Second Presentation B T C

PresentationPresentationby

Prof. Dr. Mohamed Fahmy HusseinProf. Dr. Mohamed Fahmy Hussein

The 4The 4thth Conference on Recent Technologies in Agriculture Conference on Recent Technologies in Agriculture

Challenges of Agricultural Modernization Challenges of Agricultural Modernization

Faculty of Agriculture,Faculty of Agriculture,

Cairo UniversityCairo University

Tuesday, 3-5 November, 2009Tuesday, 3-5 November, 2009

Mohamed Fahmy Hussein*

BTCBTC Solute-Transport Solute-Transport Parameters Parameters for for Three SedimentsThree Sediments

لنمذجة لنمذجة منحنى االجتيازمنحنى االجتيازاستخدام تقنية استخدام تقنية مؤشرات انتقال الذائباتمؤشرات انتقال الذائبات

* Cairo Univ., Fac. of Agric., Soil & Water Dept., Egypt,

Prelude – page-1

1) Solutes move in soils mainly with water the mass-flow (convection-advection) process, a transient process modified by the hydrodynamic-dispersion and diffusion, and this makes that processe highly complicated.

2) A given soil controls “solute-transport ” differently from any other soil, even under the saturated steady-state water flow, due to the different magnitudes of the involved parameters.

3) A mathematical-model representing that phenomenon (Fick’s Second Law) is a “general” second-order differential CDE that may be solved, for each case, under a given set of initial and boundary condition equations.

4) A closed-form analytical-solution (CfitM) is available on computer to calculate the unknown parameters.

Prelude – page-2

5) The values of the unknown-parameters once obtained on computer after BTC experiments, may be used further for the simulation of solute movements in soil. This is of primary importance to pollution, fertilization and salinization issues.

6) The purpose of this work was to run soil-column lab-experiments (BTC technique) in order to get the values of the unknowns for three soil-materials of different nature (from sandy- to clayey-textured and single-grained to aggregated soil-materials.)

7) To complete the image, the soil-moisture retention-curves (pF-curves) and the dry-sieving of the used soil-materials were studied to make a link with pore-size distribution.

Particle- and Aggregate fractions and Dry-Sieving ResultsParticle- and Aggregate fractions and Dry-Sieving Results

1 Nile bank fine earth < 2.0002 Nile bank 0.250 - 0.1253 Nile bank 0.125 - 0.0534 Salam fine earth < 2.0005 Salam sand 1.000 - 0.5006 Salam sand 0.500 - 0.2507 Calcareous fine earth < 2.0008 Calcareous 2.000 - 1.0009 Calcareous 1.000 - 0.500

10 Calcareous 0.500 - 0.250

d10, mm

Nile-bank 0.058Salam Sand 0.180B-Salam Sand 0.190Calcareous 0.068B-Calcareous 0.100

d60, mm


CU


CU (= d60/d10) is the Uniformity Coefficient,high CU value means low uniformity

Dry-Sieving Results for the Main Three SamplesDry-Sieving Results for the Main Three Samples

0102030405060708090

100

0.0100.1001.00010.000

% fi

ner

by w

eigh

t

Particle size, mm

Nile bank

Salam sand

B-Salam sand

Calcareous

B-Calcareous

Equations Used for fitting the hydraulic functions Equations Used for fitting the hydraulic functions () and and K()

• res res. mois. • s sat. moist.

• K simulated unsaturated hydraulic-conductivity

• fitness parameter (with 1/ the tension at bubbling)

• b fitness parameter (with b-1 = m * b = l)

• pore-size distrib. param. (= b m, controling slope, C, of tangent to pF curve)

• m = 1 – 1/b Mualem constraint

• m = 1 – 2/b Burdine constraint

• m and b empirical constants

• L pore connectivity parameter (fixed at 0.50 in Chemflo)

() = res + [s -res]

[ 1 + (||)b]m

K () = * eb()

K () = K sat (1 [(||)

b-1 * [1 (||)

b]-m])2

(1 (||)b)m/2

h z = ( m

z + z z

) = (zero + >1)

Soil-moisture Retention Curve (pF-curve)Soil-moisture Retention Curve (pF-curve)

0.1

1

10

100

1000

10000

100000

0.0 0.1 0.2 0.3 0.4 0.5 0.6

pre

ssu

re h

ead

, cm

v

Salam sand RETC

OBS

Nile total RETC

OBS

Calc. total RETC

OBS

Pore-size Distribution for the Three Main SamplesPore-size Distribution for the Three Main Samples

020406080

100

1 2 3

1 = sand, 2 = 1.0-.05mm, 3 = 0.5-0.25mm

macro

meso

micro

020406080

100

1 2 3

1=Nil,2=0.25-0.125mm,3=0.125-0.053mm

macro

meso

micro

020406080

100

1 2 3 4

1=cal,2=2-1mm,3=1-0.5mm,4=0.5-0.25mm

macro

meso

micro

Fick’s-Law Fick’s-Law (Second-Order Differential Eq. of (Second-Order Differential Eq. of Solute-TransportSolute-Transport in porous media) in porous media)

• soil-moisture content, dimensionless bulk-fraction

• CL solute concentration, mg.l-1

• D effective hydrodynamic dispersion coeffient, cm2.hr-1

• Z depth, nevative downward, cm

• q Darcy velocity (flux), negative downward, cm.hr-1

• S solute-decay (by a chemical or a biological

Kinetic-reaction); a sink-term usually ignored in BTC’s

BTC’s for Three Packed Fine-Earth SedimentsBTC’s for Three Packed Fine-Earth Sediments

Rectifed and modeled BTC's with NaCl added to three natural sediments

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 0.5 1.0 1.5 2.0

pore volume

C/C0

Sand total

CfitM

Nile total replicate 3

CfitM

Calcareous total

CfitM

C/C0=0.5

1 PV

Some Parameters – page-1Some Parameters – page-1

• Peclet, P ratio of mass-flow transport (xL) relative to hydrodynamic-dispersion (DL). P increases when (xL) surpasses (DL) (high P means efficient leaching).

• x mean pore-water velocity, cm/hr

• L column length, cm

• DL effective hydrodynamic-dispersion coefficient, cm2/hr

• q Darcy velocity, cm/hr

• bulk moisture-content, fraction

• longitudinal dispersivity, cm

P =

x LDL

=(q/) L

DL L

DL = D* +

x LP

DL = x d10

P + x

DL x

• Retardation factor, R,

• R<1,

this implies the presence of one or more of the following processes :● anion exclusion,

● solute precipitation

● immobile moisture.

• R>1,

● k (distribution coefficient, cm3solution/g soil)

is positive (cation exchange or anion adsorption).

• R=1,● indicates lack of solute reaction with soil.

R = 1 + k


• Distribution coefficient, k, cm3 solution /g soil

• When R<1, k will be negative (solute precipitation or anion exclusion, (-k) is the “specific anion exclusion” (cm3/g soil) and (1–R) is the “relative volume of anion exclusion” (dimensionless). BTC’s may give better appreciation of adsorption than batch-technique, where soil is mixed with a volume of solution to determine kd by Frundlich equation:

q = kd C1/n

• q concentration of adsorbed solute, mmol/kg soil,

• C concentration of added solution, mmol/kg soil

• n power term (generally considered as unity)

k =R - 1 /


• Longitudinal dispersivity, , cm: It is a length parameter that represents soil non-homogeneity (due to presence of different particle- and void-sizes that define the microscopic configuration of the solid-liquid interface.)

• It may be obtained from the slope of the BTC curve at its inflection point (at C/C0 = 0.50 in simple case). It may be close to the mean diameter of soil particles if soil was homogeneous, but it becomes larger when soil is non-homogeneous. It may appear small in numerical models due (to a technical problem known as “numerical dispersion”).


L =

(DL - D*)

x L

P

1 2 wromg and must be repeated3 4 5 6 7 8 9 10 wromg and must be repeated

R - 0.981 1.083 0.960 0.945 0.989 0.995 0.757 0.896 1.016 0.800

b g cm-31.601 1.605 1.639 1.180 1.123 1.172 1.141 1.169 1.140 1.056

s g cm-3

2.660 2.660 2.660 2.587 2.587 2.587 2.597 2.597 2.597 2.597depth cm 30 30 30 30 30 30 30 30 30 30

via pF - 0.377 0.384 0.339 0.568 0.573 0.602 0.616 0.660 0.669 0.627 - 0.398 0.397 0.384 0.544 0.566 0.547 0.560 0.550 0.561 0.593f - 0.398 0.397 0.384 0.544 0.566 0.547 0.560 0.550 0.561 0.593

factor** - 1 1 1 1 1 1 1 1 1 1ne - 0.398 0.397 0.384 0.544 0.566 0.547 0.560 0.550 0.561 0.593

- k cm3sol./kg soil 4.8 NA 9.4 25.1 5.6 2.6 119.2 49.0 NA 112.3T°C 25 29 23 32 29 23 28 28 28 28

Q cm3 minute-1 10.08 11.47 8.00 6.52 11.74 3.56 3.77 4.12 2.11 1.03D /DZ - 1.067 1.067 1.067 1.067 1.067 1.067 1.067 1.067 1.067 1.067

d cm 5.165 5.165 5.165 5.330 5.305 5.165 5.305 5.330 5.310 5.165

A cm2 20.95 20.95 20.95 22.31 22.10 20.95 22.10 22.31 22.15 20.95

q cm minute-1 0.481 0.547 0.382 0.292 0.531 0.170 0.170 0.185 0.095 0.049

K cm minute-1 0.451 0.513 0.358 0.274 0.498 0.159 0.160 0.173 0.089 0.046

kintrinsic micron27.718 8.777 6.123 4.689 8.515 2.725 2.733 2.959 1.528 0.790

x cm minute-1

1.209 1.380 0.995 0.538 0.939 0.311 0.304 0.336 0.170 0.083

c cm minute-11.233 1.274 1.037 0.569 0.949 0.312 0.402 0.375 0.167 0.104

P - 61.4 14.5 48.5 117.1 145.0 180.0 8.9 27.1 33.9 30.0

D cm2 hour-1 35.5 171.0 36.9 8.3 11.7 3.1 61.5 22.3 9.0 5.0d10 mm 0.180 0.500 0.250 0.058 0.125 0.053 0.068 0.068 0.068 0.068

D* 10-3cm2 hour-10.02127 0.28495 0.03076 0.00160 0.00486 0.00055 0.01394 0.00506 0.00204 0.00113

w - 0.295 3.958 0.427 0.022 0.067 0.008 0.194 0.070 0.028 0.016t - 1.161 0.317 0.948 4.949 2.896 8.472 1.702 2.797 4.447 6.149

L cm 0.488 2.062 0.618 0.256 0.207 0.167 3.369 1.108 0.884 1.000

Calcareous

parameter

Salam sand Nile bankBTC’s Computer Results for Samples and Size-FractionsBTC’s Computer Results for Samples and Size-Fractions

ملخصملخصكان من المستحيل عمليا. الحفاظ على حالة التشبع الرطوبى برمال الكثبان، –

الخاص بالرمال قريب للغاية من الواحد R وظهر أن معامل اإلبطاء متوسطة P على حين كانت قيمة رقم بيكليت )انعدام تفاعلها مع الذائب(الصحيح

مما )سنتيمتر0.61 إلى 0.49من (متوسطة كانت التشتتية و)61 إلى 49من (وكان المتوقع (يعنى أن كفاءة غسيل معتدلة تحت سريان مائى قريب من التشبع

الحصول على قيم صغيرة لمؤشر التشتتية - كفاءة غسيل عالية - فيما لو كان ) السريان تام التشبع قد تحقق.

180 إلى 117من ( أما غرين شط النيل فقد أعطى قيما. مرتفعة لرقم بيكليت–مما يعبر عن أعلى كفاءة )سنتيمتر0.26 إلى 0.17من (وقيما. صغيرة للتشتتية )

غسيل شاهدناها بالرواسب المستخدمة، على حين كان معامل اإلبطاء يقل عن )أى وجود قدر من الطرد األنيونى بهذا الغرين. (الواحد الصحيح

وفيما يخص التجمعات البنائية الجبرية الطينية حصلنا على مجال واسع نسبيا. لمدى –، فى حين كان مؤشر )34 إلى 9من (رقم بيكليت وإن كانت كلها قيما. صغيرة

، وتزايدت تشتتية المادة الجيرية بزيادة )سنتيمتر3.4 إلى 0.95من ( التشتتية كبيرا. ، أما )أى انخفاض كفاءة الغسيل بزيادة حجم التجمعات( حجم التجمعات البنائية

تعجيل اجتياز الذائبات أى ( معامل اإلبطاء فكان يقل بوضوح عن الواحد الصحيحلعمود التربة بفعل وجود قدر ملموس من الطرد األنيونى بالتجمعات الطينية

)الجيرية. من انخفاض رقم (وعلى النقيض مما شاهدناه فى التجمعات الجيرية –

نعتقد أن ارتفاع رقم بيكليت لكل من رواسب شط النيل ورمال الكثبان )بيكليتيعنى أن انتقال الذائبات مع حركة كتلة المياه - بهذين النوعين األخيرين من

الرواسب - هو اآللية السائدة بهما ، على حين كان انتقال الذائبات عن طريق ميكانيزم التشتت واالنتشار بهما ضئيل، ولكنه مؤثر بالتجمعات الطبنية الجيرية .

من الفوارق التى الحظناها بقيم تلك المؤشرات تتضح أهمية دراسة انتقال –الذائبات لما لها من مردود على الرى والموارد األرضية، فنرى اعتمادها عند

التعامل مع رى وصرف األراضى وتملحها وتسميدها وتلوثها.

� �شكرًا شكرًا

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Second Presentation B T C