property of fluidlastic isolator, a dynamic equation is set up based on the theory of dynamics. And the dynamic analysis is carried out. The influences of design parameters on the property of fluidlastic isolator are calculated. Dynamic analysis results have shown that fluidlastic isolator can reduce the vibration effectively. Analysis results also showed that the design parameters such as the fluid density, viscosity coefficient, stiffness (K1 and K2) and loss coefficient have obvious influence on the performance of isolator. The efficient vibration-suppressed can be obtained by the design optimization of parameters.

Erratum to: A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity

Erratum to: A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity

A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity

Loss of the fracturing fluid in hydraulic fracturing is a complex flow process that impacts the effectiveness of the technology, affecting such factors as fracture length and gas-well productivity. Many computational models have been constructed for the fluid loss coefficient, but the models do not account for the fractal character and tortuosity of the porous medium. This study considers these two parameters and proposes a fractal model to calculate the fluid loss coefficient. Fractal permeability is calculated based on the capillary-pressure curves of nine core samples. The permeability values based on fractal theory agree well with the measured values. The fluid loss coefficient determined by the fractal model is higher than the coefficient obtained by standard calculations because of high tortuosity of the porous medium. Predictions of fracture length and gas-well productivity, which depend on the fluid loss coefficient, are discussed and compared, and it is suggested that accurate determination of this coefficient is essential for optimizing hydraulic fracturing.

Controlling Fracture Height in Fracturing Effect Prediction of Oil Well Based on Uncertain Multi-Attribute Decision Making

Hydraulic fracture to oil well, creating fracture in the bottom stratum, making the crude oil flow to the bottom along the fracture are common stimulation treatment used in oil field. Controlling fracture height fracturing is controlling the extension of fracture within oil layer area, which is the key to success or failure of hydraulic fracturing. Especially, controlling fracture height to avoid pressing to wear the near water layer, which causes a sudden increase of oil water production, is particularly important to oil production. Fracture extension theory and field practice indicate that in controlling fracture height fracturing process, the fracture height extension is related with reservoir stress difference of oil layer and adjacent barrier on a certain scale of construction also it is related with the 8 parameters such as the rock Young's modulus, fracture toughness, Poisson's ratio, permeability, reservoir thickness, fracturing fluid viscosity and fluid loss coefficient and so on. This study introduces uncertain multi-attribute decision making method to the well needing controlling fracture height fracturing, takes expected minimum fracture height as the target, concentrates the 8 attribute values of oil well with OWA operator, obtains comprehensive attribute value, and sorts the expected oil well fracturing effect according to the size of comprehensive attribute value, then selects construction well according to the sort results. In this way, it not only solves the difficulty to accurately resolve fracture height of analytical method and problem of large calculation of numerical method, also provides a simple and practical method for live well selection. According to fracturing selection of Changqing oil field 5 wells and on-site application comparison of 2 wells, it is consistent with the prediction result.

Controlling Fracture Height in Fracturing Effect Prediction of Oil Well Based on Uncertain Multi-Attribute Decision Making

Hydraulic fracture to oil well, creating fracture in the bottom stratum, making the crude oil flow to the bottom along the fracture are common stimulation treatment used in oil field. Controlling fracture height fracturing is controlling the extension of fracture within oil layer area, which is the key to success or failure of hydraulic fracturing. Especially, controlling fracture height to avoid pressing to wear the near water layer, which causes a sudden increase of oil water production, is particularly important to oil production. Fracture extension theory and field practice indicate that in controlling fracture height fracturing process, the fracture height extension is related with reservoir stress difference of oil layer and adjacent barrier on a certain scale of construction also it is related with the 8 parameters such as the rock Young's modulus, fracture toughness, Poisson's ratio, permeability, reservoir thickness, fracturing fluid viscosity and fluid loss coefficient and so on. This study introduces uncertain multi-attribute decision making method to the well needing controlling fracture height fracturing, takes expected minimum fracture height as the target, concentrates the 8 attribute values of oil well with OWA operator, obtains comprehensive attribute value, and sorts the expected oil well fracturing effect according to the size of comprehensive attribute value, then selects construction well according to the sort results. In this way, it not only solves the difficulty to accurately resolve fracture height of analytical method and problem of large calculation of numerical method, also provides a simple and practical method for live well selection. According to fracturing selection of Changqing oil field 5 wells and on-site application comparison of 2 wells, it is consistent with the prediction result.

A New Analysis of Pressure Decline for Acid Fracturing

Summary Conventional pressure-decline analysis has been used successfully to determine the in-situ fluid-loss coefficients and fracture geometries of minifracture tests or full-scale hydraulic fracturing. However, it fails to interpret the pressure-decline data of acid fracturing because it has a different fluid-loss mechanism and a short testing time. This paper presents a new pressure-decline analysis for full-scale acid fracturing or acid minifracturing to estimate fluid-loss coefficients and evaluate fracture geometries for the Perkins-Kern-Nordgren (PKN) model.1,2 The models established after shut-in have comprehensively taken into consideration the influences of compressibility and thermal expansion of fluids (waste acid and CO2 gas produced by reaction) and the rock volume etched away by acid. The effects of formation temperature and reaction heat are also taken into account in this analysis. The analytical solution derived by Nordgren2 for large fluid-loss is used to calculate the fracture-width distribution along a fracture. The short-test-time data for acid fracturing can be interpreted as a simulation technique used in analyzing. The comparison of the results of conventional analysis and this new analysis for field test data shows that the conventional analysis causes a −56.2% error in the fluid-loss coefficient and underestimates the fluid-loss. The relative errors of the conventional analysis for estimating fluid efficiency and hydraulic-fracture length and width occur 186.2%, 220.8%, and 16.5% respectively.

The Effect of Wormholing on the Fluid-Loss Coefficient in Acid Fracturing

Summary In most acid fracture designs, a leakoff model developed for proppant fracturing is used to calculate the acid volume lost into the formation. Because wormholing in acid fracturing results in a few large channels near the fracture, the leakoff velocity of the fracturing fluid can be higher in acid fracturing than in proppant fracturing. This paper presents a new leakoff model that includes the effect of wormholing on the overall fluid-loss coefficient. The leakoff model is based on a volumetric model describing wormhole growth in acid fracturing. Conveniently, the leakoff velocity based on the volumetric model for wormholing is still inversely proportional to the square root of treatment time. Laboratory coreflood results are presented that support the use of the volumetric model for the linear flow region near the fracture walls. The results of the model show that the overall fluid-loss coefficient depends strongly on the number of PV required for wormhole breakthrough in a coreflood. A large number of PV to breakthrough means a slow wormhole growth rate, which occurs more commonly in dolomite compared with limestone. The effect of wormholing on the overall fluid-loss coefficient is insignificant in acid fracturing of dolomite. However, for limestone, the number of PV to breakthrough is small and wormholing increases the fluid-loss coefficient significantly, especially for a gas well. An example in the paper shows that the overall fluid-loss coefficient can be more than 100% higher because of wormholing in a typical case for a gas well in a limestone formation.

Closure Process of Transverse Cracks after Shut-in in Hydraulic Fracturing Tectonic Stress Measurements.

Closure process of a transverse crack crossing a wellbore is analyzed to discuss physical meanings of the pressure decay curve after shut-in during hydraulic fracturing tectonic stress measurements, where the crack is assumed to be perpendicular to the wellbore axis and one of the principal axes of the tectonic stress is assumed to be parallel to the wellbore axis. The analysis is based on the linear theory of elasticity and linear fracture mechanics. It is shown that the whole crack closes instantaneously when the downhole water pressure is equal to the compressive tectonic stress acting perpendicularly to the crack plane. The instantaneous crack closure appears as a point of maximum curvature on the pressure decay curve after shut-in. Therefore, the compressive tectonic stress normal to the crack plane is determined as the pressure at the point of maximum curvature. Although the point of maximum curvature appears less clearly on pressure decay curve when the fluid loss coefficient is large, the instantaneous crack closure can always be detected clearly by utilizing the relation of the inverse of the decrease rate of the downhill water pressure Vs the downhill pressure.

Interpretation of hydraulic fracture parameters by inversion of pressure curves

In this paper a new method of minifrac interpretation is developed which considers minor principal stress and fluid loss coefficient as unknowns. First, the direct problem is clearly defined by applying the contained model of Nordgren-Nolte (propagation and shut-in phases). Sensitivity of the model is studied, and it is shown that the stress has a great influence on propagation and fluid loss coefficient on shut-in. Second, an inverse method which consists of minimizing a function of the parameter space is proposed. Finally, the inverse method is applied to an actual case and it is shown that a very good approximation of σ 3 and C w can be obtained.

Lagrangian Formulation for Penny-Shaped and Perkins-Kern Geometry Models

Summary Basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models have been developed with a Lagrangian formulation combined with a virtual-work analysis. The Lagrangian formulation yields a pair of nonlinear equations in Rf or Lf and bf, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved numerically. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, can be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry. Geometry prediction of the new theory agrees well with other methods for the same models. A unique advantage of this approach, however, is that the geometry estimated from prefracturing design is consistent with the geometry determined from the pressure-decline analysis. Thus, it allows the engineers in the field to predict precisely the amount of fracturing fluid required for a designed fracture radius or length in a full-scale treatment from information gained in a minifracture treatment.

Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline

Summary A procedure is presented for designing a fracture treatment when little or no information is available. This procedure is based on fluid efficiency, which is defined as the fracture volume divided by the injected fluid volume. The fluid efficiency for a treatment was found to determine the pad size and optimum proppant schedule completely without any assumption of the appropriate fracture-geometry model or associated parameters. The efficiency was also found to determine the fluid's exposure time to temperature. This determination requires an assumption for the portion of the fracture face that is cooled during a treatment. The exposure is important for defining the fluid additives of relatively large and high-temperature treatments. The fluid efficiency can be determined from a pressure-decline analysis for a calibration treatment performed before the actual stimulation treatment. In addition, if the appropriate geometry model is assumed, the decline analysis of the calibration treatment provides inferred values of fluid-loss coefficient and fracture width and penetration. Also, for the case when the calibration treatment is smaller than the actual stimulation, analyses are presented for predicting the relative change in efficiency, width, and penetration for the treatments.

Comparison of hydraulic fracture design methods to observed field results : Nierode, D E J Pet TechnolV37, N11, Oct 1985, P1831–1839

The fracture models developed by Khristianovich and Zheltov, and Perkins, Kern, and Nordgren are compared to field, fracturing treatment data. It was found that the Khristianovich-Zheltov model agrees with the field data as adequately as the Perkins-Kern-Nordgren model, and that both models need to take changing instantaneous shut in pressure into account. A method for on-the-job fluid loss coefficient measurement is developed based on measurements of increasing instantaneous shut in pressure. Examples illustrating the fluid loss coefficient measurement method are discussed. Finally, examples are presented which show the excellent agreement between field data and production estimates based on Khristianovich- Zheltov fracture parameters. 24 references.

Dynamic Fluid Loss Characteristics of Foam Fracturing Fluids

Abstract Dynamic fluid loss measurements were conducted on core samples ranging in permeability between 0.02 to 140 md. These tests were run to measure the effect of several parameters on the foam fluid loss coefficients. The parameters tested were: core permeability, gel concentration in the liquid parameters tested were: core permeability, gel concentration in the liquid phase, foam quality, temperature, core length and differential test phase, foam quality, temperature, core length and differential test pressure. pressure. The type of foam that is used in most conventional fracturing treatments is a wall building fluid. Although this foam has excellent inherent fluid loss properties, the fluid loss values reported in this paper more closely resemble those of conventional fracturing fluids than paper more closely resemble those of conventional fracturing fluids than reported earlier. These values have been used in the successful design of field fracturing treatments. These data support the mechanism of two phase flow in porous media suggested by Holm. The fluid passing through the cores was rich in liquid phase with composition proportional to the viscosity of the liquid phase. phase with composition proportional to the viscosity of the liquid phase. The broad range of fluid loss coefficients for foam calculated in these tests are intermediate in value to those reported in similar tests by Blauer and Kohlhaas, who obtained lower values, and King, who obtained higher values. Introduction Foam has been established as a successful fracturing fluid for several years. Claims as to its efficiency in fluid leak-off control have ranged from excellent to virtually no leak-off control at al,. Yet treatment experience has indicated that foam fracs do occasionally screen out. Since excessive fluid leak-off is one potential cause of a premature job termination, an adequate knowledge of fluid loss coefficients is essential for proper design of stimulation treatments. Foam has previously been described as a non-wall building fluid. Such a fluid should have leak-off properties described by Howard and Fast by where k is permeability in darcies, is pressure drop in psi across the matrix, is fractional porosity, and p is viscosity in centipoises. There is a problem with calculating for foam, however. Since foam is a two-phase structured fluid, and the bubbles may be in the same size range as the pores of the rock matrix, the rheology of foam in porous media is not well defined. The expansion of bubbles in the foam due to pressure drop can be significant. A fluid loss coefficient can be determined empirically without knowledge of the fluid viscosity by using the equation from Howard and Fast where m is the slope of an experimental plot of fluid volume versus the square root of time, and is the cross sectional area of the filter medium in square centimeters. is useful for wall building fluids, whereas is intended for non-wall building fluids. For non-wall building fluids the slope of the experimental plot of filtrate volume will be linear with time, rather than the square root of time.

Comparison of Hydraulic Fracture Design Methods to Observed Field Results

The fracture models developed by Khristianovich and Zheltov, and Perkins, Kern, and Nordgren are compared to field, fracturing treatment data. It was found that the Khristianovich-Zheltov model agrees with the field data as adequately as the Perkins-Kern-Nordgren model, and that both models need to take changing instantaneous shut in pressure into account. A method for on-the-job fluid loss coefficient measurement is developed based on measurements of increasing instantaneous shut in pressure. Examples illustrating the fluid loss coefficient measurement method are discussed. Finally, examples are presented which show the excellent agreement between field data and production estimates based on Khristianovich- Zheltov fracture parameters. 24 references.

Fracturing With Foam

Abstract Foam has been successfully applied as a circulating fluid for workovers and drilling for several years. Now a new oilfield application has been developed for foam: formation stimulation by fracturing. Over 150 wells have been treated to date in Canada using foam as the fracturing fluid, with a high degree of success. Unique 'rheological properties of foam make it well suited to this application: high sand carrying capacity, low fluid loss coefficient, low fluid friction loss, quick load fluid recovery low formation damage, and little or no reduction of fracture conductivity due to residual fluid saturation. The cost of the treatment is competitive with that of conventional systems. Introduction Fracturing of oil and gas wells involves the injection of a fluid into a well at a sufficient rate and pressure to physically rupture the rock down hole. A crack, or fracture, is developed and extended deep into the reservoir with continued fluid injection. Sand is carried in the fracturing fluid to prop the crack open when pumping is stopped, leaving a new, more permeable route for oil and gas to flow into the wellbore. Foam has recently been successfully used in place of conventional fracturing fluids, such as oil or water, for this process. The type of foam normally used is comprised of water, surfactants and a discontinuous gaseous phase of nitrogen. The volumetric gas content, referred to as "foam quality", is generally in the range of 65% to 95% under calculated downhole treating conditions: Equation (1) Available In Full Paper. Field Operations During a Foam Frac ™ treatment, water from a tank is continuously mixed with sand in a blender, at sand-water ratios progressively increasing to as high as 8 lbs/gallon. A surfactant, or foaming agent, is then proportioned into this slurry at a ratio of .2%; to 1.0%, and the resultant fluid blend is transferred to a high-pressure triplex pumper. High-pressure nitrogen gas is manifolded into the discharge line of the triplex, and it is at this point that the foam is developed. KCl, gellants or other chemical treating agents may be added to the base water if required to improve its compatibility with the reservoir rock or fluids. Figure 1 schematically shows this process. The blender and high-pressure pumper are conventional oilfield service equipment, modified to accurately proportion the high sand ratios pumped at slow discharge rates. The high-pressure N2 gas is also available from conventional oilfield N2 service units. Figure 2 illustrates an actual job in progress. The foam injection rates and volumes are in the order of 4 to 5 times those of the liquid pump rates and volumes at the blender because of the expansion by introduction of N2. These total volumes and rates are increased by a factor F, as follows: Equation (2) Available In Full Paper. For example, using a 75% foam quality, the foam injection rate will be 4 times the fluid pump rate at the blender.