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1

Assessing the Corrosion and Scaling Potential of Drinking Water in Morocco Using Water Stability Indices

El Baroudi Hind, Ouazzani Chadia, Moustaghfir Abdellah, Er-Ramly Azzeddine, El Baroudi Youssef, Dami Abdallah, Balouch Lhousaine

Ecological Engineering & Environmental Technology

|

2024

|

Vol. 25, iss. 2

130--139

EN

Corrosion and scaling occur in water distribution systems. However, not much data is available concerning this issue in Morocco. This study aimed to evaluate the corrosive and scaling potential of drinking water in the water distribution systems of several cities in Morocco using water stability indices and other physicochemical parameters. For this purpose, 100 samples were collected, mainly from the cities in the Rabat-Salé-Kenitra region of Morocco. The results of the physicochemical analysis of 100 collected samples show that the means of the pH, total alkalinity, calcium hardness, chloride, temperature, and total dissolved solids are 7.577 ± 0.23, 173.6± 52.04 mg/l as CaCO3, 212.57 ± 98.18 mg/l as CaCO3, 418.7 ± 407.75 mg/l, 25.16 ± 1.58 °C, 597.5 ± 435.74 mg/l, respectively. The mean values of the water stability indices are 0.1158 ± 0.38, 7.345 ± 0.68, 7.132 ± 0.86, and 12.41 ± 0.35 for the Langelier saturation index (LSI), the Ryznar stability index (RSI), the Puckorius scaling index (PSI), and the aggressive index (AI), respectively. The water samples show corrosive tendencies of 41%, 75%, 97%, and 13% based on the LSI, RSI, PSI, and AI, respectively, and are considered supersaturated and likely to scale, corrosive, and non-aggressive. The water samples in Rabat, Salé, Bouknadel, and Kenitra were mostly supersaturated with a tendency to scale, with the highest percentage of stable water while the water in Khemisset and Tiflet was mostly corrosive, with Tiflet recording the highest chloride content of 3220.1 mg/l. The scaling and corrosive potential of water varied depending on the source of water in each city. Therefore, it is essential to continuously supervise the stability of water at different points of water distribution systems, create an adapted approach for each city, and instill strict national standards for the physicochemical parameters that affect corrosion and scaling to ensure safe drinking water.

2

Corrosion process assessment using a novel type of coupon installation

Musik Daniel, Wójcik Krzysztof, Sekuła-Wybańska Małgorzata, Rakoczy Rafał

Polish Journal of Chemical Technology

|

2022

|

Vol. 24, nr 4

84--88

EN

The main aim of this experimental study is to test the novel type of coupon installation. This set-up was used to carry out the corrosion process under aggressive conditions. Moreover, the effect of corrosion inhibitors on the scale-forming tendency was evaluated. The corrosive conditions were defined by using the Langelier Saturation Index (this index is an approximate indicator of the degree of saturation of CaCO3 in water) and the Ryznar stability index (this index is allowed to determine if the liquid sample is aggressive or not). Additionally, the inductively coupled plasma optical emission spectroscopy analysis was used to obtain the iron and calcium ions concentrations in the liquid samples from the tested coupon installation. The corrosion process for the established conditions was also described using the corrosion rate of the tested coupons. The obtained investigation contributes significantly by developing the novel coupon installation and demonstrating the procedure for testing the corrosion process with the application of coupons. This setup and method might be successfully applied for accelerated laboratory tests.

3

Problem uszkodzeń, konserwacji i renowacji membran wysokociśnieniowych w instalacjach odwróconej osmozy

Marjanowski Jan, Sadaj Maciej

Instal

|

2021

|

nr 2

6--12

PL

Wysokociśnieniowe technologie membranowe, szczególnie odwróconej osmozy, mają szerokie zastosowanie w uzdatnianiu wód przeznaczonych do spożycia przez ludzi, do kotłów i układów chłodzenia, a przede wszystkim w technologiach recyklingu wód procesowych. Równie istotną kwestią, co dobór odpowiedniej instalacji do procesu RO, jest odpowiednia jej eksploatacja, uwzględniająca utrzymanie jakości wody zasilającej wg wymagań producenta, a także dobór przepływów, ciśnień, dobór odpowiedniego antyskalanta. W eksploatacji membran konieczna jest także ich konserwacja w okresie postoju oraz okresowa renowacja wiążąca się z chemicznym czyszczeniem membran. Działaniami tymi nie da się całkowicie wyeliminować procesów foulingu i scalingu, jednak można je znacząco spowolnić, co pozwala na długoletnią, efektywną kosztowo eksploatację z jak najniższym zużyciem energii oraz jak najwyższym procentem odzyskanej wody.

EN

High pressure membrane technologies, especially reverse osmosis, are widely used in treatment or water for purposes of drinking, boilers and cooling systems and most of all in technologies of recycling process water. The selection of an appropriate RO system for a given process is equally important as its proper operation, taking into consideration maintaining of feed water quality according to manufacturer's requirements, as well as selection of flows, pressures and suitable antiscalant. During membranes operation it is necessary to maintain them during downtime and perform periodic renovation involving chemical cleaning of membranes. Processes of fouling and scaling cannot be completely eliminated, but they can be significantly slowed down, allowing long-term, cost-effective operation while maintaining the lowest energy consumption possible and simultaneously achieving highest possible percentage of recovered water.

4

Scaled residue reverse converter for signed numbers with low cost moduli base

Czyżak Maciej, Smyk Robert

Poznan University of Technology Academic Journals. Electrical Engineering

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2019

|

No. 98

101--114

EN

The paper presents a realization of the scaled residue reverse converter for the low cost moduli base {2n -1,2n ,2n+1} . The moduli of this type allow for the memoryless reverse conversion using the Chinese Remainder Theorem because the orthogonal projections can be obtained by shifts and additions. Moreover, the modulo reduction of the sum of projections and sign detection algorithms are shown. Also the converter architecture is presented.

5

Ocena wpływu środka hydrofobowego na mrozoodporność betonu

Kłak Adam, Kowalczyk Henryk

Materiały Budowlane

|

2019

|

nr 4

61--64

PL

W artykule opisano wpływ zastosowania ochrony powierzchniowej betonu środkiem hydrofobowym na odporność mrozową, określoną metodą powierzchniowego łuszczenia i metodą zwykłą. Próbki betonowe wykonane z cementu portlandzkiego CEM I 42,5 HSR poddano badaniu nasiąkliwości, wytrzymałości na ściskanie, podciągania kapilarnego i mrozoodporności. Obserwując wyniki badań metodą CDF, zauważono, że ochrona powierzchniowa środkiem hydrofobowym wpływa na ograniczenie podciągania kapilarnego, co pozwala na poprawę mrozoodporności. Wszystkie próbki poddane zabiegowi hydrofobizacji spełniły warunek dotyczący masy materiału złuszczonego, nie przekraczając wartości 1,5 kg/m2 zgodnie z normą PN-EN 12390-9. Próbki betonowe poddane badaniu mrozoodporności metodą zwykłą nie spełniły wymagań normy PN-B-06265. Na ich powierzchni wystąpiły spękania, a wytrzymałość na ściskanie była o ponad 20% mniejsza od wytrzymałości próbek referencyjnych.

EN

This paper investigates the effect of applying protection on concrete surface and influence of hydrophobic agent on concrete frost resistance. The investigation was conducted by a two of freeze-thaw methods: surface scaling and standard method. Concrete samples made of Portland cement CEM I 42.5 HSR were tested for water absorption, compressive strength, capillary suction and freeze-thaw resistance. It have been shown that the surface protection of the hydrophobic agent influences the capillary suction limit, which allows to improve the results during the frost resistance test. All samples subjected to the hydrophobic treatment fulfill the condition of total weight of the scaled material, not exceeding the value of 1.5 kg/m2 in accordance to PN-EN 12390-9 standard. Test results of standard method didn’t meet the requirement of PN-B-06265 standard. Cracks was visible on surface of specimen and also their compressive strength was more than 20% lower than the reference samples.

6

Mrozoodporność betonów ze zbrojeniem rozproszonym

Borowska S.A., Kosior-Kazberuk M.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

|

2018

|

Z. 24 (174)

24-29

PL

W pracy przedstawiono porównanie odporności na powierzchniowe łuszczenie pod wpływem oddziaływania mrozu betonów zawierających trzy typy zbrojenia rozproszonego (włókna syntetyczne, makro- i mikrowłókna stalowe) zastosowane w ilości 0,5 oraz 1,0% objętości mieszanki betonowej, a także betonów bez włókien. Badanie prowadzono na podstawie normy PKN-CEN/TS 12390–9: (2007), metodą Slab test, w warunkach cyklicznych zmian temperatury, w obecności 3% roztworu solnego. Na podstawie wyników badania mrozoodporności określono najbardziej efektywny rodzaj dodatku do betonu w postaci włókien oraz korzystną zawartość. Wykonano dodatkowe badania właściwości fizycznych betonów, takich jak: nasiąkliwość, podciąganie kapilarne roztworu NaCl, gęstość objętościowa.

EN

The influence of different fibers (steel, propylene, microfibers) on the frost resistance of concrete elements was analyzed. Seven types of concrete specimens with various types of fiber reinforcement at 1,0 or 0,5% volumetric ratio were selected for test. Destructive deicing salt impact in environment of cyclic freezing and thawing was determined based on the procedure of PKN - CEN/TS 12390 - 9: Testing hardened concrete - Part 9: Freeze-thaw resistance - Scaling. It was found that fibers are very important additives in concrete mixture. Frost resistance of concrete without this type of reinforcement is about five times lower than resistance of concrete with steel fibers. Moreover, frost resistance accompanying analyses such as absorbability, capillarity sorption was analyzed. Relationships between examined properties of concrete were noticed. All observations lead to comprehensive understanding of this important material.

7

Water demineralization by membrane distillation utilizing cooling water from municipal waste incinerator

Gryta M.

Polish Journal of Chemical Technology

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2018

|

Vol. 20, nr 3

65--74

EN

The membrane distillation performance was studied for production of demineralized water from surface water (river). Hot water from cooling water system of municipal waste incinerator was considered as an energy source for membrane distillation. The integration of membrane installation with such cooling water system allows to re-use up to 18 kW per 1 m2 of the membranes. The studies were performed with the application of polypropylene capillary membranes Accurel PP S6/2. The membrane modules were supplied with the feed heated to a temperature of 310 K and 330 K. The permeate flux obtained for these temperatures was 2.8 and 9.7 L/m2 h, and the distillate conductivity was 6 and 4 S/cm, respectively. The water demineralisation process was carried out for 1200 h without module cleaning. The behaviour of the permeate flux and distillate conductivity indicate that used membranes maintained their non-wettability over tested period. The performed SEM-EDS examinations confirmed, that the deposits did not fill the pores and were mainly formed on the membrane surface. The scaling intensity was definitely smaller for lower temperature (310 K) of the feed. The amorphous deposits containing beside Ca also substantial amounts of the Si were mainly formed under these conditions, whereas at higher feed temperature dominated CaCO3 scaling.

8

Effect of patient-specific model scaling on hip joint reaction force in one-legged stance – study of 356 hips

Hornova J., Kralj-Iglič V., Pedersen D. R., Daniel M.

Acta of Bioengineering and Biomechanics

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2017

|

Vol. 19, no. 4

103--108

EN

Estimation of hip joint loading is fundamental for understanding joint function, injury and disease. To predict patientspecific hip loading, a musculoskeletal model must be adapted to the patient’s unique geometry. By far the most common and cost effective clinical images are whole pelvis plain radiographs. This study compared the accuracy of anisotropic and isotropic scaling of musculoskeletal model to hip joint force prediction by taking patient-specific bone geometry from standard anteroposterior radiograms. Methods: 356 hips from 250 radiograms of adult human pelvis were analyzed. A musculoskeletal model was constructed from sequential images of the Visible Human Male. The common body position of one-legged stance was substituted for the midstance phase of walking. Three scaling methods were applied: a) anisotropic scaling by interhip separation, ilium height, ilium width, and lateral and inferior position of the greater trochanter, b) isotropic scaling by pelvic width and c) isotropic scaling by interhip separation. Hip joint force in one-legged stance was estimated by inverse static model. Results: Isotropic scaling affects all proportions equally, what results in small difference in hip joint reaction force among patients. Anisotropic hip scaling increases variation in hip joint force among patients considerably. The difference in hip joint force estimated by isotropic and anisotropic scaling may surpass patient’s body weight. Conclusions: Hip joint force estimated by isotropic scaling depends mostly on reference musculoskeletal geometry. Individual’s hip joint reaction force estimation could be improved by including additional bone geometrical parameters in the scaling method.

9

Propozycja metody zwiększania dokładności wymiarowej obiektów wykonywanych technikami przyrostowymi

Piękoś J., Siemiński P., Grygoruk R.

Mechanik

|

2016

|

R. 89, nr 12

1910--1911

PL

Artykuł przedstawia wyniki analizy wymiarowej obiektów wykonanych techniką przyrostową (drukiem 3D). Zaproponowano prostą metodę zwiększenia dokładności drukowanych modeli poprzez wprowadzenie współczynnika kompensującego błędy procesu. W oparciu o wyniki analizy modelu badawczego wyznaczono wartość współczynnika skalowania, który pozwolił na znaczne zmniejszenie wartości błędu względnego mierzonych wymiarów. W ramach pracy wykonano weryfikację poprawności zaprezentowanej metody z wykorzystaniem optycznego skanera 3D.

EN

This article presents the results of dimensional analysis of models which were made using 3D printing. We proposed a simple method of increasing dimensions of printed models using compensation scale factor. Scale factor allowed us to decrease relative error of measured dimensions. The verification of presented method was performed using optical 3D scanner.

10

The importance of accurate measurement of comminuted logging residues’ moisture contents for small-scale forest owners

Nilsson D., Pettersson R., Thörnqvist T., Nylinder M.

Drewno : prace naukowe, doniesienia, komunikaty

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2016

|

vol. 59, nr 198

99--110

EN

Bioenergy from logging residues is an important contributor to Swedish energy supplies. Thus, accurate measurements of delivered logging residues’ energy contents are very important for both sellers and buyers. Deliveries’ energy contents are highly correlated with their moisture contents, and thus are determined in southern Sweden (and elsewhere) by measuring their masses and moisture contents. There is insufficient knowledge, however, about the variation in moisture content within and between deliveries, and hence the minimum number of samples needed to obtain the required precision. Thus, these variations were examined in detail in the presented study. Nested analysis of the variance of the acquired data shows that at least nine samples are required to obtain estimates of a delivery’s moisture content with a 3% margin of error. For high volume trade, such as that between forest companies and the energy-conversion industry, current measurement practices are sufficiently accurate. For private forest owners making single deliveries, however, higher precision is required as inaccurate measurements can strongly affect prices.

11

Scaling evolutionary programming with the use of apache spark

Funika W., Koperek P.

Computer Science

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2016

|

Vol. 17 (1)

69--82

EN

Organizations across the globe gather more and more data, encouraged by easy-to-use and cheap cloud storage services. Large datasets require new approaches to analysis and processing, which include methods based on machine learning. In particular, symbolic regression can provide many useful insights. Unfortunately, due to high resource requirements, use of this method for large-scale dataset analysis might be unfeasible. In this paper, we analyze a bottleneck in the open-source implementation of this method we call hubert. We identify that the evaluation of individuals is the most costly operation. As a solution to this problem, we propose a new evaluation service based on the Apache Spark framework, which attempts to speed up computations by executing them in a distributed manner on a cluster of machines. We analyze the performance of the service by comparing the evaluation execution time of a number of samples with the use of both implementations. Finally, we draw conclusions and outline plans for further research.

12

Experimental verification of the scaling laws for CFB boilers of different designs

Mirek P., Klajny M.

Chemical and Process Engineering

|

2016

|

Vol. 37, nr 2

281--291

EN

In the paper flow dynamic similarity criteria have been presented to reflect the macroscopic flow pattern in the combustion chamber of large-scale circulating fluidised bed boilers. The proposed scaling rules have been verified on two cold models of CFB boilers operating in Tauron Wytwarzanie S.A. - El. Lagisza division (scale factor 1/20) and Fortum Power and Heat Poland Sp. z o. o. Czestochowa division (scale factor 1/10) – working with the power of 966 MW th and 120 MW th, respectively. As follows from the results of measurements, regardless of CFB boiler’s geometry the use of a defined set of criterial numbers allows to obtain satisfactory agreement between the suspension density distributions registered in the CFB boilers and scaling models.

13

Mrozoodporność betonu mostowego napowietrzonego mikrosferami

Osetek W.

Magazyn Autostrady

|

2015

|

Nr 11-12

58--60

PL

Obiekty mostowe, hydrotechniczne, a także nawierzchnie drogowe i lotniskowe są narażone na destrukcję spowodowaną cyklicznym zamrażaniem i rozmrażaniem, któremu towarzyszy łuszczenie powierzchni elementów lub pękanie materiału. Należy zaznaczyć, że zagwarantowanie mrozoodporności na wewnętrzne pękanie betonu nie jest równoznaczne z odpornością na łuszczenie powierzchniowe.

EN

The paper describes the tests of concrete resistance to surface scaling, performed by using the Swedish Boraas method. Bridges and hydrotechnical structures as well as road surfaces and airport pavements are exposed to damage resulting from cyclic freezing and thawing associated with surface scaling or material cracking.

14

Beton cementowo-polimerowy zastosowany do naprawy falochronu wyspowego w porcie Gdynia

Gruszczyński M., Aleksiun M., Paszek U.

Ochrona przed Korozją

|

2014

|

nr 12

466--474

PL

Przedstawiono ocenę różnej ilości modyfikatora polimerowego na kształtowanie mrozoodporności betonu, który został wykorzystany do naprawy konstrukcji falochronu wyspowego w Porcie Gdynia. Omówiono wyniki badań wpływu dodatku dyspersji kopolimeru styrenowo-akrylowego na odporność na powierzchniowe złuszczenie w 3% NaCl, wodoszczelność, wytrzymałość na zginanie i ściskanie oraz wielkość odkształceń skurczowych betonu. Oceny wpływu dodatku polimerowego na wielkość tych parametrów dokonano na podstawie wyników uzyskanych podczas prób w warunkach przemysłowych na próbkach betonu pobranych podczas zarobów próbnych i w czasie naprawy konstrukcji.

EN

An assessment of the effect of different amounts of polymer modifier on the freeze resistance of concrete used for structural repairs of the offshore breakwater at the Port of Gdynia is presented. An analysis of the results of tests carried out to determine the influence of a styrene-acrylic copolymer dispersion additive on the scaling resistance of concrete in a 3% NaCl solution, its water-tightness, compressive and flexural strengths and the extent of concrete shrinkage deformation is discussed. The evaluation of the influence of the polymer additive was carried out on the basis of results obtained in tests carried out in industrial conditions on concrete samples taken from trial mixes and in the course of repair of the breakwater.

15

The effect of anionic surfactant on the surface structure of nanofiltration membranes

Kowalik-Klimczak A., Religa P., Gierycz P., Bojarska M.

Challenges of Modern Technology

|

2014

|

Vol. 5, no. 2

33--38

EN

The effect of anionic surfactant on the surface structure of nanofiltration membranesAbstract: The effect of cleaning bath – sodium dodecyl sulphate solution on the surface structure of the polymer membrane used during nanofiltration of concentrated salt solutions have been presented in this paper. It was found that the use of the cleaning bath with sodium dodecyl sulphate caused a significant reduction in the separation and permeability possibilities of tested membrane.

16

Wpływ dodatku metakaolinu na odporność betonu na powstawanie odprysków pod działaniem mrozu

Máca P., Jandeková D., Konvalinka P.

Cement Wapno Beton

|

2014

|

R. 18/80, nr 1

1--7

PL

Przeprowadzono badania wpływu dodatku metakaolinu na trwałość betonu, a przede wszystkim jego odporność na działanie środków odladzających i powstawanie odprysków przy zamrażaniu. Stwierdzono, że metakaolin poprawia odporność normalnego i napowietrzonego betonu, jednak jego wpływ jest większy w przypadku nienapowietrzonego betonu. Względy ekonomiczne powodują, że korzystny dodatek metakaolinu powinien wynosić 5%.

EN

Deicing chemicals are significant corrosion factor in countries with cold winters. This paper is focused on the study of concrete durability, namely its resistance to deicing chemicals that cause concrete scaling. The admixture of metakaolin into plain and air-entrained concrete is described in this study. The experimental part of the work presents results from workability, compressive strength and scaling resistance measurements. It was found that metakaolin improves durability of both normai and airentrained concrete. However, the favourable effect of metakaolin is much more significant for plain concrete. It is concluded that with respect to the results and economical point of view the optimal replacement of cement by metakaolin is 5%. It was also concluded that state of the sampies surface that gets tested significantly influences the results. In addition to that, scaling tests are heavily influenced by experimental equipment and operators.

17

Analysis of the spatial distribution between successive earthquakes occurred in various regions in the world

Marekova E.

Acta Geophysica

|

2014

|

Vol. 62, no. 6

1262--1282

EN

The earthquake spatial distribution is being studied, using earthquake catalogs from different seismic regions (California, Canada, Central Asia, Greece, and Japan). The quality of the available catalogs, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogs, it was determined that the probability densities of the inter-event distance distribution collapse into single distribution when the data is rescaled. The collapse of the data provides a clear illustration of earthquake-occurrence self-similarity in space.

18

Prognozowanie scalingu na przykładzie wód ujmowanych otworem Bańska PGP-1

Kleszcz A., Tomaszewska B.

Technika Poszukiwań Geologicznych

|

2013

|

R. 52, nr 1

115--122

PL

W pracy przedstawiono podstawowe zagadnienia związane z problematyką wytrącania minerałów wtórnych w instalacji geotermalnej oraz wybrane wyniki z modelowania geochemicznego, zrealizowanego na przykładzie wód ujmowanych otworem Bańska PGP-1. Modelowanie wykonano na podstawie archiwalnych analiz fizykochemicznych wód termalnych eksploatowanych w latach 2008–2012, przy wykorzystaniu programu Phreeqci Interactive. Prognozowanie wytrącania substancji mineralnych z wód termalnych to zagadnienie kluczowe dla podejmowania odpowiednich środków zaradczych ukierunkowanych na bezawaryjną pracę systemu geotermalnego.

EN

The paper presents the problem of the precipitation of secondary minerals in geothermal systems and selected results of geochemical modeling of water for example, recognized by PEC Podhale Geothermal borehole Banska PGP-1. Modeling was performed using the Phreeqc Interactive and archival physico-chemical analysis of geothermal waters in operation in 2008–2012. The use of modeling to predict the precipitation of minerals from geothermal waters can contribute to take adequate measures for the trouble-free work geothermal system.

19

Wpływ jakości wody kotłowej na eksploatację oraz serwis kotłów wodnych i parowych

Ziółkowski L.

Piece Przemysłowe & Kotły

|

2013

|

9-10

46--50

PL

Kamień kotłowy na powierzchni grzewczej jest świetnym izolatorem, jego przewodnictwo cieplne jest 20 razy mniejsze niż stali kotłowej. Nie tylko termin rewizji wewnętrznej, ale też duża ilość osadzonego kamienia powinna być powodem zatrzymania pracy kotła i przeprowadzenia chemicznego czyszczenia.

EN

Limescale on heating surfaces acts as a highly efficient insulator, its thermal conductivity being 20 times lower than that of steel. The boiler should be shut down not only for a standard inspection of the interior surfaces, but also whenever a considerable amount of limescale is observed, which requires chemical cleaning.

20

Scaling of signed residue numbers with mixed-radix conversion in FPGA with extended scaling factor selection

Smyk R., Czyżak M., Ulman Z.

Computer Applications in Electrical Engineering

|

2013

|

Vol. 11

465--477

EN

A scaling technique of signed residue numbers in FPGA is proposed. The technique is based on conversion of residue numbers to the Mixed-Radix System (MRS). The scaling factor is assumed to be a moduli product from the Residue Number System (RNS) base. Scaling is performed by scaling of MRS terms, the subsequent generation of residue representations of scaled terms, binary addition of these representations and generation of residues for all moduli. The sign of the residue number is detected by using the most significant digit of the MRS representation. Basic blocks of the scaler are realized in the form of modified two-operand modulo adders with included additional multiply and modulo reduction operations. An exemplary pipelined realization of the scaler in the Xilinx FPGA environment is shown. The design is based on Look-Up Tables (LUT)(2,sup>6 x 1) that simulate small RAMs which serve as main components for the look-up realization. Also a method is shown that allows for flexible selection of scaling factors from a set of moduli products of the RNS base. This is made by forming auxiliary MRSs by permutation of moduli of the base. All formed MRSs are associated with the given RNS with respect to the base but each MRS has different set of weights. Thus for the required scaling factor, the suitable MRS can be chosen that provides for the scaling error smaller than 1.