JP4038587B2 - Suspension evaluation equipment - Google Patents

Description

ここで，Ｓ_vは粒子比表面積，kはKozeny定数である。したがって，濾材抵抗をＲ_fとすると，濾過の基本式は次式となる。
【００２５】
【式２】

濾液量νの時点でできているケークの厚さＬは，ｗを濾液1ｍ³あたりの粒子質量とすると，粒子の物質収支より，
【００２６】
【式３】

充填率Φの平均は，次式で定義される。
【００２７】
【式４】

Eq.(4)をEq.(3)に代入すると，
【００２８】
【式５】

ここで，Eq.(5)にｗ＝φ₀ρ_p／(1-φ₀)を代入すると次式を得る。ただし，φ₀はスラリー初期濃度である。
【００２９】
【式６】

となる。これをEq.(2)に代入し，
【式７】

と仮定すると，次の濾過速度式を得る。
【００３０】
【式８】

【００３１】
dt/dvの増減を調べるため，dt/dvを全微分して整理すると，次式を得る。
【００３２】
【式９】

【００３３】
ここで，νとΦ(1-Φ)(Φ-φ₀)は常に正であるが，2Φ²+(1-φ₀)Φ-2φ₀は図２に示すように負の値をとり得る。したがってd²t/dν²は｛2Φ²+(1-φ₀)Φ-2φ₀｝dΦ/dν＜0でかつ次式を満たすとき負となり，dt/dνはνの増加に対して減少する。
【００３４】
【式１０】

Eq.(9)はdΦ/dν＞0でもdΦ/dν＜0でも，dt/dνはνの増加に対して減少しうることを示している。
【００３５】
２．速度式によるデータの解析
Eq.(7)を用いてνとdt/dνの実験データからΦを計算すると，図３に示すように2つの解が得られる．そこで濾液量νに対してケーク内粒子体積LΦをプロットすると図４となる。スラリー初期高さをL₀とすると，常にLΦ≦L₀φ₀でなければならない。本実験ではL₀=20mm，φ₀=0.35であるから，常にLΦ≦L₀φ₀を満足しているのはL₂Φ₂であることがわかる。またL₁Φ₁≦L₀φ₀を満たす領域でも，粒子体積の半減（ケークがスラリーに戻る）が起こり，現実に考えられない結果となっている。
【００３６】
正しい値であるΦ₂に対しては，図２に示すように常に2Φ²+(1-φ₀)Φ-2φ₀>0であるので，濾過速度が大きくなるときには，dΦ/dν<0すなわち濾過の進行に伴い平均ケーク充填率は下がることを示している。
【００３７】
３．ルース（Ruth）式との比較
次に，ケーク内の濾液量を無視した，
【式１１】

とした，Ruth式で考えてみる。Ruth式は次式で与えられる。
【００３８】
【式１２】

dt/dνを全微分して整理し，次式を得る。
【００３９】
【式１３】

ここで，空隙率関数Φ(1-Φ)^-3および(1+2Φ)/(1-Φ)は，0<Φ<1に対して常に正であるので，d²t/dν²が負になり濾過の進行に伴い濾過速度が増大するためには，dΦ/dν<0すなわち濾過の進行に伴い平均ケーク充填率は下がることを示しており，Eq.(7)から得られた結果と同じ結果となる。
【００４０】
Eq.(11) を用いてνとdt/dνの実験データからΦを算出し，図５でEq.(7)から得られた結果と比較した。図から明らかなとおり，傾向は一致しているがΦの値はかなり異なっている。そこでケーク内濾液量と絞り出された濾液量を，図６で比較してみる。図から明らかなとおりケーク内には絞り出された液量の30%以上の濾液が含まれており，Ruth式で仮定されている
【式１４】

が成立していないことがわかる。
【００４１】
４．結論
ケーク内の濾液量を考慮した濾過速度式を導出し，その速度式により濾過の進行に伴う平均ケーク充填率の変化を算出できることを明らかにした。濾過の進行過程の解析が可能になったことにより，粒子間相互作用がケーク形成機構に及ぼす影響について，議論が可能になった。高濃度スラリーにRuth式を適用すると，平均ケーク充填率は高めに算出されることが明らかとなった。
【００４２】
＜実験的考察＞
１．使用装置、及びプログラム
次に、アルミナスラリーを用いた濾過実験を行った。濾過装置及び解析用プログラムのアルゴリズムを図７〜図１０に示した。まず、図７および図８を参照しつつ、成形体の製造装置とコンピュータ１０の構成について説明する。
【００４３】
製造装置には、懸濁液２を貯留する懸濁液貯留空間１Ａを備えた濾過器１と、この濾過器１に設けられる濾材３とが設けられている。また濾過器１の下端部において、濾材３の裏面側には、濾材３を通過して濾過器１の外部に流出する濾液５の流出用チューブ４が設けられている。また、流出用チューブ４の下方には、容器６が設けられており、この容器６は、測定機としての電子天秤７の測定部位７Ａの上面に載置されている。
【００４４】
濾過の開始に先だって、容器６の内部には予め所定量の液体５が溜められている。更に、流出用チューブ４の内部には、液体５が満たされており、流出口４Ａは容器６内の液体５に接触されている。こうしておけば、濾過器１中の懸濁液２と電子天秤７によって重量を測定される液体５とが連続した状態となっているので、濾液量の時間変化を濾過開始時点から連続的に測定することができる。また、流出用チューブ４の流出口４Ａは、竹槍状に斜めに切り落とされており、チューブ内への空気の進入を規制すると共に、濾液が速やかに下方の液体５と接触できるようになっている。
【００４５】
また、懸濁液貯留空間１Ａに圧力を加える加圧装置８が設けられている。加圧装置８はコンプレッサーであり、この加圧装置８と濾過器１とには、加圧用管９が接続されている。
次に、図８を参照しつつ、記録装置としてのコンピュータ１０の構成について説明する。コンピュータ１０には、ＲＯＭ及びＲＡＭを備えた中央情報処理装置（ＣＰＵ）１２と、ＣＰＵ１２と外部との間で信号の授受を行うＩ／Ｏポート１６とが設けられている。また、Ｉ／Ｏポート１６を介して接続される周辺機器として、ディスプレイ１３、プリンタ１４、キーボード及びマウス１５が設けられている。更に、所定のプログラム及びデータの読み書きを行うハードディスク１７と、プログラム等が書き込まれたＣＤ−ＲＯＭ１８などが設けられている。
【００４６】
次に、図９及び図１０を参照しつつ、コンピュータ１０によって実行可能なプログラムについて説明する。
図９は、電子天秤からのデータを取り込む手順を示すフローチャートである。プログラムをスタートさせたら、まず初期値（データ取り込みを行う所定の時間間隔と、濾過終了時間に関するデータを含むもの）を入力する（Ｓ９０）。
【００４７】
次に、所定の時間間隔が経過したか否かを判定する（Ｓ１００）。本実施形態では、加圧濾過開始後から極めて短い時間後（例えば、２秒後）から、所定の時間間隔（例えば、５秒間）ごとに、濾過開始後の時間と、その時間における濾液量とを一組としたデータを取り込み始める。所定時間が経過したら、データを取り込み（Ｓ１１０）、濾過終了時間に至ったか否かを判定する（Ｓ１２０）。濾過終了時間に至っていない場合には、ステップ１００に戻り、所定の時間毎にデータの取り込み（Ｓ１１０）を行う。また、濾過終了時間に至ったら、プログラムを終了する。
【００４８】
次に、図１０を参照しつつ、濾過開始後の時間と濾液量とが一組となった複数組のデータ列からケークの充填率を求めるプログラムのフローチャートについて説明する。まず、基礎となる理論式（例えば、ルースの式(Eq.(10))、濾過の基本式(Eq.(2))、或いは、本発明者が開発した式(Eq.(7)、Eq.(2-14)、Eq.(2-142)、Eq.(2-15)など）を設定する（Ｓ２００）。次に、その理論式に必要となるパラメータ値及び、許容誤差値Ｄ０を入力する（Ｓ２１０）。なお、誤差値Ｄとは、理論式とデータ列との間の誤差を評価する値であり、例えば各データにおける誤差（理論式における値とデータとの差）を二乗して加え合わせたものを用いることができる。また、許容誤差値Ｄ０とは、繰り返し計算の繰り返しを終了するために、予め設定する値である。
【００４９】
次に、データ列を入力し（Ｓ２２０）、理論式とデータ列との間の誤差値Ｄを計算する（Ｓ２３０）。ここで、誤差値Ｄと許容誤差値Ｄ０との大小を比較し（Ｓ２４０）、誤差値Ｄが許容誤差値Ｄ０よりも大きいときには、パラメータ値を変更した後に（Ｓ２５０）、ステップ２３０に戻る。一方、ステップ２４０において、誤差値Ｄが許容誤差値Ｄ０以下であれば、そのときのパラメータ値を利用してケークの充填率を計算する（Ｓ２６０）。
なお、上記のプログラムは、例えばコンピュータ読み取り可能な記録媒体であるＣＤ−ＲＯＭなどに記録させておくことができる。
【００５０】
２．実験方法
実験には濃度35vol%(φ₀=0.35)のアルミナスラリーを使用した．アルミナ粒子は易焼結アルミナ（住友化学製，AES-11E），分散剤はポリアクリル酸アンモニウム(東亞合成，A-30SL)，分散媒は蒸留水を使用し，分散剤の添加量は0.16，0.24，0.36，0.6g/100g-aluminaとした。粒子の体積基準の比表面積は2.39x10⁷m^-1、真密度は3.98x10³kg・m^-3であった。分散剤濃度は希薄であるため，媒液の粘度，密度はそれぞれ10^-3Pa・s，10³kg・m^-3とした。所定の量の試料粉体と分散剤を蒸留水に入れ，ボールミルで1h撹拌し，10min間真空脱泡し20℃に保ってから濾過実験を行った。スラリーの見かけ粘度と分散剤吸着量を，B型粘度計（トキメック製，BL型）と全炭素量分析器（東レエンジニアリング，TOC-650）によりそれぞれ測定した。
【００５１】
定圧濾過実験は，内径35mmのアクリル製シリンダーに高さ20mmになるようにスラリーを注入し，圧縮空気を使用して濾過圧力100, 200, 300 kPaで行った。濾材にはセルロース混合エステルタイプのメンブランフィルター(アドバンテック東洋製，A020A047A)を使用した。濾材は焼結金属板の上に置き，変形を防いだ。濾液量は電子天秤により計測し，濾過開始１秒の時点から、所定の時間間隔（１秒毎）でパソコンに取り込んだ。
【００５２】
３．実験結果および考察
図１１に分散剤吸着量，図１２に見かけ粘度の測定結果を示した。
濾過圧力100 kPaと300 kPaの場合のRuthプロットを図１３及び図１４に示した。両図から明らかなとおり，100 kPaの場合は濾過開始直後に濾過速度が増大するのに対し，300 kPaの場合には濾過直後は濾過速度は遅くなり，しばらくしてから急激に濾過速度が増大する。なお、図に示していないが，200 kPaも同様の傾向を示し，著しい圧力依存性があることがわかる。
【００５３】
図１５及び図１６にケークの平均充填率変化を示した。図１５及び図１６の結果は図１３及び図１４の結果に対応しており、100 kPaの場合は濾過初期に極めて緻密なケークが形成され，ケークの成長とともにケーク充填率は下がっていった。それに対して300 kPa の場合は，濾過初期に形成されるケーク密度は100 kPa の場合ほど高くなく，しばらくして密度が増大しその後急激に減少した後，一定に近づいた。
【００５４】
図１７及び図１８にケーク厚さと平均充填率の関係を示した。最終充填率に及ぼす分散剤添加量の影響を見てみると，0.16gでは最終充填率が濾過圧力を上げても変わらないが，それ以上の添加量では濾過圧力に応じて充填率は増大していた。また100kPaでは0.16, 0.14g，300kPaでは0.16, 0.36gではケーク厚さによらず一定の充填率に近づくが，0.60gでは濾過の進行とともに充填率は増大していた。濾過圧力が300kPaで分散剤添加量の場合は，充填率分布を持つ層が薄いが，他の条件ではより厚い層で分布を持っていた。
【００５５】
４．考察
ケーク形成機構を論ずるには，データが少なく今後のさらなる実験が必要であるが， ケークが一様な充填率で積層されているのではないことがわかったことは，セラミックスの鋳込み成形プロセスを解析する上で重要である。濾過の初期に充填率が増大したり減少したりする現象の解明は今後の研究に待たれるが，考えなければならない因子は，外力である流体抗力とケークの降伏強度および体積粘性のような圧縮変形速度であると思われる。これらの因子により濾過ケーク形成機構が解明されれば，分散剤添加量などによって変化する粒子間相互作用が濾過ケーク形成機構に及ぼす影響を定量的に可能となり，定圧濾過試験は新たなスラリー評価技術として威力を発揮することが期待される。
【００５６】
５．結論
本発明者が新しく導出した濾過速度式が，濾過ケーク形成過程を解析するのに有効であることを実験により確かめ，定圧濾過試験が新たなスラリー評価手法として有効であることを示した。
【００５７】
＜他の理論式＞
上記の解析結果と実験事実より，dt/dνがνの増加に対して減少しうるのは，dΦ/dν<0の場合のみであることがわかった。
しかし，厚さl₁で充填率φ₁のケークの場合，dt/dνは次式で与えられる。
【００５８】
【式１５】

このケークの上に新たに厚さl₂で充填率φ₂(<φ₁)ケークが形成すると，
【００５９】
【式１６】

【００６０】
【式１７】

したがって，ケークが積層していく限り，dΦ/dν<0は起こり得るが，dt/dνがνの増加に対して減少することはあり得ない。
【００６１】
では，なぜ「理論」Eq.(7)から解が得られたのであろうか。
Eq.(7)の前提はケークは積層するのではなく，新たに均質な充填率Φのケークが形成されるとしている。すなわち既に形成されているケークは，Φに膨張するかスラリー化して新たに充填率Φの均質なケークを形成するかである。したがって，Eq.(7)の前提は数式的にはあり得ても，現実にはあり得ない。
そこで、ろ過速度式の基礎式K-Z式から考察する。
【００６２】
【式１８】

【００６３】
上記の基礎式では，ろ液はケークの上部で絞り出され，絞り出されたろ液がケークをdν/dt速度で透過するとしている。この前提がある限り，上述のように，dΦ/dν<0は起こり得るが，dt/dνがνの増加に対して減少することはあり得ない。
しかし，ケークの最下部で絞り出しが起きれば，dt/dνがνの増加に対して減少することはあり得るかもしれない。
【００６４】
濃度φ₀のスラリーに圧力Pをかけたら，高さl₀'のスラリーが充填率φ₁で高さl₁のケークに一様に収縮した。
【００６５】
【式１９】

ケーク内の高さlにおけるdν/dtは，
【００６６】
【式２０】

ケークの圧力損失は、
【００６７】
【式２１】

【００６８】
【式２２】

【００６９】
次に，高さl₁'(<l₁)のスラリーが充填率φ₂で高さl₂のケークに一様に収縮したとすると，
【００７０】
【式２３】

よって，
【００７１】
【式２４】

dt/dνがνの増加に対して減少するためには，
【００７２】
【式２５】

でなければならない。Eq.(2-5)より，
【００７３】
【式２６】

また、Eq.(2-10)が成立するためには，
【００７４】
【式２７】

【００７５】
【式２８】

φ₂>φ₁>φ₀より
【００７６】
【式２９】

よって，Eq.(2-13)は成立する。
【００７７】
P=100kPaの場合
図２０に示すように，ろ過直後から図１９に示すモデルでケークの形成が行われるため，LΦの値は減少する。φ_i=φ_∞となると，順次φ_i-1→φ_∞，φ_i-2→φ_∞，φ_i-3→φ_∞，…とケーク上部でろ液は絞り出され，LΦの値は増大しdt/dνは増大に転ずる。
【００７８】
P=300kPaの場合
φ₀より少し大きな充填率のケークが成長しLΦは増大する。あるところで図１９に示す挙動が一気に起こり，図２１のL₂Φ₂のラインまでLΦは減少し，その後上部にケークが形成される。
【００７９】
計算手順
P=100kPaの場合
Eq.(2-9)を Eq.(2-5)を使って書き換えると，
【００８０】
【式３０】

で，実験より
【００８１】
【式３１】

となる。これをEq.(2-14)に代入すると、
【００８２】
【式３２】

となる。したがってφ₁,φ₂,φ₃,…とl₁,l₂,l₃,…を順次決定できる。
【図面の簡単な説明】
【図１】 高濃度スラリーの定圧濾過において、濾過のごく初期段階に濾液量の増加と共に濾過速度が増加する現象を示すグラフである。
【図２】 ケークの充填率と2Φ²+(1-φ₀)Φ-2φ₀の値との関係を示すグラフである。
【図３】 濾液量とケークの充填率との関係を示すグラフである。
【図４】 濾液量とケーク内粒子体積との関係を示すグラフである。
【図５】 濾液量とケークの充填率との関係を示すグラフであり、ルース式と本発明者が開発した式との比較を示すものである。
【図６】 濾液量とケーク内濾液量との関係を示すグラフである。
【図７】 本実施形態の濾過装置とコンピュータとを示す図である。
【図８】 コンピュータの構成図である。
【図９】 濾過液量を取り込むときのプログラムの流れ図である。
【図１０】 ケークの充填率を計算するプログラムの流れ図である。
【図１１】 分散剤と吸着量との関係を示すグラフである。
【図１２】 分散剤と見かけ粘度との関係を示すグラフである。
【図１３】 濾過圧力100kPaにおけるルースプロットを示すグラフである。
【図１４】 濾過圧力300kPaにおけるルースプロットを示すグラフである。
【図１５】 濾過圧力100kPaにおける濾液量とケークの充填率との関係を示すグラフである。
【図１６】 濾過圧力300kPaにおける濾液量とケークの充填率との関係を示すグラフである。
【図１７】 濾過圧力100kPaにおけるケークの充填率と厚さとの関係を示すグラフである。
【図１８】 濾過圧力300kPaにおけるケークの充填率と厚さとの関係を示すグラフである。
【図１９】 ケーク形成の様子を示すモデル図である。
【図２０】 濾過圧力100kPaにおける濾液量とケーク内粒子体積との関係を示すグラフである。
【図２１】 濾過圧力300kPaにおける濾液量とケーク内粒子体積との関係を示すグラフである。
【符号の説明】
１…濾過器
１Ａ…懸濁液貯留空間
２…懸濁液
３…濾材
４…流出用チューブ
４Ａ…流出開口
５…濾液
７…電子天秤（測定機）
８…加圧装置
１０…コンピュータ（記録装置）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a suspension evaluation method, a program for executing the method, and an evaluation apparatus thereof.
[0002]
[Prior art]
Generally, it is known to filter a liquid in which insoluble particles are suspended using a filter medium. This filtration process is used in many industries, such as casting molding, fine ceramic molding, coating film, sludge wrinkles, and the like.
[0003]
In the filtration process, trial and error, so-called craftsmanship, occupies a large weight. This is because the dynamic change of the suspension cannot be grasped during the filtration process. Relying on the operator's intuition in this way is not preferable because it increases the efficiency of filtration.
[0004]
[Problems to be solved by the invention]
The present invention has been made in view of the above-described circumstances, and its purpose is to propose a theory in the process of filtration and to provide a method for evaluating a suspension to be filtered based on the theory. With the goal.
[0005]
[Means for solving the problems, operation of the invention, and effect of the invention]
As a result of intensive studies to achieve the above object, the present inventor has found that the relationship between the filtrate and the filtration time immediately after the start of filtration has a great influence on the properties of the cake. It came to complete.
[0006]
The present inventor has been diligently examining the filtration process, and has obtained the following knowledge. That is, according to the Ruth equation, which is a general filtration analysis method, the amount of filtrate (v) and the inverse of the flow rate of the filtrate (dt / dv) are directly proportional to each other. It will be close. According to this Ruth equation, it is sufficient if at least the filtration start point and the final point are known. Conventionally, in addition to these two time points, intermediate two or three time points are added to obtain a straight line on the graph. Was estimating the necessary parameters.
[0007]
However, the present inventor tried to set the filtrate and the filtration time immediately after pressurization in order to perform a more detailed analysis of the filtration process, and as shown in FIG. In a very short time immediately after that, he found a measurement point (convex friction) that deviates from the loose equation. According to the analysis of the present inventor, as the filtration process progresses, the filtrate is squeezed out from the “softer cake” generated in the initial stage of filtration, so that a measurement point deviating from the loose equation is generated. It was considered a thing.
[0008]
In order to detect this friction, the amount of filtrate is measured at small time intervals immediately after the start of filtration.
In order to improve the efficiency of filtration, it is preferable to pressurize the filtrate. Here, “pressurization” means applying pressure to the suspension to make it higher than the external pressure, and the method is not limited. Examples include pressurization by gravity, pressurization by a compressor such as a compressor, and pressurization by centrifugal force, but are not limited thereto. The filtration efficiency can also be improved by sucking the filtrate.
[0009]
“Immediately after the start of filtration” means the shortest possible time from the start of filtration. For example, in the Ruth equation, as described above, a straight line can be drawn if there are at least two points of data, so data at many points in time has not been required. There was no need to measure.
[0010]
“Immediately after” means 10 minutes after the start of filtration, preferably 5 minutes, more preferably 2 minutes, more preferably 1 minute, more preferably 30 seconds, more preferably 10 seconds, most preferably It means one second later.
[0011]
“Small time interval” means an interval that is short enough to measure a change in the amount of filtrate in a short time immediately after the start of filtration. As described above, in the conventional filtration method, the measurement interval of the filtrate amount is extremely long (for example, an interval of several minutes to several tens of minutes) because it is based on the Ruth equation. For this reason, the novel knowledge of the present inventors, that is, the knowledge that the characteristics of the liquid to be filtered (suspension) can be evaluated from the state of the cake (that is, the change in the filtrate amount) within a very short time immediately after the start of filtration. I couldn't find a headline. For this reason, a small time interval is any interval between about 1 millisecond and about several minutes, preferably any interval between about 1 millisecond and about 1 minute, more preferably about 1 millisecond to about 1 minute. Any interval between 30 seconds, more preferably any interval between about 1 millisecond and about 10 seconds, more preferably any interval between about 1 millisecond and about 5 seconds, most preferably about 1 Set to any interval between milliseconds and about 2 seconds.
[0012]
The “filtrate amount” means a numerical value indicating the properties of the filtrate by mass, weight or volume, and among these numerical values, it is preferable to measure the mass of the filtrate.
[0013]
In addition, as an analysis method of data (a data obtained by combining a time after the start of filtration and a filtrate amount at that time), for example, a basic expression of filtration, a loose expression, an expression developed by the present inventor (each method) This will be described later in detail). However, the main point of the present invention is that the amount of filtrate is measured at a small time interval immediately after the start of filtration, and there is no great difference depending on the analysis method.
[0014]
A second invention includes a filter having a suspension storage space for storing a suspension to be filtered and a filter medium, a measuring instrument for measuring the amount of filtrate passing through the filter medium and flowing outside, An apparatus for manufacturing a molded body, comprising: a recording device that records measurement values measured by a measuring machine at predetermined intervals.
[0015]
In the production apparatus of the present invention, the amount of filtrate that has flowed out after passing through the filter medium is measured, and the measured values are recorded at predetermined intervals, so that the time after the start of filtration and the amount of filtrate are a set of data. Can be obtained continuously. By analyzing this data set, it is possible to obtain numerical values such as the filling rate of the molded body and to quantify the structure of the molded body.
[0016]
In addition, it is preferable to provide the pressurization apparatus which applies a pressure to suspension storage space in this apparatus further. However, when a general compressor is used as a pressurizing device, the present invention can be implemented by providing at least a manufacturing device (that is, a filter, a measuring machine, and a recording device) having the above-described configuration. Will.
[0017]
Moreover, as a measuring machine which measures the amount of filtrate, Preferably the weight measuring machine (balance) which measures the weight of a filtrate is used, More preferably, an electronic balance is used. In particular, in the measurement at a small time interval, since the amount of filtrate is often small, it is important to obtain the difference.
[0018]
Furthermore, when measuring the weight of the filtrate, it is continuous between the position where the filtrate flows out from the filter (that is, the back side of the filter medium) and the measurement site of the measuring instrument (in the case of an electronic balance, the top plate surface). It is preferable that it can be made into the state. That is, when the filtrate flows out from the filter and is measured after falling as a droplet, the weight of the droplet is measured discontinuously. For this reason, in the case of measurement at a small time interval, a value added intermittently by the weight of the droplet is measured, and it is difficult to measure a small change in weight. In order to satisfy the above requirements, for example, an outflow tube through which the filtrate flows out to the back surface side of the filter medium and a container that can be stored in the measurement site of the measuring machine can be provided. A predetermined amount of liquid is stored in advance in such a container, and the outlet is brought into contact with the liquid in the container while the liquid is present inside the outflow tube. Then, since the suspension in the filter and the liquid on the measuring device side are in a continuous state, the time change of the filtrate amount can be continuously measured.
[0019]
The third invention is a program for analyzing a plurality of sets of data strings in which the time after the start of filtration and the amount of filtrate are one set, and obtaining a cake filling rate by a computer,
(1) calculating an error value between the plurality of sets of data strings and the theoretical formula after setting an appropriate parameter value as an initial value in a predetermined theoretical formula having one or a plurality of parameters;
(2) Until the error value is equal to or less than a preset allowable error value,
(I) appropriately changing the parameter value; and (ii) calculating an error value between the plurality of sets of data strings and the theoretical formula;
(3) A step of calculating a filling rate of the cake from the final parameter value is provided.
[0020]
In the above invention, examples of the predetermined theoretical formula include a basic formula for filtration, a loose formula, and a formula developed by the present inventor (each formula will be described in detail later).
Further, before the step (1), (4) a step of fetching a plurality of sets of data strings in which the time after the start of filtration and the amount of the filtrate become one set can be provided. In such a program, a series of operations can be performed from taking in the data string to calculating the cake filling rate.
[0021]
According to the present invention, the cake filling rate can be obtained from a plurality of sets of data strings in which the time after the start of filtration and the amount of filtrate are a set.
The above-described problem can also be solved by a computer-readable recording medium that records the program described in the third invention.
It is also possible to process the data sequence of the elapsed time of filtration and the amount of filtration and output it by drawing FIG. 1, FIG. 3, FIG. 4, FIG. The operator can also evaluate the suspension by visually judging the results of these figures.
[0022]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described in detail with reference to the drawings. However, the technical scope of the present invention is not limited by the following embodiments, and various changes can be made without changing the gist thereof. It can be carried out with modification. Further, the technical scope of the present invention extends to an equivalent range.
[0023]
First, the theoretical consideration of each equation capable of performing cake analysis will be described in detail.
<Theoretical considerations>
1. Derivation of filtration rate formula
In general, a cake having a thickness L having a distribution of the filling factor φ in the thickness direction is considered. If the flow rate when a fluid of viscosity μ is passed through this cake with pressure P is dv / dt, this relationship is expressed by the Kozeny-Carman equation, and this cake has a thickness with a filling rate Φ and no filling rate distribution. Lq cake can be replaced by Eq. (1).
[0024]
[Formula 1]

Where S _v Is the particle specific surface area, and k is the Kozeny constant. Therefore, filter media resistance is R _f Then, the basic equation for filtration is
[0025]
[Formula 2]

The thickness L of the cake made at the time point of the filtrate amount ν is the w of 1m of filtrate. ^Three Per particle mass, from the mass balance of particles,
[0026]
[Formula 3]

The average of the filling rate Φ is defined by the following equation.
[0027]
[Formula 4]

Substituting Eq. (4) into Eq. (3),
[0028]
[Formula 5]

Here, Eq. (5) includes w = φ ₀ ρ _p / (1-φ ₀ Substituting), we get However, φ ₀ Is the initial slurry concentration.
[0029]
[Formula 6]

It becomes. Substituting this into Eq. (2),
[Formula 7]

Assuming that, the following filtration rate equation is obtained.
[0030]
[Formula 8]

[0031]
In order to investigate the increase / decrease in dt / dv, the following equation is obtained when dt / dv is fully differentiated and arranged.
[0032]
[Formula 9]

[0033]
Where ν and Φ (1-Φ) (Φ-φ ₀ ) Is always positive, but 2Φ ² + (1-φ ₀ ) Φ-2φ ₀ Can take a negative value as shown in FIG. Therefore d ² t / dν ² Is {2Φ ² + (1-φ ₀ ) Φ-2φ ₀ } It becomes negative when dΦ / dν <0 and the following equation is satisfied, and dt / dν decreases with increasing ν.
[0034]
[Formula 10]

Eq. (9) shows that dt / dν can decrease with increasing ν regardless of dΦ / dν> 0 or dΦ / dν <0.
[0035]
2. Analyzing data using velocity equations
Using Eq. (7) to calculate Φ from experimental data of ν and dt / dν, two solutions are obtained as shown in Fig. 3. Therefore, FIG. 4 is a plot of the particle volume LΦ in the cake against the filtrate amount ν. Slurry initial height L ₀ Then LΦ ≦ L ₀ φ ₀ Must. In this experiment, L ₀ = 20mm, φ ₀ = 0.35, so LΦ ≦ L ₀ φ ₀ L is satisfied ₂ Φ ₂ It can be seen that it is. L ₁ Φ ₁ ≦ L ₀ φ ₀ Even in the region that satisfies the conditions, the particle volume is halved (the cake returns to the slurry), which is an unthinkable result.
[0036]
Φ is the correct value ₂ Is always 2Φ as shown in Fig. 2. ² + (1-φ ₀ ) Φ-2φ ₀ > 0, so when the filtration rate increases, dΦ / dν <0, that is, the average cake filling rate decreases with the progress of filtration.
[0037]
3. Comparison with Ruth formula
Next, the amount of filtrate in the cake was ignored.
[Formula 11]

Consider the Ruth formula. The Ruth equation is given by
[0038]
[Formula 12]

dt / dν is fully differentiated and arranged to obtain the following equation.
[0039]
[Formula 13]

Where porosity function Φ (1-Φ) ^-3 And (1 + 2Φ) / (1-Φ) is 0 <Φ D is always positive for <1 ² t / dν ² In order for the filtration rate to increase as filtration proceeds and dΦ / dν <0, that is, the average cake filling rate decreases with the progress of filtration, which is the same as the result obtained from Eq. (7).
[0040]
Using Eq. (11), Φ was calculated from the experimental data of ν and dt / dν, and compared with the result obtained from Eq. (7) in FIG. As is clear from the figure, the trends are consistent, but the values of Φ are quite different. Therefore, the amount of filtrate in the cake and the amount of filtrate squeezed out are compared in FIG. As is clear from the figure, the cake contains more than 30% of the squeezed liquid, which is assumed by the Ruth equation.
[Formula 14]

It can be seen that is not established.
[0041]
4). Conclusion
It was clarified that the change rate of the average cake filling rate with the progress of filtration can be calculated by deriving the filtration rate equation considering the amount of filtrate in the cake. It became possible to discuss the influence of interparticle interactions on the cake formation mechanism by enabling analysis of the process of filtration. When the Ruth equation was applied to high-concentration slurry, it was found that the average cake filling rate was calculated higher.
[0042]
<Experimental considerations>
1. Device used and program
Next, a filtration experiment using an alumina slurry was performed. The filtering device and the analysis program algorithm are shown in FIGS. First, the structure of the molded body manufacturing apparatus and the computer 10 will be described with reference to FIGS.
[0043]
The manufacturing apparatus is provided with a filter 1 having a suspension storage space 1 </ b> A for storing the suspension 2, and a filter medium 3 provided in the filter 1. At the lower end of the filter 1, an outflow tube 4 for the filtrate 5 that passes through the filter medium 3 and flows out of the filter 1 is provided on the back side of the filter medium 3. A container 6 is provided below the outflow tube 4, and this container 6 is placed on the upper surface of a measurement site 7A of an electronic balance 7 as a measuring machine.
[0044]
Prior to the start of filtration, a predetermined amount of liquid 5 is stored in the container 6 in advance. Further, the inside of the outflow tube 4 is filled with the liquid 5, and the outlet 4 </ b> A is in contact with the liquid 5 in the container 6. In this way, since the suspension 2 in the filter 1 and the liquid 5 whose weight is measured by the electronic balance 7 are in a continuous state, the time change of the filtrate amount is continuously measured from the start of filtration. can do. Further, the outlet 4A of the outflow tube 4 is cut off obliquely in a bamboo basket shape so as to restrict the ingress of air into the tube and the filtrate can quickly come into contact with the lower liquid 5. .
[0045]
Further, a pressurizing device 8 that applies pressure to the suspension storage space 1A is provided. The pressurizing device 8 is a compressor, and a pressurizing tube 9 is connected to the pressurizing device 8 and the filter 1.
Next, the configuration of the computer 10 as a recording apparatus will be described with reference to FIG. The computer 10 is provided with a central information processing device (CPU) 12 having a ROM and a RAM, and an I / O port 16 for exchanging signals between the CPU 12 and the outside. Further, a display 13, a printer 14, a keyboard and a mouse 15 are provided as peripheral devices connected via the I / O port 16. Further, a hard disk 17 for reading and writing predetermined programs and data, a CD-ROM 18 on which programs and the like are written, and the like are provided.
[0046]
Next, programs that can be executed by the computer 10 will be described with reference to FIGS. 9 and 10.
FIG. 9 is a flowchart showing a procedure for fetching data from the electronic balance. When the program is started, first, initial values (including a predetermined time interval for taking in data and data relating to the filtration end time) are input (S90).
[0047]
Next, it is determined whether a predetermined time interval has passed (S100). In this embodiment, after a very short time (for example, 2 seconds) after the start of pressure filtration, the time after the start of filtration, and the amount of filtrate at that time, every predetermined time interval (for example, 5 seconds). Start importing a set of data. When the predetermined time has elapsed, data is fetched (S110), and it is determined whether or not the filtration end time has been reached (S120). If the filtration end time has not been reached, the process returns to step 100, and data is taken in every predetermined time (S110). When the end time of filtration is reached, the program is terminated.
[0048]
Next, a flowchart of a program for obtaining the cake filling rate from a plurality of sets of data strings in which the time after the start of filtration and the amount of filtrate become one set will be described with reference to FIG. First, the basic theoretical formula (for example, the loose formula (Eq. (10)), the basic formula for filtration (Eq. (2)), or the formula developed by the present inventors (Eq. (7), Eq (2-14), Eq. (2-142), Eq. (2-15), etc.) (S200) Next, the parameter value and the allowable error value D0 required for the theoretical equation are set. (S210) The error value D is a value for evaluating the error between the theoretical formula and the data string, and for example, the error in each data (the difference between the value in the theoretical formula and the data) is squared. In addition, the allowable error value D0 is a value set in advance in order to end the repeated calculation.
[0049]
Next, a data string is input (S220), and an error value D between the theoretical formula and the data string is calculated (S230). Here, the difference between the error value D and the allowable error value D0 is compared (S240). If the error value D is larger than the allowable error value D0, the parameter value is changed (S250), and the process returns to step 230. On the other hand, if the error value D is equal to or smaller than the allowable error value D0 in step 240, the cake filling rate is calculated using the parameter value at that time (S260).
The above program can be recorded on a CD-ROM, which is a computer-readable recording medium, for example.
[0050]
2. experimental method
In the experiment, a concentration of 35 vol% (φ ₀ = 0.35) alumina slurry was used. Alumina particles are easily sintered alumina (Sumitomo Chemical Co., AES-11E), the dispersant is ammonium polyacrylate (Toagosei, A-30SL), the dispersion medium is distilled water, and the amount of dispersant added is 0.16. 0.24, 0.36, 0.6 g / 100 g-alumina. The specific volume surface area of the particles is 2.39x10 ⁷ m ^-1 True density is 3.98x10 ^Three kg ・ m ^-3 Met. Since the dispersant concentration is dilute, the viscosity and density of the liquid medium are 10 ^-3 Pa · s, 10 ^Three kg ・ m ^-3 It was. A predetermined amount of the sample powder and dispersant were placed in distilled water, stirred for 1 h with a ball mill, vacuum degassed for 10 min and kept at 20 ° C, and then a filtration experiment was conducted. The apparent viscosity and the amount of dispersant adsorbed on the slurry were measured with a B-type viscometer (manufactured by Tokimec, BL type) and a total carbon analyzer (Toray Engineering, TOC-650).
[0051]
The constant pressure filtration experiment was performed at a filtration pressure of 100, 200, and 300 kPa using compressed air by injecting slurry into an acrylic cylinder with an inner diameter of 35 mm to a height of 20 mm. A cellulose mixed ester type membrane filter (manufactured by Advantech Toyo, A020A047A) was used as the filter medium. The filter medium was placed on a sintered metal plate to prevent deformation. The amount of filtrate was measured with an electronic balance, and was taken into a personal computer at predetermined time intervals (every 1 second) from the point of 1 second after the start of filtration.
[0052]
3. Experimental results and discussion
FIG. 11 shows the results of measuring the dispersant adsorption amount, and FIG. 12 shows the apparent viscosity.
Ruth plots at filtration pressures of 100 kPa and 300 kPa are shown in FIGS. As is clear from both figures, the filtration rate increases immediately after the start of filtration at 100 kPa, whereas the filtration rate decreases immediately after filtration at 300 kPa, and increases rapidly after a while. To do. Although not shown in the figure, it can be seen that 200 kPa shows the same tendency and has a significant pressure dependence.
[0053]
15 and 16 show changes in the average filling rate of the cake. The results of FIGS. 15 and 16 correspond to the results of FIGS. 13 and 14. In the case of 100 kPa, a very dense cake was formed at the initial stage of filtration, and the cake filling rate decreased with the growth of the cake. On the other hand, at 300 kPa, the cake density formed at the beginning of filtration was not as high as at 100 kPa, and after a while the density increased and then decreased rapidly and then approached a constant level.
[0054]
17 and 18 show the relationship between the cake thickness and the average filling rate. Looking at the effect of the dispersant addition amount on the final filling rate, the final filling rate does not change even when the filtration pressure is increased at 0.16 g, but at higher addition amounts, the filling rate increases with the filtration pressure. It was. In 100kPa, 0.16, 0.14g and 300kPa, 0.16, 0.36g approached a constant filling rate regardless of the cake thickness, but at 0.60g, the filling rate increased with the progress of filtration. When the filtration pressure was 300 kPa and the dispersant was added, the layer with the filling rate distribution was thin, but under other conditions, the thicker layer had the distribution.
[0055]
4). Consideration
Discussing the mechanism of cake formation requires less data and further experiments in the future. However, the fact that the cake is not laminated at a uniform filling rate is an analysis of the ceramic casting process. It is important to do. Elucidation of the phenomenon in which the filling rate increases or decreases in the early stages of filtration is awaited for further research, but factors that must be considered are compression forces such as external forces such as fluid drag, cake yield strength, and volume viscosity. It seems to be deformation speed. If the formation mechanism of the filter cake is elucidated by these factors, it will be possible to quantitatively determine the effect of the interaction between particles, which varies depending on the amount of dispersant added, on the formation mechanism of the filter cake. The constant pressure filtration test is a new slurry evaluation technology. It is expected to demonstrate its power as.
[0056]
5. Conclusion
The present inventors have confirmed by experiment that the newly derived filtration rate equation is effective for analyzing the filtration cake formation process, and showed that the constant pressure filtration test is effective as a new slurry evaluation method.
[0057]
<Other theoretical formulas>
From the above analysis results and experimental facts, the fact that dt / dν can decrease with increasing ν is dΦ / dν It turns out that it is only when <0.
But thickness l ₁ Fill rate φ ₁ In this case, dt / dν is given by
[0058]
[Formula 15]

New thickness on top of this cake ₂ Fill rate φ ₂ ( <φ ₁ When the cake is formed,
[0059]
[Formula 16]

[0060]
[Formula 17]

Therefore, as long as the cakes are stacked, dΦ / dν <0 can occur, but dt / dν cannot decrease with increasing ν.
[0061]
Then why was the solution obtained from "theory" Eq. (7)?
The premise of Eq. (7) is that the cake is not laminated, but a new cake with a uniform filling rate Φ is formed. That is, the cake that has already been formed is expanded to Φ or slurried to newly form a homogeneous cake having a filling rate Φ. Therefore, the assumption of Eq. (7) is mathematically possible but not in reality.
Therefore, we will consider the basic formula KZ formula for filtration rate.
[0062]
[Formula 18]

[0063]
In the above basic equation, the filtrate is squeezed out at the top of the cake, and the squeezed filtrate permeates the cake at the dν / dt rate. As long as this assumption is made, as described above, dΦ / dν <0 can occur, but dt / dν cannot decrease with increasing ν.
However, if squeezing occurs at the bottom of the cake, dt / dν may decrease with increasing ν.
[0064]
Concentration φ ₀ When pressure P is applied to the slurry, the height l ₀ 'Slurry fill factor φ ₁ At height l ₁ Shrink uniformly into the cake.
[0065]
[Formula 19]

Dν / dt at height l in the cake is
[0066]
[Formula 20]

Cake pressure loss is
[0067]
[Formula 21]

[0068]
[Formula 22]

[0069]
Next, the height l ₁ '( <l ₁ ) Slurry is filling rate φ ₂ At height l ₂ If the cake shrinks uniformly to
[0070]
[Formula 23]

Therefore,
[0071]
[Formula 24]

In order for dt / dν to decrease with increasing ν,
[0072]
[Formula 25]

Must. From Eq. (2-5)
[0073]
[Formula 26]

For Eq. (2-10) to hold,
[0074]
[Formula 27]

[0075]
[Formula 28]

φ ₂ > φ ₁ > φ ₀ Than
[0076]
[Formula 29]

Therefore, Eq. (2-13) holds.
[0077]
When P = 100kPa
As shown in FIG. 20, the cake is formed with the model shown in FIG. φ _i = φ _∞ Then, φ _i-1 → φ _∞ , Φ _i-2 → φ _∞ , Φ _i-3 → φ _∞ The filtrate is squeezed out at the top of the cake, the value of LΦ increases and dt / dν starts to increase.
[0078]
When P = 300kPa
φ ₀ A cake with a slightly higher filling rate grows and LΦ increases. At a certain point, the behavior shown in FIG. ₂ Φ ₂ LΦ decreases to the line, and then a cake is formed at the top.
[0079]
Calculation procedure
When P = 100kPa
If Eq. (2-9) is rewritten using Eq. (2-5),
[0080]
[Formula 30]

From the experiment
[0081]
[Formula 31]

It becomes. Substituting this into Eq. (2-14),
[0082]
[Formula 32]

It becomes. Therefore φ ₁ , φ ₂ , φ _Three , ... and l ₁ , l ₂ , l _Three , ... can be determined sequentially.
[Brief description of the drawings]
FIG. 1 is a graph showing a phenomenon in which filtration rate increases with increase in the amount of filtrate at the very initial stage of filtration in constant pressure filtration of a high concentration slurry.
[Figure 2] Cake filling rate and 2Φ ² + (1-φ ₀ ) Φ-2φ ₀ It is a graph which shows the relationship with the value of.
FIG. 3 is a graph showing the relationship between the filtrate amount and the cake filling rate.
FIG. 4 is a graph showing the relationship between the filtrate amount and the particle volume in the cake.
FIG. 5 is a graph showing the relationship between the filtrate amount and the cake filling rate, and shows a comparison between the loose equation and the equation developed by the present inventors.
FIG. 6 is a graph showing the relationship between the amount of filtrate and the amount of filtrate in the cake.
FIG. 7 is a diagram illustrating a filtration device and a computer according to the present embodiment.
FIG. 8 is a configuration diagram of a computer.
FIG. 9 is a flowchart of a program for taking in a filtrate amount.
FIG. 10 is a flowchart of a program for calculating a cake filling rate.
FIG. 11 is a graph showing the relationship between the dispersant and the amount of adsorption.
FIG. 12 is a graph showing the relationship between the dispersant and the apparent viscosity.
FIG. 13 is a graph showing a loose plot at a filtration pressure of 100 kPa.
FIG. 14 is a graph showing a loose plot at a filtration pressure of 300 kPa.
FIG. 15 is a graph showing the relationship between the filtrate amount and the cake filling rate at a filtration pressure of 100 kPa.
FIG. 16 is a graph showing the relationship between the filtrate amount and the cake filling rate at a filtration pressure of 300 kPa.
FIG. 17 is a graph showing the relationship between cake filling rate and thickness at a filtration pressure of 100 kPa.
FIG. 18 is a graph showing the relationship between cake filling rate and thickness at a filtration pressure of 300 kPa.
FIG. 19 is a model diagram showing a state of cake formation.
FIG. 20 is a graph showing the relationship between the amount of filtrate and the volume of particles in the cake at a filtration pressure of 100 kPa.
FIG. 21 is a graph showing the relationship between the filtrate amount and the particle volume in the cake at a filtration pressure of 300 kPa.
[Explanation of symbols]
1 ... Filter
1A: Suspension storage space
2 ... Suspension
3 Filter media
4 ... Outflow tube
4A ... Outflow opening
5 ... Filtrate
7 ... Electronic balance (measuring machine)
8 ... Pressure device
10. Computer (recording device)

Claims (1)

A filter having a suspension storage space for storing a suspension to be filtered and a filter medium , an electronic balance that is a measuring machine for measuring the amount of filtrate that passes through the filter medium and flows out to the outside, and the measuring machine A suspension evaluation device comprising: a recording device that records measurement values measured at a predetermined interval; and a pressurization device that pressurizes the suspension storage space, wherein the suspension evaluation device includes: The suspension is characterized in that an outflow tube through which the filtrate flows out is provided, and the tip of the outflow tube is brought into contact with a liquid stored in advance in a container provided at a measurement site of the measuring machine. Liquid evaluation device.

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