Authors: Shiqi Xu | Chengyang Fan | Peijian Song | Chuanyou Liu
Source: Frontiers in Chemical Engineering (article, 2022-12-15)
Field: Chemistry — Analytical Chemistry

Prediction of wax deposit thickness in waxy crude oil pipelines using improved GM(1,1) model In this paper, the GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>arccos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation and GM(1,1) model with function transformation are established by using arccosine function transformation method and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mi>arccos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> function transformation method, and the GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation is established by using function transformation theory, and GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation is established by using translational transformation theory on the basis of this model. The prediction accuracy of GM(1,1) model, GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mi>arccos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation, GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mi>arccos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> transformation, GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation, and GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation are compared by modeling with the field pipeline data and the indoor loop data. The influence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m9"><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:math> value in GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m10"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mi>arccos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> transformation on prediction accuracy is discussed, and the influence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m11"><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:math> value in GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m12"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation on prediction accuracy is discussed. With the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m13"><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m14"><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:math> values, the average relative error show a trend of decreasing and then increasing, by comparing the average relative errors under different <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m15"><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m16"><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:math> values, the optimal a value and c value and the optimal prediction accuracy are obtained. The results show that the GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m17"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation in the indoor loop has an average relative error of 0.6490% when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m18"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.114</mml:mn></mml:mrow></mml:math> , which is the minimum average relative error compared to other models and achieves the highest prediction accuracy. The GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m19"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation in the field pipeline has an average relative error of 1.94156% when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m20"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>0.555</mml:mn></mml:mrow></mml:math> , which is the minimum average relative error compared to other models and achieves the highest prediction accuracy. Among the five models, only the GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m21"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation has fitted and predicted values that are closer to the actual thickness values in the indoor loop experimental data and the field pipeline data, and the predicted values are more consistent with the actual conditions in the field pipeline. This paper verifies the feasibility of using the GM(1,1) model with function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m22"><mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math> transformation to predict the wax deposition thickness of the pipe wall, and provides a reference for subsequent research on accurate prediction of wax deposition thickness. Algorithm ; Computer science Petroleum Processing and Analysis ; Computational Drug Discovery Methods