Mathematical models of anaerobic digestion for the treatment of swine
                  effluents

Fagundes, Daisa Stéfano; Orrico Junior, Marco Antonio Previdelli; Orrico, Ana Carolina Amorim; Seno, Leonardo Oliveira

doi:10.1590/1983-40632015v4531052

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Pesquisa Agropecuária Tropical

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Biosystems Engineering • Pesqui. Agropecu. Trop. 45 (2) • Apr-Jun 2015 • https://doi.org/10.1590/1983-40632015v4531052 copy

Mathematical models of anaerobic digestion for the treatment of swine effluents¹ 1 Manuscript received in Jul./2014 and accepted for publication in Apr./2015 (http://dx.doi.org/10.1590/1983-40632015v4531052).

Modelos matemáticos da biodigestão anaeróbia para o tratamento de efluentes de suínos

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Pig breeding results in the production of large amounts of waste, which can cause serious environmental problems, when handled incorrectly. This study aimed at testing mathematical models to estimate the parameters of anaerobic biodigestion in biodigesters as a function of the composition of swine effluents with and without separation of the solid fraction and hydraulic retention times (HRT). Semi-continuous biodigesters fed with swine effluents with and without separation of the solid fraction and managed for 15, 22, 29 and 36 days of hydraulic retention were used. The potential of biogas and methane production, as well as the reduction of total solids, volatile solids and chemical oxygen demand, were assessed as a function of the effluents composition. HRT was the variable that most influenced the variation of the models, followed by the contents of total and volatile solids. Uni and multivariate models presented high confidence indices, being classified as “great” at predicting the potentials of biogas and methane production and “good” at predicting the reductions of total solids, volatile solids and chemical oxygen demand. The models obtained in this study can be used to reliably predict the parameters of the anaerobic biodigestion process of swine effluents in semi-continuous tubular biodigesters.

KEY-WORDS:
Methane; biodigester; biogas

Variable	Min	Max	MV	SD
TS (%)	1.23	2.20	1.74	0.38
N (% in TS)	3.03	4.41	3.77	0.34
P (% in TS)	3.25	5.64	4.14	0.56
VS (%)	1.09	1.98	1.21	0.68
K (% in TS)	4.72	9.17	7.07	1.39
CH4 (%)	63.10	75.90	69.65	4.27
CH₄ VSadd (L/ kg VSadd)	448.12	1,160.00	760.47	250.12
TSR⁴ (%)	47.24	76.19	63.56	6.76
VSR (%)	50.44	80.04	68.85	6.89
CODR (%)	57.66	82.55	69.19	7.75

Variable	HRT	TS	N	P	VS	K	CH₄	CH₄sva	TSR	VSR	CODR
HRT	-	ns	ns	ns	ns	ns	0.45^ p < 0.01;	0.47^ p < 0.01;	0.39^* * p < 0.05;	0.40^* * p < 0.05;	0 71^* ***** p < 0.001.
TS	-	-	0.65^* ***** p < 0.001.	0.67^* ***** p < 0.001.	0 92^* ***** p < 0.001.	-0.42^* * p < 0.05;	-0.77^* ***** p < 0.001.	-0.75^* ***** p < 0.001.	0.56^* ***** p < 0.001.	0.37^* * p < 0.05;	0.56^* ***** p < 0.001.
N	-	-	-	0.52^ p < 0.01;	0.77^* ***** p < 0.001.	ns	-0.60^* ***** p < 0.001.	0.55^ p < 0.01;	ns	ns	ns
P	-	-	-	-	0.79^* ***** p < 0.001.	ns	-0.79^* ***** p < 0.001.	-0.80^* ***** p < 0.001.	ns	ns	ns
VS	-	-	-	-	-	ns	_-0 78^* ***** p < 0.001.	-0.75^* ***** p < 0.001.	0.49^* * p < 0.05;	ns	0.50^ p < 0.01;
K	-	-	-	-	-	-	0.36^* * p < 0.05;	0.40^* * p < 0.05;	ns	ns	ns
CH₄	-	-	-	-	-	-	-	0.98^* ***** p < 0.001.	ns	ns	ns
CH₄sva	-	-	-	-	-	-	-	-	ns	ns	ns
TSR	-	-	-	-	-	-	-	-	-	0.96^* ***** p < 0.001.	0.61^ p < 0.01;
VSR	-	-	-	-	-	-	-	-	-	-	0.48^ p < 0.01;
CODR	-	-	-	-	-	-	-	-	-	-	-

Model	R₂	RMSE	aic	p	Index d	r	Index c	Performance
Univariate
CH₄ = 59.80 + 0.24 * HRT	0.91	0.59	12.74	< 0.001	0.98	0.96	0.93	Great
CH₄ = 67.10 - 0.62 * TS	0.00	2.01	24.39	0.121	0.06	0.05	0.00	Very poor
CH₄ = 68.36 - 0.64 * N	0.01	2.00	24.39	0.151	0.10	0.09	0.01	Very poor
CH₄ = 77.69 - 2.61 * P	0.35	1.62	19.44	0.010	0.70	0.59	0.42	Poor
CH₄ = 67.10 - 0.69 * VS	0.00	2.01	26.35	0.232	0.06	0.05	0.00	Very poor
CH₄ = 68.91 - 0.48 * K	0.06	1.95	25.37	0,213	0.35	0.25	0.09	Very poor
Multivariate
CH₄ = 57.62 + 0.24 * HRT + 7590.12 * TS - 8443.02 * VS	0.94	0.50	23.80	< 0.001	0.98	0.97	0.95	Great
Univariate
CH₄ VSadd = 327.81 + 8.46 * HRT	0.89	23.68	105.27	< 0.001	0.97	0.94	0.91	Great
CH₄ VSadd = 556.02 - 6.06 * TS	0.00	70.30	138.09	0.198	0.02	0.01	0.00	Very poor
CH₄ VSadd = 582.54 - 9.87 * N	0.00	70.25	138.09	0.291	0.01	0.04	0.00	Very poor
CH₄ VSadd = 951.40 - 89.64 * P	0.34	57.11	133.44	0.050	0.01	0.58	0.00	Very poor
CH₄ VSadd = 556.04 - 6.69 * VS	0.00	70.30	138.09	0.346	0.02	0.01	0.00	Very poor
CH₄ VSadd = 646.52 - 15.99 * K	0.05	68.33	138.09	0,289	0.34	0.23	0.08	Very poor
Multivariate
CH₄ VSadd = 327.81 + 8.46*HRT	0.90	22.23	105.27	< 0.001	0.97	0.95	0.92	Great

Model	R²	RMSE	AIC	p	Index d	r	Index c	Performance
Univariate
CODR = 51.77 + 0.87 * HRT	0.90	2.26	30.11	< 0.001	0.97	0.95	0.92	Great
CODR = 67.15 + 3.29 * TS	0.00	7.17	65.11	0.213	0.10	0.07	0.01	Very poor
CODR = 69.45 + 1.15 * N	0.00	7.18	65.11	0.349	0.05	0.04	0.00	Very poor
CODR = 113.14 - 8.60 * P	0.30	6.01	61.40	0.049	0.65	0.55	0.35	Very poor
CODR = 67.15 + 3.66 * VS	0.00	7.17	65.11	0.123	0.10	0.07	0.01	Very poor
CODR = 91.74 - 2.75 * K	0.15	7.22	64.36	0.055	0.52	0.40	0.21	Very poor
Multivariate
CODR = 40.03 + 1.01 * HRT + 3.57 * P - 1.32 * K	0.91	2.32	35.90	< 0.001	0.98	0.95	0.93	Great

Model	R²	RMSE	AIC	p	Index d	r	Index c	Performance
Univariate
CH₄ = 69.44 + 0.16 * HRT	0.83	0.56	14.45	< 0.001	0.95	0.91	0.87	Great
CH₄ = 73.39 + 0.07 * TS	0.00	1.36	13.92	0.143	0.01	0.01	0.00	Very poor
CH₄ = 83.43 - 2.78 * N	0.29	1.14	8.44	0.040	0.64	0.54	0.34	Very poor
CH₄ = 78.74 - 1.41 * P	0.08	1.31	11.92	0.087	0.36	0.28	0.10	Very poor
CH₄ = 75.03 - 2.79 * VS	0.01	1.35	11.92	0.102	0.15	0.12	0.02	Very poor
CH₄ = 73.00 + 0.06 * K	0.00	1.36	13.86	0.213	0.08	0.06	0.00	Very poor
Multivariate
CH₄ = 73.58 + 0.14 * TRH - 1.06 * N	0.88	0.47	16.15	< 0.001	0.97	0.94	0.91	Great
Univariate
CH₄ VSadd = 513.75 + 18.18 * HRT	0.91	43.29	124.57	< 0.001	0.98	0.96	0.93	Great
CH₄ VSadd = 1028.07 - 36.43 * TS	0.00	148.65	164.05	0.112	0.05	0.03	0.00	Very poor
CH₄ VSadd = 1450.72 - 123.63 * N	0.08	112.96	154.55	0.078	0.00	0.41	0.00	Very poor
CH₄ VSadd = 1182.18 - 38.05 * P	0.02	68.94	137.84	0,096	0.00	0.15	0.00	Very poor
CH₄ VSadd = 1009.70 + 54.62 * VS	0.00	69.67	139.08	0,127	0.08	0.04	0.00	Very poor
CH„ VSadd = 986.42 + 6.94 * K	0.02	69.10	137.84	0,0945	0.21	0.14	0.03	Very poor
Multivariate
CH₄ VSadd = 513.75 + 18.18 * HRT	0.92	40.58	124.57	< 0.001	0.98	0.96	0.94	Great

Model	R²	RMSE	AIC	p	Index d	r	Index c	Performance
Univariate
TSR = 46.60 + 0.56 * HRT	0.45	4.82	54.31	0.039	0.78	0.67	0.52	Fair
TSR = 24.89 + 25.82 * TS	0.34	5.28	57.28	0.045	0.70	0.58	0.41	Poor
TSR = 96.99 - 10.12 * N	0.17	5.92	60.90	0.056	0.52	0.41	0.21	Very poor
TSR = 87.99 - 7.28 * P	0.10	6.17	62.24	0.067	0.41	0.31	0.13	Very poor
TSR = 61.16 - 2.35 * VS	0.00	4.08	47.01	0.189	0.05	0.03	0.00	Very poor
TSR = 57.60 + 0.63 * K	0.04	3.99	47.01	0.098	0.29	0.21	0.06	Very poor
Multivariate
TSR= 10.70 + 0.56 * HRT + 25.82 * TS	0.81	2.80	41.10	< 0.001	0.95	0.90	0.85	Very good
Univariate
VSR = 51.38 + 0.62 * HRT	0.56	4.30	50.71	0.012	0.84	0.75	0.63	Medium
VSR= 36.88 + 21.90 * TS	0.24	5.68	59.57	0.051	0.62	0.49	0.30	Very poor
VSR = 104.28 - 10.33 * N	0.17	5.92	60.90	0.076	0.53	0.42	0.22	Very poor
VSR = 96.00 - 7.67 * P	0.11	6.16	62.18	0.089	0.44	0.33	0.14	Very poor
VSR = 67.70 - 2.37 * VS	0.00	4.06	46.89	0.234	0.05	0.03	0.00	Very poor
VSR = 64.66 + 0.56 * K	0.03	3.99	46.89	0.078	0.26	0.19	0.05	Very poor
Multivariate
VSR = 20.94 + 0.62 * HRT + 21.90 * TS	0.83	2.71	39.84	< 0.001	0.95	0.90	0.86	Great

Model	R²	RMSE	AIC	p	Index d	r	Index c	Performance
Univariate
CODR = 54.52 + 0.40 * HRT	0.63	2.38	31.82	0.001	0.87	0.80	0.70	Good
CODR = 51.86 + 9.28 * TS	0.12	3.70	45.91	0.089	0.45	0.34	0.15	Very poor
CODR = 84.17 - 5.42 * N	0.13	3.68	45.66	0.077	0.45	0.36	0.16	Very poor
CODR = 91.53 - 7.34 * P	0.42	2.37	31.66	0.045	0.78	0.65	0.51	Fair
CODR = 73.83 - 17.60 * VS	0.11	2.95	38.51	0.084	0.45	0.33	0.15	Very poor
CODR = 61.31 + 0.36 * K	0.02	3.09	38.51	0.098	0.23	0.16	0.03	Very poor
Multivariate
CODR = 56.43 + 0.38 * HRT + 7.85 * TS + 2.24 * N - 5.43 * P	0.89	1.33	20.29	< 0.001	0.97	0.94	0.91	Great

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[TFN01] TS = total solids; N = nitrogen; P = phosphorus; VS = volatile solids; K = potassium; CH₄ = % methane; CH₄ VSadd = methane production per kg of added VS; TSR = total solid reduction; VSR = volatile solid reduction; CODR = chemical oxygen demand reduction.

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Mathematical models of anaerobic digestion for the treatment of swine effluents1 1 Manuscript received in Jul./2014 and accepted for publication in Apr./2015 (http://dx.doi.org/10.1590/1983-40632015v4531052).

Modelos matemáticos da biodigestão anaeróbia para o tratamento de efluentes de suínos

ABSTRACT

Mathematical models of anaerobic digestion for the treatment of swine effluents¹ 1 Manuscript received in Jul./2014 and accepted for publication in Apr./2015 (http://dx.doi.org/10.1590/1983-40632015v4531052).