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    Abstract Esterification of adipic acid and oleyl alcohol in a solvent-free system featuring a stirred tank reactor containing commercially immobilized Candida antarcticalipase B was performed. The process was carried out using an artificial neural network (ANN) trained by the Levenberg-Marquardt (LM) algorithm. The effects of four operative variables, temperature, time, amount of enzyme,and impeller speed, on the reaction yield were studied. By examining different ANN configurations, the best network was found to consist of seven hidden nodes using a hyperbolic tangent sigmoid transfer function. The values of the coefficient of determination (R ) and root mean squared error (RMSE) between the actual and predicted responses were determined to be 1 and 0.0058178 for training and 0.99467 and 0.622540 for the testing datasets,respectively. These results imply that the developed model was capable of predicting the esterification yield. 23602
    The operative variables affected the yield, and their order of contribution was as follows: time > amount of enzyme >temperature > impeller speed. A high percentage of yield
    (95.7%) was obtained using a low level of enzyme (2.5%
    w/w), and the temperature, time, and impeller speed were
    66.5°C, 354 min (about 6 h), and 500 rpm, respectively. A
    simple protocol for efficient substrate conversion in a
    solvent-free system evidenced by high enzyme stability is
    indicative of successful ester synthesis.
    Keywords: lipase, adipate ester, artificial neural network,
    stirred tank reactor, optimization
    1. Introduction
    Esters of adipic acid are a broad and perse family of
    synthetic lubricants that can be used in automotive and
    industrial oil applications either as sole basestocks or as
    blendstocks with other functional fluids. Excellent tribo-
    logical properties, low volatility, high flash point, shear
    stability, and high viscosity index are some of the advant-
    ages offered by these high performance lubricants [1].
    While stable against oxidative and thermal breakdown,
    adipate esters are highly biodegradable and thus environ-
    mentally friendly. Adipates are also widely used in other
    applications such as plasticizers, food packaging, paint
    strippers, perfumes, cosmetics, and coatings [1,2]. The
    simplest and most direct route for the synthesis of adipate
    esters is reaction of adipic acid and a monohydric alcohol
    in the presence of an acid catalyst [3].
    Chemical synthesis of adipate esters poses some dis-
    advantages such as high temperature, prolonged reaction
    period, corrosion of equipment, formation of byproducts,and high pollution [4].
     
    Use of enzymes as biocatalysts for
    preparation of these high-value-added esters can overcome
    such drawbacks. Enzymatic synthesis of adipate ester in
    the presence of organic solvent has been previously report-
    ed [2,5]. However, solvent toxicity, high cost due to low
    productivity, and costly downstream processing including
    evaporation and recycling of the solvent are some of the
    problems inherent in solvent-based systems [6]. So far,
    there have been few studies on the enzymatic synthesis of
    adipate esters in a solvent-free system.
    One of the most important stages in any biotechno-
    logical process is optimization of the reaction conditions
    without increasing the cost [7]. Due to the nonlinear beha-
    vior and complicated structure of biochemical processes, it
    is always difficult to predict the effects of independent
    variables on the reaction yield. The sensitivity of enzymes
    in response to variables may potentially increase the com-
    plexity of models. Most classic statistical methods require
    screening for effective parameters and a unimodel objec-
    tive function [8].
    In recent years, application of artificial neural networks
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