61
Volume 5, Issue 10: Special Issue
(EJAR)
ISSN: 2181-2020
MPHAPP
THE 6TH INTERNATIONAL SCIENTIFIC AND PRACTICAL
CONFERENCE “MODERN PHARMACEUTICS: ACTUAL
PROBLEMS AND PROSPECTS”
TASHKENT, OCTOBER 17, 2025
in-academy.uz
DETERMINATION OF A MATHEMATICAL MODEL OF THE EXTRACTION
PROCESS USING FILTRATION AND MASS EXCHANGE EQUATIONS
Ilhamo Kh.Sh.
Tashken Pha maceu ical Ins i u e, Tashken ci y, Republic o Uzbekis an
e-mail: [email p o ec ed]
h ps://doi.o g/10.5281/zenodo.17318408
Rele ance: As in scien i ic and echnical, indus ial, social and o he sphe es, he s udy o
p ocesses h ough ma hema ical modeling based on digi al echnologies, which allows p edic ing
hei esul s, is becoming inc easingly impo an in pha maceu ical p oduc ion. The use o
ma hema ical modeling, which sa es bo h ime and cos s in he p oduc ion o d ugs o he c ea ion o
a new d ug wi h an op imal composi ion, emains one o he p essing issues o pha maceu ical
p oduc ion.
The pu pose o he s udy: he main pu pose o he a icle is o ma hema ically model he p ocess
o ex ac ing use ul subs ances om medicinal plan aw ma e ials and o de e mine he impo an
ac o s a ec ing he ex ac ion p ocess, he echnological pa ame e s o ex ac ion and he
cha ac e is ics o medicinal plan ex ac s, as well as o s udy he ole and ele ance o he use o
ma hema ical modeling me hods.
Me hods and echniques: The p oduc ion o medicines based on medicinal plan collec ions
equi es he ex ac ion o medicinal plan collec ions. Al hough he e a e se e al ex ac ion me hods,
hey can be di ided in o s a ic and dynamic me hods ha can be ca ied ou con inuously o
pe iodically. As is known, he c ushed aw ma e ials o ex ac ion a e loaded in o a pe cola o
( eac o ) and ligh ly comp essed. Then, an ex ac an is passed h ough he aw ma e ial laye a a
ce ain speed, and his ex ac an lea es he ex ac o eac o en iched wi h biologically ac i e and
o he ex ac i e subs ances o he aw ma e ial. The e iciency o his p ocess depends on he na u e
o he ex ac o , he hyd odynamic condi ions o he p ocess, he physical and mechanical p ope ies
o he aw ma e ial, he po osi y o he laye , and many o he ac o s. The e o e, de e mining he
op imal alues is e y impo an o he echnological pa ame e s o he p ocess. Based on hese, we
build a ma hema ical model o he p ocess o washing he medicinal plan collec ion placed in a
cylind ical eac o wi h an ex ac an . In his case, i is necessa y o de e mine he op imal speed o
he mo emen o he ex ac an h ough he laye o he medicinal plan collec ion, aking in o accoun
he pa icle size o he placed medicinal plan collec ion in ela ion o i s placemen densi y. We
assume ha he po ous medium o he medicinal plan aw ma e ial in pe cola o s and he ex ac o
a e mu ually pene a ing sys ems, and he ex ac an o ms a il a ion p ocess wi h he plan aw
ma e ial. In his case, we assume ha he mo emen occu s only along he e ical z axis, and we
assume ha he e is no mo emen along he ho izon al x and y axes. Fo he ma hema ical model o
he p ocess, he model o in e pene a ing sys ems o X.A. Rakhma ulin, o he il a ion p ocess, he
equa ion o mo ion o he ex ac an in a po ous medium acco ding o Da cy's law and di e en ial
equa ions o mass exchange depending on empe a u e we e ob ained. A e some ma hema ical
ans o ma ions, a o mula was ob ained, which depends on he ex ac an p essu e p0 o he
sepa a ed subs ance, on Q - on he low a e o he ex ac o , on he S-equi alen diame e o he
po ous mass, on he iscosi y o he ex ac o , on he pe meabili y o he po ous mass consis ing o
medicinal plan s and on o he hyd odynamic pa ame e s o he p ocess. By adding o his se ies o
di e en ial equa ions, an idealized di usion model o he ex ac o mo ion and di e en ial equa ions
o mass exchange depending on empe a u e, wi h equa ions aking in o accoun bounda y condi ions,
62
Volume 5, Issue 10: Special Issue
(EJAR)
ISSN: 2181-2020
MPHAPP
THE 6TH INTERNATIONAL SCIENTIFIC AND PRACTICAL
CONFERENCE “MODERN PHARMACEUTICS: ACTUAL
PROBLEMS AND PROSPECTS”
TASHKENT, OCTOBER 17, 2025
in-academy.uz
we o m a sys em o closed di e en ial equa ions o he ma hema ical model o he ex ac ion
p ocess.
Resul s: The ma hema ical model o he ex ac ion p ocess, consis ing o a sys em o
di e en ial equa ions wi h pa icula de i a i es, was nume ically sol ed in he Ma hCAD p og am,
and he nume ical esul s ob ained we e qui e close o he expe imen al da a, and i was calcula ed
ha he concen a ion o bioac i e subs ances eleased du ing he ex ac ion p ocess eaches i s
maximum alue a a empe a u e o 80°-90°C and a du a ion o he ex ac ion p ocess o 70-80
minu es.
Conclusions: Sol ing he esul ing equa ion allows us o de e mine he le el o pe meabili y
o he ex ac an in he aw ma e ial laye . By inc easing he p essu e, we can change he low a e o
he ex ac an and achie e i s maximum pene a ion in o he medicinal plan collec ion. As a esul ,
he hyd aulic esis ance o he medicinal plan aw ma e ial laye inc eases, and he elease o
bioac i e subs ances inc eases due o he mass ans e p ocess. The alues o he hyd odynamic
pa ame e s o he p ocess and hei e ec on he ex ac ion allow us o de e mine he op imal
pa ame e s o he ex ac ion p ocess.
