Utafiti huu unachunguza kama apparent au effective kinetic parameter inayohesabiwa kutoka methane hydrate growth experiments inaweza kutabiriwa kwa simple and interpretable data model. Researcher alitumia observations 30 zilizochukuliwa kutoka experimental study iliyochapishwa hapo awali; akachagua pressure, hydrate equilibrium temperature na subcooling kama inputs za multiple linear regression model. Seven different variable combinations zililinganishwa kwa same 10-fold cross-validation method.

Most successful model, Model 7, ilitumia pressure, equilibrium temperature na subcooling together. Kwa model hii, cross-validated R² value iliripotiwa 0,9682, root mean square error 3092,5 W/m²K na mean absolute error 2429,1 W/m²K. Arrhenius model iliyotathminiwa kwa same data na validation method ilitoa R² = 0,9540, RMSE = 3712,0 W/m²K na MAE = 2967,0 W/m²K. Regression model ilitoa lower prediction error katika examined dataset kwa sababu ilijumuisha additional operating variables.

Hata hivyo quantity inayotabiriwa si pure reaction constant iliyopimwa directly at molecular scale. Parameter ime-derived kutoka experimental interface growth rate, hydrate formation heat, hydrate density na heat-transfer coefficient. Kwa hiyo inapaswa kutathminiwa kama apparent parameter yenye combined effects za thermodynamic driving force, heat and mass transfer, interfacial phenomena na experimental setup. Model pia si physical hydrate-growth law; inatoa only dataset-specific empirical approach kwa experiments zinazofanana na same conditions.

Kwa mtazamo wa Uturuki: Study inatoa useful methodological example kwa kutathmini small experimental datasets kwa transparent models katika natural-gas transmission pipelines, subsea pipeline systems, flow assurance, high-pressure processes na energy engineering nchini Uturuki. Ili approach itumike Uturuki, independent experimental data zinazojumuisha local gas compositions, pipe and reactor geometries, flow conditions, salinity, inhibitors, mixing level na heat-mass-transfer conditions lazima zikusanywe. Model inapaswa kuvalidateiwa kwa external data kabla ya transfer to different systems, repeated au nested cross-validation itumike na model ipanuliwe kwa physical variables. Kutokana na study hii, hydrate blockage risk, safe operating limit au inhibitor requirement ya pipeline yoyote nchini Uturuki haiwezi kuhesabiwa directly.

Maelezo ya Kina

Ni problem gani inayoshughulikiwa na research?

Katika high-pressure and low-temperature conditions, water molecules zinaweza kuunda cage-like crystalline structures kupitia hydrogen bonds na kukamata small gas molecules kama methane ndani ya cages hizo. Solid crystalline structures zinazopatikana huitwa gas hydrates.

Katika systems ambako natural gas inasafirishwa kupitia long pipelines, fluid kupoteza heat kwenda environment au cooling kutokana na pressure drop kunaweza kupeleka system kwenye temperature-pressure region ambapo hydrates ni stable. Growth and agglomeration ya hydrate crystals inaweza kupunguza pipe cross-section, kuongeza pressure loss na katika advanced stage kusababisha pipeline blockage.

Kwa hiyo haitoshi kujua tu hydrates ni thermodynamically stable katika temperature na pressure gani. Ni muhimu pia kuelewa nucleation rate, growth rate na muda unaoweza kuhitajika kabla ya kuwa operational risk.

Methane hydrate formation inapitia stages zipi?

Figure 1 on page 4 ya study inagawanya typical gas-consumption curve katika four qualitative stages:

1. Stage I — Gas dissolution and induction: Gas dissolves katika aqueous phase; induction period hutokea hadi stable hydrate nuclei zionekane macroscopically.
2. Stage II — Rapid growth: Stable nuclei hukua na gas incorporated rapidly into hydrate phase. Hii ndiyo steepest region ya gas-consumption curve.
3. Stage III — Slowing growth: Crystal structures zinaendelea kukua, lakini gas-consumption rate inaanza kupungua.
4. Stage IV — Stable or limited condition: Gas consumption inakuwa very slow. Stage hii mara nyingi inahusishwa na mass-transfer limitations.

Research inalenga hasa kinetic parameter inayoderiveiwa kutoka hydrate growth experiments. Hata hivyo katika real experiment, interfacial reaction, gas transport through liquid, diffusion to crystal surface na removal of formation heat from environment zinaweza kutokea simultaneously.

Kwa nini “kinetic parameter” ni apparent au effective parameter?

Ideal intrinsic kinetic constant inapaswa kuwakilisha only molecular reaction rate at hydrate-water-gas interface. k parameter katika examined study haikupatikana kutoka direct molecular measurement. Ilihesabiwa kutoka interface motion rate observed katika previously published experiments pamoja na thermal-balance expressions.

Kwa hiyo k value inaweza kujumuisha combined effects hizi:

• True reaction kinetics at hydrate surface,
• Gas dissolution and transport in liquid phase,
• Mass-transfer resistance at interface,
• Removal of heat released by hydrate formation,
• Geometry and mixing conditions of experimental vessel,
• Thermodynamic driving force produced by pressure and fugacity,
• Transport limitations developing in hydrate film or porous structure.

Researcher kwa hiyo anasisitiza kwamba model haitabiri “intrinsic reaction constant”, bali apparent kinetic parameter inayoakisi combined effects za experimental system.

Role ya Arrhenius approach

Katika conventional kinetic studies, temperature dependence mara nyingi inaelezwa kwa Arrhenius equation:

\[ k=A\exp\left(-\frac{E_a}{RT_{\mathrm{eq}}}\right) \]

Hapa:

• k: Kinetic parameter au rate constant,
• A: Arrhenius pre-exponential factor,
• E_a: Activation energy,
• R: Universal gas constant,
• T_eq: Equilibrium temperature in Kelvin.

Arrhenius model inatoa physical basis kwa effect ya temperature on reaction rate. Kinyume chake, standard form haijumuishi pressure, subcooling, gas fugacity au experimental transport conditions explicitly kama separate variables.

Main approach ya study si kubatilisha Arrhenius model; ni ku-test kama transparent regression model yenye additional variables kama pressure na subcooling inaweza kuboresha empirical fit kwenye same dataset.

Dataset iliyotumika

Data zilichukuliwa kutoka 2001 methane-hydrate film-growth experiments za Freer na colleagues. Kuna total observations 30. Kila observation ina variables hizi:

• Pressure, P,
• Hydrate equilibrium temperature, T_eq,
• Bulk au experimental-environment temperature, T_b,
• Subcooling, ΔT = T_eq − T_b,
• k parameter iliyohesabiwa kutoka experimental data.

Kuwa na observations 30 pekee kunahitaji model complexity ibaki limited. Kwa sababu hiyo researcher alichagua multiple linear regression kama primary model badala ya highly parameterized methods kama artificial neural networks.

Kinetic parameter ilihesabiwaje?

Study kwanza inatoa heat balance kwa moving hydrate interface:

\[ \lambda_H\rho_H\frac{dX}{dt}=K(T_{\mathrm{eq}}-T_b) \]

Hapa:

• λ_H: Heat of hydrate formation au dissociation,
• ρ_H: Methane-hydrate density,
• dX/dt: Advance rate ya hydrate interface,
• K: Overall reaction au transfer coefficient,
• T_eq − T_b: Subcooling.

Relationship ya overall coefficient na kinetic pamoja na heat-transfer resistances ilielezwa kama:

\[ \frac{1}{K}=\frac{1}{k}+\frac{1}{h} \]

Hapa h ni heat-transfer coefficient ya experimental system. Rearranging expressions hizi mbili kunatoa:

\[ \frac{1}{k}=\frac{T_{\mathrm{eq}}-T_b}{\lambda_H\rho_H\left(dX/dt\right)}-\frac{1}{h} \]

equation.

Constants zilizotumika katika calculation ni:

Interface rate katika experimental source ilitolewa kwa µm/s na kubadilishwa kuwa m/s kabla ya calculation. Ili kuhakikisha unit consistency in watts katika thermal equation, hydrate heat pia inapaswa kubadilishwa kutoka kJ/kg kwenda J/kg; kwa kuwa study haijashare calculation code, implementation details za conversion hii haziwezi ku-auditiwa directly.

Scatter plots kwenye page 13 zinaonyesha nini?

Figure 2 inachora k parameter separately dhidi ya four variables:

• Pressure: Strong na approximately monotonic increase katika k kadiri pressure inavyoongezeka.
• Equilibrium temperature: k generally inaongezeka equilibrium temperature inapoongezeka.
• Bulk temperature: Data zinacluster around 1, 2 na 4 °C na hazionyeshi clear linear trend.
• Subcooling: k inaonekana kuongezeka distinctly kadiri ΔT inavyoongezeka.

Researcher amesema hakutambua important outlier na hakuondoa observation yoyote kwa sababu ya small dataset. Hata hivyo relationships zinazoonekana kwenye plots zinahusu only this experimental range na hazimaanishi hydrate growth ni fundamentally linear.

Correlation analysis

Pressure, equilibrium temperature na subcooling zina correlations above 0,9 with k. Kinyume chake direct relationship ya bulk temperature ni very weak.

Hata hivyo correlations among inputs themselves pia ni very high. Especially correlation ya 0,987 kati ya P na T_eq inaonyesha serious multicollinearity. Kwa hiyo coefficients katika final model hazipaswi kutafsiriwa kama independent physical effects au causal changes.

Kwa nini bulk temperature haikuingizwa kwenye final model?

Bulk temperature ilionyesha weak direct correlation with k. Pia subcooling tayari inahesabiwa kwa relation:

\[ \Delta T=T_{\mathrm{eq}}-T_b \]

Kuongeza T_b, T_eq na ΔT simultaneously kwenye model kungeunda mathematically redundant information. Kwa hiyo researcher aliondoa bulk temperature kutoka candidate-model set na ku-focus pressure, equilibrium temperature na subcooling.

Hata hivyo kutumia ΔT hakumaanishi information kutoka T_b imeondoka kabisa. Effect ya bulk temperature ipo indirectly ndani ya subcooling variable.

Random forest importance analysis

Study pia imetoa exploratory random-forest variable-importance values pamoja na Pearson correlation:

Regressor results zinaweka subcooling highest, pressure na equilibrium temperature close to each other, na bulk temperature very low. Ordering hii inaendana na general trend katika correlation analysis.

Kinyume chake, study haijaeleza jinsi “Random Forest Classifier” ilivyotumika kwa continuous target variable, kama k values zilibadilishwa kuwa classes, au hyperparameters zipi zilitumika. Researcher pia hakutumia analysis hii kama main basis ya model selection; aliwasilisha only kama exploratory comparison.

Which regression models were compared?

Multiple linear regression structure

General multiple linear regression model imetolewa kama:

\[ Y=\beta_0+\beta_1X_1+\beta_2X_2+\cdots+\beta_nX_n+\varepsilon \]

Hapa Y ni predicted output, X variables ni inputs, β₀ intercept, β coefficients ni model weights za inputs na ε unexplained error term.

Kwa study hii final Model 7 equation ni:

\[ k=-37157{,}28+15892{,}08P-5901{,}97T_{\mathrm{eq}}+2162{,}22\Delta T \]

P ni MPa, T_eq na ΔT ni °C; predicted k unit ni W/m²K.

Pressure coefficient ni positive, equilibrium-temperature coefficient negative na subcooling coefficient positive. Ingawa equilibrium temperature alone ina positive correlation with k, coefficient yake inakuwa negative katika multivariable model kwa sababu variables zina strong interrelationships. Coefficients hizi hazipaswi kutafsiriwa kama magnitudes za separate physical mechanisms.

Method flow kwenye page 16

Figure 3 inaonyesha research workflow kama:

1. Data preparation na preprocessing,
2. Definition ya all candidate features,
3. Preliminary exploratory analysis,
4. Variable selection kupitia correlation na physical reasoning,
5. Building MLR models with selected inputs,
6. Prediction ya experimental kinetic parameter,
7. Comparison ya models using common validation metrics.

Flowchart inaonekana ku-label output kama “intrinsic rate parameter”. Kinyume chake main text inaeleza clearly kwamba calculated parameter si pure intrinsic constant na ina system-level effects. Kuna terminological inconsistency kati ya wording kwenye figure na more cautious definition kwenye text.

10-fold cross-validation ilitumika vipi?

Total dataset iligawanywa katika 10 parts. Katika kila round nine parts zilitumika kwa training na remaining one kwa testing; process ilirudiwa mpaka kila part ikatumika once kama test data.

Kwa kuwa total ni only observations 30, kila test fold ina approximately three observations. Hii inafanya data use efficient, lakini R² na error metrics katika each fold zinaweza kuathiriwa na very few observations.

Study haijaripoti random seed iliyotumika kuunda folds, kama data zilishuffled, cross-validation ilirudiwa mara ngapi, au standard deviation ya performance across folds. Kwa hiyo variation chini ya different fold split haijulikani.

Pia seven candidate models zililinganishwa kwa same cross-validation results na best one ikachaguliwa. Kwa kuwa no separate external test set au nested cross-validation ilitumika, reported final performance inaweza kuwa na some optimism from model selection.

Validation metrics zilizotumika

Coefficient of determination

\[ R^2=\frac{\sum_{i=1}^{n}(\hat{y}_i-\bar{y})^2}{\sum_{i=1}^{n}(y_i-\bar{y})^2} \]

R² inaonyesha extent ambayo predictions zinawakilisha observed variability. Value approaching 1 inaonyesha stronger fit. Hata hivyo high R² alone haithibitishi relationship ni causal au physically correct.

Root mean square error

\[ RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(\hat{y}_i-y_i)^2} \]

RMSE inapenalize large errors zaidi kwa sababu ya squaring. Katika study hii unit yake ni same as k, yaani W/m²K.

Mean absolute error

\[ MAE=\frac{1}{N}\sum_{i=1}^{N}|y_i-\hat{y}_i| \]

MAE inaonyesha average absolute prediction difference na ni less sensitive than RMSE kwa large individual errors.

Results za seven regression models

Kati ya single-variable models, pressure model M1 ilitoa best result. Pressure alone ilifikia R² = 0,9207 na kueleza large portion ya variation katika k ndani ya dataset.

Kuongeza equilibrium temperature au subcooling kwa pressure kuliboresha performance. Kati ya two-variable models, M5 inayotumia P na ΔT ilitoa best result kwa R² = 0,9480.

Three-variable M7 ilitoa highest R² pamoja na lowest RMSE na MAE kati ya all compared regressions.

Comparison ya predicted na experimental values

Figure 4 on page 22 inalinganisha k values predicted na Model 7 na experimentally derived values. Most points zinacluster around diagonal line inayowakilisha perfect agreement.

Fit inaonekana generally strong kwa low na medium k values. Kinyume chake around 50.000–65.000 W/m²K, some points zinadeviate more visibly kutoka ideal line. Hii inaonyesha absolute errors zinaweza kuongezeka katika high-k region.

Residual plot inaonyesha nini?

Supplementary Figure S1 on page 23 inaonyesha difference kati ya experimental value na prediction dhidi ya predicted k. Residuals zipo both above na below zero line na study inasema hakuna clear systematic pattern.

Hata hivyo katika high-prediction range kuna residuals approaching about +10.000 na −5.000 W/m²K. Kwa sababu data count ni small, strong conclusions haziwezi kutolewa kuhusu normal distribution ya residuals, constant-variance assumption au influential observations.

Study haijaripoti residual normality, heteroscedasticity, leverage values, Cook’s distance au prediction intervals.

Comparison na Arrhenius model

Regression model iliongeza R² kwa 0,0142 relative to Arrhenius model; ikapunguza RMSE kwa 619,5 W/m²K na MAE kwa 537,9 W/m²K.

Arrhenius model imesemwa kutoa activation energy approximately 173 kJ/mol. Hata hivyo Arrhenius pre-exponential coefficient, jinsi parameters zilirefit katika each cross-validation fold, na uncertainty ya activation energy hazijaelezwa.

Figure 5 on page 24 inaonyesha both Arrhenius na MLR predictions around ideal-fit line. Close results za two approaches zina-support dominant role ya temperature katika dataset. Additional advantage ya MLR ni uwezo wa kutumia pressure na subcooling information separately.

Better statistical fit ya MLR model inamaanisha nini?

Lower error inaonyesha MLR inafuatilia variation ndani ya examined observations 30 slightly better kuliko Arrhenius model. Hii haimaanishi:

• MLR represents hydrate-growth physics more accurately than Arrhenius model,
• Pressure au temperature coefficients ni causal quantities,
• Model inaweza kutumika safely outside study range,
• Model ni valid kwa different reactors na gas compositions,
• Intrinsic molecular reaction constant inatabiriwa.

Arrhenius equation inatoa physical interpretation kupitia temperature na activation energy, huku MLR ikiwakilisha multivariable pattern katika dataset more flexibly. Research inachukulia approaches hizi mbili kama complementary rather than competing tools.

Possible meaning ya strong pressure effect

Pressure ilikuwa strongest predictor kati ya single-variable models. Study inaunganisha hii na effects za pressure on gas fugacity, hydrate-formation driving force na amount of methane available at interface.

Hata hivyo katika dataset, pressure na equilibrium temperature zina extremely strong correlation ya 0,987. Kwa hiyo pressure coefficient haiwezi kusemwa kuwakilisha pressure-specific effect alone. Katika experimental design, pressure change ilienda pamoja na change in equilibrium temperature.

Strengths za study

• Simple and explainable model appropriate for small dataset imechaguliwa.
• Seven different input combinations zimelinganishwa using same validation method.
• Effects za pressure, temperature na subcooling zimetathminiwa separately and together.
• Model imetathminiwa not only kwa training fit bali kwa 10-fold cross-validation.
• RMSE na MAE zimeripotiwa alongside R².
• Arrhenius model imelinganishwa using same data and validation approach.
• Researcher ameeleza explicitly kwamba MLR si physical mechanism.
• Multicollinearity na dataset-specific validity zimekubaliwa katika source.
• Prediction-observed na residual plots zimewasilishwa.
• Future combination ya physics-based na data-driven methods imependekezwa.

Main limitations za study

• Study ni preprint ambayo haijapitia peer review.
• Dataset ina only observations 30.
• All data zimetoka single older experimental study.
• No independent external validation kutoka different laboratory, reactor au setup.
• Very high correlation kati ya pressure na equilibrium temperature.
• No standard errors au confidence intervals zinazoonyesha stability ya regression coefficients.
• Multicollinearity measures kama variance inflation factor hazijahesabiwa.
• Random seed na repeat count ya cross-validation folds hazijaelezwa.
• No performance distribution au standard deviation across folds.
• No separate external test set au nested cross-validation.
• Dependence structure ya data within same experimental series haijatathminiwa.
• Model assumes only linear relationship.
• Interaction terms au nonlinear terms hazijachunguzwa.
• Normality na constant variance ya residuals hazijatestwa statistically.
• Jinsi Random Forest Classifier ilivyotumika kwa continuous target haijaelezwa.
• Regression na analysis codes hazijashareiwa.
• Raw observations 30 hazijawasilishwa kama complete table katika article.
• Arrhenius pre-exponential coefficient na activation-energy uncertainty hazijatolewa.
• Gas fugacity, interfacial area, diffusivity na mass-transfer coefficient hazijajumuishwa directly katika model.
• Model haijatestwa kwa different gas compositions, salts, inhibitors au flowing systems.

Important reporting issues katika source

• Method schematic on page 16 ina-label output “intrinsic rate parameter”, wakati main text inasema parameter ni apparent na ina system effects.
• Jinsi Random Forest Classifier ilivyotumika kwa continuous k target haijaelezwa.
• Ingawa R² explanation inatumia phrase “R-squared / adjusted R-squared”, adjusted R² haijaripotiwa separately kwenye table.
• Random-split details na repeat count ya cross-validation hazijatolewa.
• Arrhenius fit pre-exponential factor na uncertainties hazijawasilishwa.
• Code na complete data table zinazowezesha reproduction ya calculations hazijashareiwa.
• Despite strongly correlated inputs katika Model 7, coefficient uncertainties hazijatolewa.
• Unit conversions zilizotumika katika calculation ya k hazijaelezwa at code level.

Which conclusions are supported?

• Katika examined observations 30, pressure, equilibrium temperature na subcooling zina strong statistical relationships na k parameter.
• Bulk temperature alone ina weak linear relation with k.
• Pressure ilikuwa most successful predictor kati ya single-variable models.
• M7 inayotumia P, T_eq na ΔT together ilitoa lowest cross-validation error among tested regressions.
• Arrhenius model pia ilionyesha strong prediction performance kwenye same dataset.
• Use ya additional operating variables iliboresha dataset-specific empirical fit.
• Simple linear models zinaweza kuwa transparent surrogate tools kwa examining small hydrate-kinetics datasets.
• MLR na Arrhenius approaches zinaweza complement one another kwa different purposes.

Which conclusions are not proven?

• Haithibitishi model ni intrinsic hydrate-growth law at molecular scale.
• Haionyeshi regression coefficients ni independent causal effects.
• Haionyeshi model ni valid katika other reactors, pipelines au gas compositions.
• Haitabiri blockage time ya real pipeline.
• Haihesabu need for hydrate inhibitor au dispersant chemical.
• Haitenganishi heat- and mass-transfer effects.
• Haithibitishi MLR ni physically superior to Arrhenius model.
• Haionyeshi high R² establishes a new general physical law.
• Haionyeshi model inaweza safely extrapolate kwa pressures na temperatures outside data range.

Mbinu na Matokeo ya Utafiti

Method summary

Final model na application range

\[ k=-37157{,}28+15892{,}08P-5901{,}97T_{\mathrm{eq}}+2162{,}22\Delta T \]

Equation hii ilitathminiwa only ndani ya approximate ranges katika study:

Use ya equation outside ranges hizi haijavalidateiwa na study. Kwa sababu linear model haienforce physical limits, inappropriate inputs zinaweza kutoa negative au unrealistic predictions.

Basic performance comparison

Mean absolute error ya Model 7 corresponds to approximately eight percent ya dataset mean k value ya about 29.696 W/m²K. Hata hivyo ratio hii alone haionyeshi error distribution across observations au larger errors katika high-k region.

Researcher’s future-work suggestions

• Expand experimental database,
• Examine broader pressure and temperature ranges,
• Add different gas compositions na reactor configurations,
• Use gas fugacity directly as input,
• Add interfacial area, diffusivity na mass-transfer coefficient to model,
• Carefully compare more advanced machine-learning models,
• Preserve interpretability in small datasets,
• Hybridize physics-based hydrate models with data-driven methods.

Statistical-evaluation limit

Performance values katika study zilipatikana kwenye single dataset ya observations 30. Kwa kuwa no independent experimental external test data ipo, R² = 0,9682 haiwezi kutafsiriwa kama general-use success.

Strong correlation kati ya pressure, equilibrium temperature na subcooling haimaanishi automatically model prediction ni invalid, lakini inaweza kufanya coefficients kugawanywa sensitively among variables na kuwa unstable on new data. Kwa hiyo primary use ya model ni approximate prediction ya k values under similar conditions, si independent physical interpretation.

Dokezo la Chanzo na Mbinu

Full original title: A Data-Driven Approach for Estimating an Experimentally Derived Kinetic Parameter in Methane Hydrate Growth

Author: Chinedu Charles Alamezie

Author order: Study has one author.

Equal first author au equal contribution: None.

Corresponding author: Chinedu Charles Alamezie

Institutional affiliation: School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, Scotland, United Kingdom

Corresponding-author email: ccalamezie@hotmail.com

ORCID: No ORCID information in uploaded version.

DOI:10.2139/ssrn.6944011

Journal: Not published in peer-reviewed journal.

Original journal publisher: None.

Publication platform: SSRN

Publication date: 15 June 2026

Page count: 33

Source type: Preprint research study containing secondary experimental-data analysis na regression modeling

Peer-review status: Study haijapitia peer review. Every page ya uploaded version inasema preprint is not peer reviewed.

Official link:Official SSRN preprint page

Makala hii ya Kiswahili imeandaliwa kwa kuchunguza text ya uploaded study, equations, four main figures, supplementary residual plot, six tables, correlation matrix, random-forest importance values, seven regression equations, cross-validation results, Arrhenius comparison, conclusions na recommendations.

External sources zilitumika only kwa bibliographic verification ya author name, institution, SSRN publication date, DOI, page count na official link. Hakuna new result kutoka external sources iliyoongezwa kwenye scientific findings za study.

Main limitations ni small single-source dataset, strong correlations among variables, lack of independent external validation, absence ya repeated au nested cross-validation, no uncertainty estimates for regression coefficients, na predicted parameter combining thermodynamic and transfer effects rather than representing pure intrinsic kinetics. Model inapaswa kuonekana si kama general law replacing physical hydrate-growth equations, bali kama transparent dataset-specific surrogate model inayoweza kutumika under similar experimental conditions.