Wyznaczenie liczby Damköhlera i jej znaczenie w projektowaniu zabiegów matrycowego kwasowania

During the matrix acidizing of carbonate formations, channels with high permeability are created, known as wormholes. The effectiveness of this type of treatment depends primarily on the structure, geometry, and the depth of penetration of the wormholes beyond the damaged zone. This should be ensured by a properly developed acidizing fluid, which in the case of carbonate formations most often consists of solutions of hydrochloric acid and/or organic acids such as acetic or formic acid. Additionally, in the case of high-temperature formations, additives are used to reduce the reaction rate of acid with the reservoir rock. The Damköhler number (Da) is an important factor that influences the model of the wormholes created. It represents the ratio of the rate of the reaction between the acid and the rock to the rate of its convection along the wormhole. The aim of the study was to determine the Damköhler number for four selected acidizing liquid–rock systems and to confirm that the structure of the wormholes depends on this variable. As part of the work, rheological tests of gelled acidizing liquids using a viscoelastic surfactant were conducted. The reaction rate tests were carried out on core plugs cut from Pińczów limestone and Guelph dolomite, which are characterized by relatively low permeability and porosity coefficients: 9.11–14.23 × 10−15m2 and 28.51%–29.10%, respectively, in the case of Pińczów limestone and 3.69–7.48 × 10−15m2 and 7.67%–9.38%, respectively, for Guelph dolomite. A rotating disk apparatus was used to determine the kinetics of the reaction of these rocks with two types of acidizing liquids. Then, core flow tests were performed on the core plugs using the AFS-300 system for the same types of rocks and liquids. The core plugs of Pińczów limestone used in these tests had a permeability coefficient ranging from 9.65 to 26.27 × 10−15m2 and a porosity coefficient ranging from 28.78% to 31.29%. On the other hand, samples of the Guelph dolomite had permeability coefficients of 7.48 to 61.52 × 10−15m2, while the porosity was much lower, ranging from 7.63% to 10.60%. After the core flow tests, the Damköhler number was calculated for each identified wormhole, using X-ray computed microtomography combined with an analysis of the geometric parameters. The types of structures that are formed in carbonate rocks as a result of matrix acidizing and their impact on the effectiveness of treatment are described in the theoretical part of this publication. Seven models of carbonate acidizing, which are used to estimate the influence of the parameters of the treatment and the properties of the liquid and rock on the efficiency of the acidizing process, are also discussed. Particular attention was paid to the theory of the Damköhler number, the value of which determines the formation of wormholes. The tests showed that at 80°C the overall reaction rate for each of the four acidizing liquid–rock systems was controlled by the mass transport rate. It was found that a gelled 15% HCl solution using TN-16235 viscoelastic surfactant reduced the overall reaction rate by reducing the mass transport rate. In the case of Pińczów limestone, the addition of 7.5% TN‑16235 surfactant reduced the De value from 4.45 × 10−6cm2/s to 3.53 × 10−6cm2/s; for Guelph dolomite De decreased from 2.25 × 10−6cm2/s to 1.97 × 10−6cm2/s. The values of the acidizing liquid pore volumes required to break through the core plug (PVbt) were determined based on the core flow tests. The lowest values of this parameter for Pińczów limestone were 0.26 for a 15% HCl solution and a velocity of 2.93 cm/min and 0.28 for a gelled 15% HCl solution and a velocity of 0.30 cm/min. For the Guelph dolomite rock, they were 0.88 for a 15% HCl solution and a velocity of 3.68 cm/min and 0.25 for a gelled 15% HCl solution and a velocity of 1.00 cm/min. Gelling a liquid with TN-16235 viscoelastic surfactant thus enables efficient matrix acidizing of carbonate formations with lower pumping rates. It was also found that the model of dissolution of the porous medium by a given acidizing liquid depended on the value of the Damköhler number. For wormholes created in the plugs of Pińczów limestone using the 15% HCl solution, the calculated values of Da were in the range of 0.244 to 0.026 (optimal value: 0.031); for the gelled 15% HCl solution it ranged from 0.145 to 0.008 (optimal value: 0.097). The optimal value for Da was considered to be the value for which wormholes were able to penetrate the entire length of the core with minimal acid spending described by PVbt. For wormholes etched in the Guelph dolomite rock by the 15% HCl solution, the calculated values of Da ranged from 0.104 to 0.030 (optimal value: 0.066), and for the gelled 15% HCl solution they ranged from 0.188 to 0.030 (optimal value: 0.069). The research methodology presented in this paper allows the Damköhler number to be determined for acidizing liquid–rock systems, and thus facilitates the preparation of technology for matrix acidizing of carbonate formations in such a way as to make these treatments as effective as possible. Keywords: matrix acidizing, Damköhler number, viscoelastic surfactant

Analytical representations of the Residence Time Distribution (RTD) associated with Hyporheic Exchange beneath Dune-like bedforms at different sediment bed depths

The hyporheic exchange below dune-shaped bedforms has a great impact on the stream environment. One of the most important properties of the hyporheic zone is the residence time distribution (RTD) of flow paths in the sediment domain. Here we evaluate the influence of an impervious layer, at a dimensionless sediment depth of db*=2πdbλ where λ is the dune wavelength, on the form of the hyporheic exchange RTD. Empirical RTDs were generated, over a range of db*values, from numerical particle tracking experiments in which 10000 particles sinusoidally distributed over a flatbed domain were released. These empirical RTDs are best represented by the Gamma, Log-Normal and Fréchet distributions over normalized bed depth of 0<=db*≤1.2,1.2<db*≤3.1, and db*>3.1, respectively. The depth dependence of the analytical distribution parameters is also presented, together with a set of regression formulae to predict these parameters based on db*with a high degree of accuracy (R2>99.8%). These results contribute to our understanding of the physical and mixing processes underpinning hyporheic exchange in streams and allow for a quick evaluation of its likely impact on nutrient and contaminant processing (e.g., based on the magnitude of the Damköhler number). Keywords: Dunes, bedforms, residence times distribution, sediment depth effect, Hyporheic residence times, analytical representation, two parametric distributions, Damköhler Number.

SBES/FGM Simulation of Film-Cooled Surface Heat Transfer and Near-Wall Reaction

Accurate numerical prediction of surface heat transfer in the presence of film cooling within aero-engine sub-components, such as blade effusion holes and combustor liners, has long been a goal of the aero-engine industry. It requires accurate simulation of the turbulent mixing and reaction processes between freestream and the cooling flow. In this study, the Stress Blended Eddy Simulation (SBES) turbulence model is used together with the Flamelet Generated Manifold (FGM) combustion model to calculate the surface heat flux upstream and downstream of an effusion cooling hole. The SBES model employs a blending function to automatically switch between RANS and LES based on the local flow features, and thus significantly reduces the computational cost compared to a full LES simulation. All simulations are run using ANSYS Fluent®, a commercial finite-volume CFD solver. The test case corresponds to an experimental rig run at MIT, which is essentially a flat plate brushed by a uniform freestream of argon with ethylene seeded inside, and is cooled by either a reacting air or non-reacting nitrogen jet inclined at 35 degrees to the freestream. Calculations are performed for both reacting and non-reacting jet cooling cases across a range of jet-to-stream blowing ratios, and compared with the experimental data. The effects of mesh resolution are also investigated. Calculations are also performed across a range of Damköhler number (i.e. flow to chemical time ratio) from zero to 30, with unity blowing ratio, and the differences in the maximum surface heat flux magnitude in the reacting and non-reacting cases at a specific location downstream of the hole are investigated. Results from these analyses show good correlation with the experimental heat flux data upstream and downstream of the cooling hole, including the heat flux augmentation due to local reaction. Results from the Damköhler number sweep also show a good match with the experimental data across the range investigated.

A New Mathematical Framework for Describing Thin-Reaction-Zone Regime of Turbulent Reacting Flows at Low Damköhler Number

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent flow in the case of a low Damköhler number. In the cited paper, the theory is also supported by Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent premixed combustion is argued. The present work aims at complementing the theory with a new mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c ( x , t ) is considered to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c ( x , t ) < 1 , where molecular transport plays an important role, and (ii) equilibrium products, c ( x , t ) = 1 . The two zones are separated by an infinitely thin reaction sheet, where c ( x , t ) = 1 and | ∇ c | is fixed in order for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable, its second moment, and instantaneous characteristic functions. Averaging of these equations yields exact, unclosed transport equations for the conditioned reaction-progress-variable moments and Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet. The closure problem for the derived equations is beyond the scope of the paper.