Awesome before we begin this morning looking into the message I want to just update you on something that we do every single year at about this time It's that time of year where we are beginning to prepare for big give How many of you have been a part of the big give before and years past most of you So big give if you're unaware of it is every year at the holiday seasons we give back locally and we give back globally To the different ministries that we support and locally we primarily partner with a underprivileged underserved public school and bless the kids in that public school. We've done this for many many years and At the end of November we always receive what's called the big give offering That's above and beyond our ties and our offerings that goes towards these big give endeavors This year we have three things that we are going to be giving to we just wanted to announce them to you One is the global partner that we are going to be partnering with this year is Brother Abraham in India once again, so we're very very excited about that. We are going to build another Christian school in India that is going to be used to reach Hindu students and introduce them to the gospel through Education and so I talked to Abraham on Wednesday needs the best early. I need India I need radiant to help India again. I said, we're your man. We're there. So we're gonna we're gonna do that. So that's global The other thing that we are doing is we are partnering locally with another school and this year It's a KPS Magnus school spring Valley elementary school in parchment Which busses kids in from Edison Northside kind of all over it is a school that has over 94% of its students are on government assistance or Government lunch programs and it's really really an underserved School and I went there Jane and I went there on the first day of school this year to welcome all the students in because we knew that We were gonna be serving that school and these kids are incredible. They're bright. They're sharp. They're beautiful The teachers are passionate. They have incredible leadership. Now what we have done over the last six years Is we've gotten into a pattern of providing cold weather gear coats hats boots and gloves We buy it all we go in and do a big thing in the school We let the kids pick out their own stuff and the reason why we did that is about seven years ago. We asked KPS Tell them the zoo public schools. How can we solve a problem? What's one major problem that you have and they said we have kids that don't have coats and stuff like that So we said we're gonna solve that problem. Well, guess what we did and this year The school that we're partnering with said look, we need some coats We need some gloves and some hats, but primarily our kids are good on that But we've got all kinds of other needs that are really gonna help these kids grow learn have a positive experience That radiant could really help us out now our first response was well, we do coats. That's what we do So if you don't like coats, I don't know. We got coats But then the Lord just reminded us the issue is not about what we want to give the issues what they need and So the school said what we really need is we need several things we need we do need some cold weather gear So we said check we're gonna take care of that.  Selflessly and we're so grateful for that, but what we're talking about the school needs these sensory items. They need some kits of school supplies for these kids to be able to take home on weekends and actually do their homework they They have some reading incentive clubs and some programs that need funding and then like some awards some different things and Some tools for the teachers. We've got a whole list that they gave to us and so this year We said, you know what? We're gonna take care of all that and so we've got we've got a whole list of things that that school would Never be able to get that we're gonna take care of a hundred percent and so we're very excited about that and then and Then the other piece of the big give is we always get to go into the school and we get to do a big Day with the students, but because we're not doing the coats We're not doing that, but what we asked the school is hey How could we help in that way and they said you know most of these kids? Don't get field trips because that's one of the first thing that gets cut out of these budgets They don't get field trips educational field trips and we said what if we what if radiant we're to partner with you and After the first of the year we plan a really cool field trip for these kids and we'll come along and we'll be Chaperones and kind of integrate with them and they said oh, we'd love that. Where do you want to go? So here's what we've done. We just rented out the air zoo and we're gonna take all these kids to the air zoo and I'm just gonna bless them we just want to love them We just want them to know that Jesus loves them and we want to be the hands and the heart of God extent So that's local And then the third thing that you already know about is we're believing and part of the big give offering is Going to go towards helping us finish out our prayer room in downtown that we purchased and now we're renovating listen guys this last week We've already had a couple of miracles of things HVAC units that have been donated and I mean God's just already doing some cool things We're gonna need some help to finish it out though And so that we're ready to go after the first of the year downtown Praying and lifting up the name of Jesus from the heart of the city. So all of that's kind of the big gift On the weekend of November 23rd and 24th is gonna be our big give offering and we wanted you to know We want you to begin praying right now Many of you already have and on that day and then even after that you're gonna be able to give towards those those Initiatives turn with me in your Bibles this morning to Ephesians Chapter 6 Ephesians chapter 6 this is part 10 of the battle it's part 2 Teaching about the armor of God now next weekend is going to be the the culmination of this series called the battle and It's a message. You're not gonna want to miss. I've been waiting for this message I'm gonna talk about the return of the Lord as the culmination of the battle and You're not gonna want to miss it. It's it's something I've had written and prepared since August And I keep going Lord. Do I get to preach this? He's like no not yet No, not yet. No, not yet And so when I when I decided and figured out that next weekend is gonna be the culmination He's like now you get to preach that and so it's gonna be like drinking out of a fire hydrant I've got 57 scriptures that I've got to deliver in 31 minutes So it's a good thing that we believe in the supernatural and the miraculous around here So pray with me. Okay Ephesians chapter 6 look at verse number 13 Paul writes therefore take up the whole armor of God that you might be able to withstand in The evil day and having done all to stand firm stand therefore having fastened on the belt of truth and having put on the breastplate of righteousness and As shoes for your feet having put on the readiness given by the gospel of peace and all Circumstances take up the shield of faith with which you can extinguish the flaming darts of the evil one And take the helmet of salvation and the sword of the spirit, which is the word of God Praying at all times in the spirit with all prayer and supplication Now as I've said every single weekend. I'll say it again. The Christian life is not like a battle the Christian life It is a battle. This is not a cruise ship. This is a battleship. We are not on a Carnival grounds or fairgrounds. We are on a battlefield and The the enemy that we are squaring off against in the battle the battle The battle for God's will to be done in our life the battle for his kingdom to come on earth as it is in heaven Verses the enemy having his way and he comes only to steal to kill and to destroy That battlefield Primarily is in the realm of our thinking. It's in the realm of our mind or will and our emotions and We're not facing off against flesh and blood people are not our enemy The Bible says that we do not war or battle against flesh and blood But we fight against principalities and powers and spiritual hosts of wickedness and heavenly places The the enemy of your soul is the liar the deceiver the tempter his name is Satan and his Angels his legions that are called demons It is a spiritual war But praise God that he is an inferior foe because we worship the great I am who is the one who was who is and who is to come and his holy angels and his saints that are praying By kingdom come that will be done on earth as it is in heaven and we are fighting in a battle not for victory But we are fighting from a position of victory already But we need to keep that in mind guys that people are not our enemy That even though that the enemy oftentimes will use people to get to us People represent what Jesus died on the cross to win most and so we've got to learn to see differently We've got to see the battlefield. We've got to identify who the enemy is and we have to know what our Weaponry is and as we've said over the last couple weekends, we have to put on the armor of God That's what Paul is communicating Put on the full armor of God in other words get dressed for battle and this armor that Paul Lists off for believers is indicative of what a Roman soldier would wear when he went into battle Now keep this in mind that when Paul is writing this he's most likely in prison And he's in prison for one reason. Did he steal somebody's car? No Did he cheat on his taxes? No Did he murder somebody? No He's in prison for one reason for preaching the gospel of Jesus in an environment and an empire that is hostile towards the gospel And he's imprisoned in he's imprisoned behind bars probably chained up He has a secretary who's writing for him this letter and he's trying to illustrate to Christians How we need to position ourselves to walk in God's will and God's victory in an environment where there's spiritual There's natural. There's relational implications that are causing difficulty And he looks up most likely and within close proximity to him. There is a Roman guard Who is dressed in the armor of a Roman centurion? Representing the most powerful military Force that the world is ever known when a Roman soldier or a legion of soldiers walked into a village or walked into a city They were the most intimidating thing that they had ever heard cobblestone roads with nails on the bottom of their boots Marching in formation clanging their sword into their shield Marching in perfect order with the authority of the most powerful person in the world behind them So Paul when he's trying to illustrate about you and I how we put on the armor of God He says put on the full armor of God put on the Belt of truth and we covered that ground the belt of truth that that Guards everything else the breastplate of righteousness Which is our position in Christ that he who knew no sin God the Father Made Jesus who knew no sin to be sinned for us so that we might become the righteousness of God in Jesus Christ and we arm ourselves with that truth that In Christ Jesus I am perfectly right before God that I have right standing before God not because I've earned it But because Jesus freely has given it and it protects my heart it protects the most vulnerable part of me So that when the enemy attacks, I'm protected because of my position in Christ I am belted or girded up by the belt of truth Not by lies not by public opinion not by what other people think not what my what my past says not by the whispers of the enemy but I am Girded and strengthened by the truth the name talks about the feet shod with the preparation of the gospel and That's so important. He says put on the boots in other words the boots of the Let's just the ESV says it funny I like the King James how many know sometimes you got to go old school and the King James is the most old school Translation of the Bible that you can find in English, but I love how it expresses some things sometimes It says having your feet shod with the preparation of the gospel of peace Try that office next time you see somebody's shoes that you like don't I love those shoes You're wearing go boy. You are shod with some excellent shoes You are shod well look at my wife's shods That's just sounds good, doesn't it Paul says have your feet shod Or put on the readiness that comes from the gospel of peace see a remand soldier when he put on boots They were shin guards all the way up to their knees went all the way down But on the bottom of the shoes were spikes or cleats and they serve two purposes When you were engaged in a battle remember Paul says stand firm Stand firm when you're facing an enemy stand firm Don't get pushed back a Roman soldier could anchor himself into the ground so that when a huge Infantry group were coming at them in a huge line. They could stand their ground and not be pushed back The other purpose was just like a professional athlete has cleats on the bottom of their shoes it gives them The ability to navigate or to move quickly in very muddy or slippery terrain So if you've ever seen a professional athlete make cuts like a football player makes a cut You're just like how did they do this because they got a cleat They're able to move and if you've ever watched somebody who didn't have cleats Trying to play a sport and the ground is wet. They slide. They slip all over the place So what is Paul saying? He says put on your feet or Spiritually put on your feet a sense of urgency that comes because of The fact that you're ready or you are prepared in the gospel That the gospel the power of the gospel actually gives you the ability to stand like pulses and first Corinthians 15 verse 58 he says therefore my beloved brother and be steadfast and immovable Always bounding in the work of the Lord knowing that in the Lord your labor is not in vain So he says be steadfast be immovable So when the enemy comes the gospel gives us immovability it anchors us and then there needs to be a sense of Urgency in a way that we live our lives navigating slippery terrain and circumstances through life because we're moving and we're being Driven by a sense of urgency that the gospel is not just for us, but it's for others We need to be passionate about the gospel church Some of us don't even know what the gospel is. I mean the gospel literally means good news It's good news. How many like good news as opposed to fake news or bad news Everybody loves to get good news when you get a letter from the IRS and it just says internal revenue service How many know that can be bad news? Until you open it up and it says hey, we charge you too much on your taxes So we're giving you more money back. How many know in that moment? That's good news Good news bad news the gospel the word gospel means good news And that's what we're supposed to focus on That we're supposed to be ready with the gospel number one The gospel is the power of God into salvation for us the gospel has saved us that we are sinners God is holy God could have judged us but instead of judging us as Jesus said He came into the world not to condemn the world But to save the world to rescue and to redeem us back to the father and we didn't he didn't do it by Giving us a checklist of things that we needed to do to be right with God God Jesus paid it all so that anyone who by faith believes in Jesus can be reconciled and be made right with God nobody's off limits Anybody can be saved do we believe that the gospel is good news for everybody? The other half of the room Hey, we're gonna do an altar call at the end of the service the gospel can work for you, too Listen if you've been saved to the bone and you know what it is to have been in darkness and God brought you into the light You know that it gives you standing before God and that's our solid foundation. It's in the gospel It's in the power of the gospel But then it should also move us and motivate us to want to share that good news with other people because the gospel is not just Some good news it is the greatest news of all time and if it saved you it can save other people You know one of the things I love about the the fact that These shoes that he's talking about had cleats is if you go and read Romans chapter 16 verse 20 It says this and the God of peace Will soon crush Satan underneath your feet I love that verse the God of peace Think about that. That's not a very peaceful thing To crush somebody under their your feet And the gospel it says that it's the gospel of peace the peace that it's talking about is the peace that we have with God The peace that we have with God Do you know that when you are without Christ you are actually an enemy of God that you are under judgment and under the wrath of God? Because we're sinners Because we're broken because we deserve judgment But then he opens the door through Jesus and says if anyone will step through this door You can find forgiveness you can be reconciled to God and in that moment that single act of Surrendering our life to Jesus and finding peace with God actually becomes a military movement of destroying the enemy and putting a Cleated foot on the head of the serpent and destroying him God says and the God of peace Will soon crush Satan under your feet. You know where the devil belongs. He doesn't belong in your head. He belongs under your feet You are victorious in Jesus Okay, now I want to talk to you about The shield of faith real quickly and then the last two which are The helmet of salvation and the sword of the spirit so the shield of faith Everybody knows a soldier when he goes out into battle. He takes a shield Roman soldier had a four foot by two foot shield It says so that you can extinguish the fiery darts of the enemy Arrows of the enemy if you've ever seen gladiator you notice from that era The way that a army would proceed against a foe Before they would send the infantry out they would Shoot catapult huge rocks bombs and then they would shoot fiery arrows From the archers ahead of time to take out as many of the soldiers as they could before it came down to hand-to-hand combat And so when Paul's using this reference of fiery darts It was a very powerful tool that especially the Germanic people used against Rome So they would take these arrows these archers and they could shoot them up to a half a mile in the air And when they came down they came down with a hundred pounds per square inch of force So you would hold your shield the shield was made of wood and hardened leather and sometimes even pieces of metal that were put on there in order to Block the fiery darts of the enemy and Paul says that the shield that you and I are to use against the fiery darts of the enemy is faith the shield of faith You ever thought about what the fiery darts are that come against you? I'll tell you what they are the devil by his very nature is an accuser and a slanderer That's what he does.  He says he was a liar He's the father of lies in other words by saying the father of lies. It means that all lies originate in Satan every lie Has its root in its genesis.  He is lies personified Just as much as Jesus doesn't know the truth. He is the truth So what does the enemy do his greatest tactic against the life of a believer is lies in accusations?   That's so faith. It's it's faith in God It's faith in what he has said, you know that there are some things listen that as a believer when you read God's word You're going to have to believe it even when it doesn't seem to be your experience The Bible says I'm forgiven. I don't feel forgiven by faith You know what the Bible says to be generous, so I don't want to be generous by faith The Bible says that I am the head and not the tail the above only and not beneath guess what? I don't feel above right now. I feel pretty below, but I'm gonna lift up the shield of faith It's what it's talking about extinguishing those flames of the enemy the other part of it that I think is so significant is a better Translation of shield of faith would be this faithfulness shield of faithfulness and It's not talking about your faithfulness. It's talking about God's faithfulness God's faithfulness church is like a shield for us Do you know that that second Timothy? I think it's chapter 2 or chapter 3. It says Something there it says that when we are faithless God remains faithful Anybody in this room ever been faithless before where you just it's like I'm having a hard time believing or I didn't keep my word Raise your hand if that's please then we'll shift into liars for all those If you've ever been faithless, how does the enemy remind you of your faithfulness He's like, oh, you really blew it there. How come you don't believe God? Come on. You should have done better But you know in that moment even when you're faithless when your arms feel tired in the middle of the battle It's when you can lift up the shield of his faithfulness His faithfulness listen to the the writer of the Psalm verse 28 verse 7 says the Lord is my strength and shield In him my heart trusts and I am helped It's his faithfulness Love the old him great is thy faithfulness Morning by morning new mercies. I see thou changes not thy compassions. They fail not as thou has been thou forever will be Great is thy faithfulness. We can rely on his faithfulness You see the world tells us if you if you want to be safe if you want to get by if you want to succeed You depend on yourself in the kingdom. We depend on him We depend on him. Okay now All that's introduction. So here we go. You ready for the real message? I'm kidding sort of okay So let me talk to you about the last two. These are I believe the most important of the pieces of armor It's all important, but these two last pieces a helmet of salvation and the sword of the spirit are where the rubber really hits the red because when Peter in First Peter chapter 4 when he's talking about armor He says that we're supposed to arm ourselves with the same way of thinking in other words Christ went through the cross. He suffered as a good soldier to save us He had a long view and he armed himself with a certain way of thinking that brought about victory and salvation When we talk about the helmet of salvation We're talking about the most pivotal piece of equipment For a Roman soldier because it protected their head and contrary to popular belief if you lose your head you can't fight anymore I mean you can lose an arm maybe and still you know swing.  He had huge prospects to go pro and then when I was probably up till 12 13 years old he played professional softball and so weekends that I would spend with my dad I would go on the road and kind of be the bat boy for his team He played for Budweiser he played for Miller High Life and a bunch of different teams played in the world series of softball slow pitch He was an amazing base baseball player or softball player and I wanted to be as good as dad My dad had this big equipment duffel bag and in that bag is where he carried all of his ball gloves his ball caps His bats his jackets.  This is back in the old days and and so and my dad also had a bag of Redman chewing tobacco in there which by the way one day I decided that must just be like chewing gum And so I put a whole bunch of my mouth chewed it and swallowed all the juice and I'm still sick. That was uh, that's 42 years ago.  There's a certain level of confidence That a winner of somebody who knows their victorious has when they go into competition or into battle And what I know for a lot of us as christians as followers of jesus We've become trained more by defeat in slavery Than we have by victory in christ and royalty We've been trained in a pattern of defeat compromise We know that when the enemy comes oh, I know I always cave into this temptation I know I always see myself that way or I'm defined by how many times I've messed up And we just kind of have an assumption much like a slave has who's been beaten over and over and over again That we just kind of learned to survive instead of thrive But a couple of things I want to highlight about this helmet of salvation number one Is it's called a helmet of salvation another word for salvation is victory A helmet of victory and it's it's it's not just salvation that we're saved and someday we'll go to heaven But as long as we're here on earth, we're probably going to be defeated and just struggle along No, it's a helmet of salvation that we put on now And it's a helmet of victory now And we put it on it's not our helmet look at verse number 11 in Ephesians chapter 6 Paul says to put on the whole armor of Whose armor is it? It's god's armor We're like the little boys truffling through his dad's bag pulling out his armor and saying Every time dad goes to battle He wins and so i'm putting his helmet of victory and his helmet of salvation on because here's what I know The god that you and I serve is undefeated. He's never lost a battle When god rouses himself to go into victory. He doesn't hope he's going to win. He is victory personified Listen to this scripture. I love this isaia 59. This is what paul is drawing from when he's talking about this helmet of salvation It says this it says he put this is god. He put on righteousness as a breastplate And a helmet of salvation on his head The best Hebrew translations of the old testament say he put on a helmet of victory So here's the picture That when god's people are in trouble in the old testament when the enemy comes to destroy them When the accuser comes to accuse them when they are downtrodden And they begin to pray to god and ask god for help it says that god is so passionate about his people He rouses himself up like a man of war and he straps on his armor of holiness and truth And he puts on a helmet of victory. How many know you got to be pretty good and pretty successful to call your helmet a helmet of victory There are some helmets when you see them walk into the field you go. Oh, that's a winner And there's some helmets when they walk out of the field you're just like Hmm When the patriots walk out on the field, I don't like the patriots Come on, right? Come on brother. I don't like the patriots. I don't like tom brady, but I respect him Because he's a threat. He's 42 years old And a guy can still bomb the ball. He's never tasted sugar a day in his life. I don't think Guys, he's a winner When he walks on that field you respect that helmet When the lions walk out on the field It's like whoa Hey, now listen. I rip on the lions.  Mary passes bad reffing calls terrible trades I mean they can change the uniforms all they want They can redesign the little line on the side of the helmet They can get a brand new football field, but what you can't change is the attitude of a winner I mean we all cringe in the fourth quarter, don't we? We will do it today. We will watch it and go.  And then when we win, we're like, whoa That was close Thank you. Look and here's what we all know We know that the day that the lions go to the super bowl We need to lift up our heads for our redemption draw at nine The eastern sky is gonna crack open Jesus and his holy angels will return Because the greatest prophetic sign anywhere is the lions going to the super bowl when that happens I don't care what's happening in israel when the lions go to the super bowl. We will know It's the difference between A helmet of victory And a helmet of Now the bible says that the helmet Is god's helmet That it says in isaia is a helmet of victory So here's what I want you to know when you put on the armor of god What is a helmet of salvation helmet is a attitude a mindset of victory That is rooted not in some Self-help self motivational deepak chopra new age optimism We're talking about a attitude and a mentality of victory that is so overwhelmingly Confident in the power of the cross and the resurrection And that every step that you are taking you are walking in partnership with god That his angels have been given charge over you that the steps of a righteous person are ordered and that the one who formed the worlds Formed you and your purpose before he even established the foundations of the world And that he who began a good work and you will be faithful to complete it until the day of the lord jesus It's an attitude It's where we see when we see the enemy we see we see victory. We don't see fear When the enemy comes against us, we're not relying on our own strength. It's a it's a mentality And we're putting on dad's helmet. We're putting on dad's hat because dad's a winner and when we put it on Let me tell you the other piece of it when you have on the whole armor of god Daily when you put on you say today i'm walking in truth today I'm holy and righteous because of what jesus accomplished today I have the shield of god's faithfulness and i'm believing in him today I have the helmet of salvation my mindset my attitude are correct when you put on the armor of god Think of a soldier with all of his armor on You don't know the person under the armor. You're just able to identify the armor If you're six foot four And you're in relatively good shape and you put a tom brady jersey on all of his equipment his pads and a helmet on You walk out people are just going to read the back of the jersey and go that's tom brady When you put on the armor of god And you come out into the battlefield the enemy doesn't see you and all your weakness He sees god and all of his strength Because you're wearing his armor Okay, last thing and i'm glad i had musicians to make it more dramatic Sword of the spirit This church is called a gladius This is the same sword that a roman soldier would have carried I know john brought out a broad sword An inferior sword This is an actual Style of gladius that a roman soldier Would have been skilled in and just as paul or whoever wrote hebrus chapter 4 verse 12 said the word of god is living and active And sharper than any two-edged sword When paul says take up the sword of the spirit Which is the word of god. He's talking about the only offensive Part of our weaponry You'll notice that all the armor cover the front side of a soldier And that's because we're not meant to retreat There's nothing to protect our back because we stand firm and we engage the enemy And we've been given one Tool one weapon Which is the word of god the sword of the spirit two-edged sword And oftentimes we limit our understanding of a two-edged sword By thinking that it's just the bible It's interesting that there are two greek words In the new testament i'm about to get nerdy with you for a second New testament was written in greek. There's two greek words that are used for word of god The first one is the word logos John chapter 1 it says in the beginning was the word logos and the word was with god and the word was god That's talking about jesus is the living logos the living Expression of all that god is he's the living word There is the written word of scripture that you and i have that is the greatest gift that god's ever given to humanity Other than jesus the living word This is god's Will and god's thoughts and god's truth written down for us. This is the logos But the word that paul uses in Ephesians 6 when he says the sword of the spirit Which is the word of god he doesn't use the word logos. He uses the word reyma Which means a fitly Spoken word From god in a given moment or situation So paul says the reyma word of god Why is the word of god that he's referring to a two-edged sword because there's two edges To make the word of god The weapon that defeats the enemy every single time the first one is the written word. We need the written word the written word The logos plus the spoken word reyma equals victory See two-edged sword one side is the written word the other side is god's Spoken word in every circumstance and situation In matthew chapter 4 verse 4 jesus is tempted By the enemy he's been fasting for 40 days And satan appears at his moment of weakness and he challenges his identity says if you are the son of god Turn these stones into bread Right And you might notice something that when satan comes to tempt jesus he does it by quoting the bible to him The enemy knows the bible better than you do probably Better than i do He says come on if you are the son of god Turn these stones into bread and jesus's reply is this he says It is written man does not live by bread alone But by every word that proceeds new king james From the mouth of god that word proceeds Is more than just every word that god has ever spoken Proceeds as a continual Sense meaning that it's a word that he's speaking now and he continues to speak how many know that god is always speaking to us His holy spirit is always speaking to us And what jesus said is the way that we live the way that we survive Is on what god is speaking to us in any given moment We need that proceeding word of god. We need both. We need the written word And we need the spoken word. Here's my experience. Here's how we end up wielding the sword of the spirit, which is a two-edged sword One side is the written word. The other side is the spoken word But you can't have Effectively the sharpness of the spoken word If you don't have a history in the written word Let me tell you that In almost every battle i've ever faced The enemy has come at me And his tool of choice is lies Because lies produce fear Lies produce discouragement Lies paralyze us So he'll always bring a lie The way that you defeat a lie, which is a sword is with the spirit of truth He's always come at me with a lie and here's how i've defeated those lies Since i was 14 years old every single day minus maybe a couple i've read Same pattern through the bible that my grandfather taught me i read three old testament chapters Three Psalms one proverb three new testament chapters 10 chapters Takes me 40 minutes And most of the time when i read the bible I don't have angels that show up in my living room going I've come to make an announcement It is not spiritual other than i'm spending time with god and i'm reading his word There's been a few Moments of encounter in my life where i've encountered the lord really powerfully in the middle of those moments Most of the time though it's reading and i'm taking it in because it's renewing my mind and here's what i'm doing I'm creating a database of the word of god in my heart To where i know the bible the reason i can stand up here and quote verses Isn't because i crammed all week it's because i've read these things over and over and over i've read the bible through four times a year for I don't know how many years and that's not a i'm just saying this is this is not This is not rocket science I've gotten it into my heart just like david said how shall a young man keep his ways pure before the lord He said your word. Oh lord. Have i hidden in my heart that i might not sin against you How does faith come faith comes by hearing and hearing by the word of god Receive with meekness the implanted word of god which is able to save your soul Be a doer of the word not just a hearer of the word only so you get the word in you And then when the enemy comes at you with a lie You're able to wield the sword of the spirit because the holy spirit who dwells in you is able to go To the file cabinet of your heart in your mind and he's able to recall Hey, remember this verse remember this story remember this truth And then i go to the written word and i reread it and then the holy spirit breathes fresh new life into a revelation for that moment And i stand on that and i begin to tell the lie Chink nope.  He is faithful. He is steadfast.  I already know too much Many of you know too much. You've gotten too much of it in you. You can't unknow what you know Now it's just a matter of letting that out and letting the armor of god completely envelop you I believe that god's called us to victory. He's called us to see like he sees He's called us to stand in his strength and in his mind and to put on the armor of god It's our responsibility and if we'll do that victory belongs to us Would you stand up with me this morning? Come on. That's good news. Isn't it church? It's good news I got fired up. I'm sorry. I'm I got swords and bibles up here. You just I mean that's a good day right there Would you just buy your heads with me this morning? Today, I want to ask you one question The question is this what Is the holy spirit speaking to you right now? What's he saying to you? You've heard what I've had to say you've heard what god's word says the written word But what's the rainbow? What's the holy spirit speaking to you today? For some of us it's courage Stand in the middle of the fight For some of us it's faith He's saying I'll be faithful to you No matter what For some of us it's provision. He's letting you know that Even though it seems like you're not going to have enough even though You're wondering where help is going to come from god is able he will provide Some of us he's speaking conviction He's trying to pick us up off the ground and saying it's time for you to stand It's time for you to be strong Some of us it's a conviction that we've taken off our armor laid aside and Taken the battle casually It's conviction some of us are here and we know we're not right with god You know how you begin to win the battle? First step in winning the battle Is surrendering to the lord You see in order to win you have to surrender When you surrender He comes in and forgives when he's when you surrender He becomes lord of all of your life when you surrender and wave the white flag He doesn't take you as a prisoner of war. He adopts you as a son or a daughter And today many of us in this room. We're on the borderline. Maybe you're here And you know you're not right with god Maybe you're here and you've never made jesus christ your personal lord and savior asked him to forgive your sins and you've Confessed and I said I repent god. I'm gonna turn my life around. I want to serve you And today the holy spirit's drawing you he's saying today's your day Today will you wave the white flag? Will you surrender to the lord or will you continue to battle on your own strength? Will you continue to even fight against god?  It's gonna ask you to raise your hand right where you're at. Just raise it high all over the room Say that's me. I see your hand Who else? Looking over the room who will surrender and find victory. Thank you. I see that hand Over here. I see your hands god bless. God bless. God bless. God bless. Yes you So this is the beginning of victory sir. I see your hand All the way on the far end I see your hand You can put your hands down Right now. I'm just gonna lead us in a prayer This prayer is an invitation And confession And I want everyone in the room to pray it out loud it with those who just raised their hands Let's say this together heavenly father I come in jesus name And I confess I've sinned I've lived for myself Today I repent and I come home I believe in jesus That he is the son of god Believe he died on the cross And rose from the dead To save me Today I surrender God you can have me Come into my heart Be my lord and savior I turn my back on the world I turn my back on my flesh And I turn my back on the devil From this day forward I set my eyes on jesus And i'm gonna follow you As a good soldier Of jesus christ Thank you for loving me Saving me in jesus name Amen and amen come on church. You just prayed that prayer


The Tom O'Brien Show is produced every business day. Tom, take your phone calls toll-free at 1-877-927-6648. Internationally at<PHONE_NUMBER>. Oh, that's a beautiful day. Good eye, man. Jim from Minneapolis. We are taken by storm. Taken by storm, baby. I love that. That's a great saying, man. Hey, what's happening, Brella? Good morning, gentlemen. How you guys doing today? Good, man, yourself? Oh, man. It's been the most incredible couple of days. And when I called in on Friday, Lifecoin busted out of that key validation on the two-hour chart. OK. And it just never looked back. It did a 100-point ABC up. And now it's very extended the way I look at it. But, holy mo- I mean, it went up to $420 last night. Now, Tom O'Brien. Welcome, folks. This is Tom O'Brien of TFNN. We have five days a week. We go seven hours a day. We go 24 hours a day on the internet at itfnn.com. Always remember, folks, whatever you think about, you bring about whatever you focus on grows. So, everyone's having a great day, safe day. The TGIF, folks, let's make it a great one. Express your love. Be impeccable with your word. Impeccability of the word can be measured by a level of self-love. If you love yourself, you'll express that love and interactions with the others, and that action will produce a like reaction. Mugger to eyes. Let's take a look at it out here. We have the Dow Industries trading up $333. Nasdaq is up 85. S&Ps are up 29. That's a gain of 1.2% in the Dow Industries, 1% in the Nasdaq, and 9.10s in 1% in the Nasdaq. Gold contract, slamming the gold contract down $18.80, trading at $14.64. We have the silver contract down $0.44, $16.61, an ounce, light sweet crude, up $0.75, $59.18, a barrel, notes and bonds. You get the 10-year note, down $14.6, trading out here at a price point, excuse me, folks, of $1.50, and we have the Silver Contract down $1.00, excuse me, folks, of $128.28, 30-year off $24.157.19. Both of them have done, thus far, folks, as this. They went into their strength from Tuesday. They got about half the amount of value of volume inside the 10-year. They got about 2 thirds of the amount of volume on the 30-year, and they have rejected lower price. So bottom line is that the notes and bond market is still saying they want higher price, lower yield, which is pretty amazing when you have the market's at all-time highs. Kingdala, Kingdala, $300 ticks, trading $97.710. The euro is at $110. The yen is at $108.59, and the pound is at $131 to 1, the U.S. dollar. My phone number is<PHONE_NUMBER>. Give us a call, folks. One note's going on in your world, and the world of the S&Ps, let's take a look at them. What do we have? We go over and we take a look at the spy. You're going to see the spies trading up $290, you're at $314.95, and you're high, that is going for is $315.48, and that was the high that was established on the 27th of November, and there's no reason that they can't try to jam this up into this level as we get into the close. Let me just see this intraday for a second. Yeah, there's no reason they can't jam that, and we've been at the same place now on the whole trading date. NVX100, we take a look at the NVX, NVX right now, not quite as close to the highs as the S&P. NVX, the high inside the three queues is 206.05. We hit that also on the 27th right now. You're trading out at 20488. Bottom line is that the contraction inside the queues are quite a bit, actually. You get 11 million shares, we're going into 17 million, which in itself was a low volume all-time high, and then we came off those highs with 28 million shares and 31 million. We're gonna take a look at the backs. This is what's intriguing out here too, folks, is that the rates are still staying low as of today. Okay, bottom line. JPMorgan though, guess what? Breaking topside in a huge way. JPMorgan in four days has gone from $128 to $135.46. This is an all-time high for JPMorgan. We bring this back, we put this on a weekly basis. What you're gonna see, it's quite a thrust. One week for a stock that is trading at $135 to move $8 in a week is pretty amazing. Right now, they're gonna make up a $424 billion. We're gonna take a look at Bank of America with BAC out here is trading at a price point $33.73. Now that's taken up the top of the consolidation that's been trying to, it's not getting away from it. It has to get further away about a couple points away from the $33.60, but bottom line, you are $33.73 right now. We're gonna take a look at, now that being said, now watch what happens there. If you happen to be in candlestick charting, what you're gonna have out here folks is on a weekly basis, you are gonna have a hanging man in all the indices and what is the hanging man? Well, hanging man is when you're at highs and on a weekly basis, the SAP had gone down to a 307, climbed all the way back up to 315 and if you get a close next week under these highs out here that'll be saying that yeah, you're still gonna go south. That's in your spy, that's in your NDX100. Now the cues, if you're pulling this up on your cues, what you wanna be aware of is that there's still a bad tick inside the systems and this one on the cues looks like it's one of the longest hanging man you've probably seen in a long period of time. Well, that thing is not correct. We didn't go to 193 this week. You're looking at it, it's gonna say 193 to 205 and what you're going to see, it was the day, I forget what day it was. Let me see. Put it up five days, it might have been Monday. Yeah, so on Monday, we went to 199, we didn't go to 193, if I do this intraday, you're not gonna see that tick that is shown on many quote sites folks. So the bottom line is not out there. Some of the gold, let's go over the gold contract, take a look at gold. We had a big jobs number come in, bottom line is that as the jobs number come in, the S&Ps go top side, they bring gold down, they bring bonds down, but they guess what, they didn't bring them down that far. Gold right now is down $18.60. You are trading at a price point of 1464.50, well the swing is still lower and you're backing down, and you're backing down to the strength of Tuesday. The strength of Tuesday, it's right out, it's 1465, 40, I'd like to actually see this close a buck higher than we are right now, and the volume characteristic, we've done the 298,000 today going to 400,000, so you're still coming down at light of volume, I would absolutely like to see that rejection though of a size, of a lower price. Silver, silver out here is always a wild market, this is the wild west, there's no two ways about that. Silver's down 40 cents, 44 cents, now what silver is doing, silver is breaking the consolidation that it's been in, so this is a serious business when you take a look at silver and you get volume behind the move, yeah, so this is not a great move, yeah. We will come back, I'm gonna go over that silver market, folks, our phone number is<PHONE_NUMBER>, stay right there folks, come right back.


This is stock number 9487. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used light duty truck headquarters. Today we are checking out this super clean 2011 Toyota Tacoma Double Cab Short Box. This truck has the four liter V6 motor from this HD video You will be able to tell that this truck is extremely clean inside and out and all the way around Front bumper is in really nice shape. It does have the factory fog lights. No dense dings or cracks on this front bumper Headlights are in pretty nice condition This truck has the factory 17-inch alloy rims and on these rims are brand new Goodyear Wrangler Fortitude 265-65 R17 tires These tires are brand new. We put these on in our shop during our safety inspection So four brand new tires all the way around Barcelona Red is the color Like to point out that we do shoot all of our videos in 1080p So if you have HD capabilities on your computer Tablet or smartphone device turn them on now because it's like you're right here looking at the truck with me and Definitely the best way for you to get a good idea of the overall condition of the vehicle without actually being here Brand new tire on this side as well And as you go down this side of the truck you can see just how clean the body is how reflective and mirror like that paint is We take these HD videos So if you are far away Whether you're far away or whether you're close by and just can't make the trip down You can still see the truck here the truck and have confidence in the vehicle that you're looking at Before you get here. This one does have a raider truck cap With it color matched We saw a lot of these trucks out of state So we want to make sure that our customers have the confidence that they're dealing with the right vehicle and the right people Factory running boards are an excellent shape back rim is in really nice condition and these back tires have just as much tread Our brand new as well just as much tread. They're brand new. So Like I said, we put those on in our safety inspection, which we do what you are mandatory mandatory have to do an inspection in Wisconsin, so We make sure everything's right with the vehicle before you buy it. So it's turnkey product Frame and underbody is very clean. All those lower rockers are an excellent shape As we come around to the back Rear bumper is in really nice condition as well. It does have a receiver hitch and wiring Tailgate is in really nice shape, too And it does come with a bed mat. You also have a power outlet back here and a couple little storage boxes it does have the side rail tie-downs with the cleats and Very clean inside the back area As we come around to this side of the vehicle just as clean as that passenger side This back room is in nice shape as well Like I said as we go down this side of the truck Just as clean as that passenger side. I didn't see any denser dings down this side of the vehicle very very nice Inside the SR5 package gives you the gray cloth interior. There are no rips or tears on the seat Really nice condition. It does come with factory floor mats. You can see the carpeting. It's nice and clean underneath Power windows power locks and power mirrors Comes with stability control roll stability control and power mirror controls right there as we hop inside this truck we will Get the information center going here Well, maybe we won't get there. Oh, there we go. You can see that this truck has 50,000 and 14 miles instrument cluster is very nice and clean It has audio controls on the steering wheel is leather wrapped and you have cruise controls on that side You get turned-out four-wheel drive CD player. They're your climate controls automatic transmission passenger format and seat is in really nice condition no rips or tears on that This one has a temperature and compass display up here and then in the mirror you get your backup camera Very nice and clean inside this truck And we'll take a quick look at the back seats and then we will check out under the hood Back seats are just as clean as the front seats once again. There's no rips or tears back here Does have the latch child safety system the sliding rear window These seats do fold up for extra storage and then they do fold down. There's the headrest for that seat And we have factory floor mats throughout back here as well Let's take a quick look under the hood Like I said all of our vehicles go through a hundred thirty point inspection This one's no different. It has been fully safety and inspected by our service shop Has a fresh oil and filter change all the fluids have been checked and topped off This truck has been gone through 100% has four brand new tires This is 100% ready to go To see more pictures of this truck or one of our other 400 new and used cars trucks SUVs minivans Wranglers half tons you name it. We got it go to our website www.summitauto.com full pictures and descriptions of every single vehicle on our lot Videos of every single used vehicle that we have all at summit auto.com Thank you so much for checking out the video if you want to make this truck yours Give us a call right now nine two zero nine two one zero eight five zero Ask for one of our sales associates to make this truck yours today once again that number is nine two zero nine two one Zero eight five zero thanks again for checking out the video if you want to check out more videos Go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos you see there In fact in a second you'll see a link to subscribe to our YouTube channel on your left a link to more used inventory video Truck videos like this one on your right if you have not been to our website on the bottom a link to this truck on our Website click those check us out and we really look forward to helping with this super clean 2011 Toyota Tacoma double cab short box. Thanks again


So, we will discuss or we continue our discussion on non ideal reactor models and we are looking at a multi parameter model or a two parameter model. So, in the last lecture we just started our discussion on this of course, like depending on geometry will have different kind of model is not a it is not like like you will have just one equation which will have two parameters and that is applicable to any reactor system. So, I will just give you one example right now and then we will see how it varies from reactor to reactor and we will have the two parameter model applicable to different reactor system, but then the equations would change accordingly. So, what we are looking at is the formulation for a two parameter model fine. So, we are looking at a normal CSTR and now looking at a geometry of the CSTR. So, it is like this and you have a nozzle here and you have a nozzle here and there is a stirrer and you have a feed coming in and there is the overflow that is happening and then there is a product that is coming out. Now, you will have nice mixing inside because of intense agitation right, but there is a possibility that you will have certain pockets in the reactor which are away from the stirrer or impeller and they may act like stagnant pockets or dead zones or relatively dead zones or relatively dead and there is another possibility that you will have a feed coming in and part of it will go and mix here or get inside a core, but then there is a possibility that part of it will bypass and go along with the outgoing stream. So, apart from dead zones you will have another non-ideality coming in picture which is called as bypass. So, there are three possibilities that you have a bypass then you have dead zones and of course, you will have the main core or well mixed zone right and all I know is this that well mixed zone is something similar to a CSTR whereas, these two things I do not know how to incorporate them so for at least how to incorporate them in the actual reactor model, but then if I know that there is something called as bypass there is a possibility of bypass there is a possibility of dead zones in that case I should incorporate them and one parameter for this and one parameter for this you will have two parameters as simple as that. So, it becomes a two parameter model and this is applicable to a stirred reactor that I am talking about if you have some other system there also you may have multi parameters not necessarily two, but bypass and dead zones are normally observed in many reactors many real reactors and there is always some one parameter associated with one of these effects. So, in general a reactor or reactor model that considers bypass and dead zones can be considered as a two reactor sorry two parameter model for a mixed reactor for a mixed reactor or back mixed reactor or stirred reactor I am not calling it as CSTR now because CSTR is ideal reactor that we always say this is stirred reactor stirred tank in which you may see bypass and dead pockets. I am going to look at some other situations as well where you will have will come across two reactor two parameter models or multi parameter models this is one example. Now, we will try and elaborate this further try and give a mathematical treatment to it and try and predict the conversion if possible. Now, first of all how do we know that there is a possibility of bypass how do you know that there is a possibility of dead zone who will tell you again the tracer experiment. See that is the importance of tracer experiment is such a useful technique that tells you the health of the reactor health in the sense what kind of flow patterns are there inside what is happening inside a stomach. So, I may treat this particular reactor this is my real reactor equivalent to something like this see bypass means it is not spending time in the reactor at all. So, it is just going out sorry it is going out. So, bypass is directly going out that means not spending time in the reactor whereas, some part is remaining here dead zones which is not seeing turbulence at all. So, I can look at this particular reactor as a set or network like this. So, there is an inlay that is coming in part of it is going to a CSTR sorry a CSTR part of it is bypassing and how do I represent the dead zone there is a dead zone here.  So, from outside I will look at a big reactor, but part of it is dead means the actual active volume is much less or relatively less. So, V D is something that I need to subtract from the total volume. So, V D plus this I may call this as V S. So, V S plus V D is V. So, V is equal to V S plus V D right. So, now this is my inlet concentration is C A 0 I am giving now a mathematical treatment to this particular system flow rate V 0 part of it is going here V S and part is going here bypass V B and just calling it as V B. Now, what is coming out or what is there inside is C A S right this is C A 0 same C A 0 nothing happening. Whereas, because the reaction something is happening here C A S is different from C A 0 right V D I do not have to worry much about only volume wise I have problem there. So, V 0 here the total volumetric flow rate I am assuming it to be constant say liquid phase reaction which is nothing but V B plus V S right and this is C A the resultant concentration. So, ultimately I am going to look at C A. So, this is nothing but C A here this is C A right and this is C A 0. So, C A 0 coming out is C A here again coming out is C A this is C A 0 what happens inside is I have just formulated a network. So, this is how I am going to look at this particular reactor this reactor for me is this as far as the modeling is concerned. Now, it becomes very easy for me to write down the equations for this because every part of this particular network I am well aware of how to write equation for it how to give mathematical treatment to it. So, let us do that let me draw it again because I will I will always need to refer it again and again while writing equations sorry. So, I will spend some time in this C A C A 0 right V B V S C A S C A 0 V 0 is equal to V B plus V S all right. Now, so coming in in is equal to out. So, let me write whatever is coming in and I may take a balance at this particular point at this point at this point whatever coming in is C A 0 into V B V B into C A 0 plus C A S into V S is equal to plus C A S into V S is equal to C A into V B plus V S or nothing but V 0 right. So, let us go ahead C A is equal to that means C A is equal to V B C A 0 V B C A 0 plus C A S V S divided by V 0 that is outlet concentration. I am interested in outlet concentration. So, let us go ahead C A is equal to that means C A is equal to V B C A 0 V B C A 0 plus C A S V S divided by V 0 that is outlet concentration. I am interested in outlet concentration so in this I know the inlet concentration I know the flow rate what I do not know is what is V B or what is V S once I know V B I can get V S because V S is nothing but V 0 minus V B I do not know what is C A S right these two are known and these three are to be found out. Once I get these I can get a value of C A and that is nothing but my conversion as simple as that. So, fine let us go ahead let us assume let me retain the same figure and then keep writing equations. So, same figure now that balance this one C A I just will write expression for this now before. So, let me as let me say that alpha is equal to V S by V 0 what is V S? V S is the volume of this reactor and what is V is a total volume that is alpha is a fraction of volume which is active sorry fraction of volume which is a total volume that is active that is nothing but alpha right then let me assume beta is equal to V B by V 0 V B by V 0. So, your total flow rate V 0 so out of which V B goes as bypass so this is bypass ratio bypass ratio beta beta V B by V 0. In that case my this expression look at this expression C A let me write it here C A is equal to beta into C A 0 plus 1 minus beta into C A S plus 1 minus beta into C A S plus look at this expression I am using beta there I just divide numerator and denominator by V B and solve fine or no need to do that C V B by V 0 is equal to beta and V S is nothing but 1 minus beta. So, I have express C A in terms of C A 0 and C A S in terms of and again with the parameter beta. Now, what about C A S now where does how will you get a value beta and all will see later by the way like can you guess where will it come from it will come from a tracer experiments how much bypass is occurred tracer experiment will tell me right. So, beta values to be determined through tracer experiments independently. Now, in this expression if beta is known what remains is only C A S. Now, how do we calculate C A S?  So, outlet concentration of the C S T R can be very well found out by writing material balance here. So, C A S I just write a balance for this I just write a balance for this I write a balance for this C A S to be found out. So, V S into C A 0 inlet plus sorry minus V S into C A S outlet minus reacted K C A S into V S is equal to 0 is a normal C S T R balance is a C S T R balance. So, C A S now can be written in terms of alpha and beta. So, this expression this equation and this equation I do not need this equation for this. So, let me say the C A S is equal to C A 0 into 1 minus beta into V 0 divided by 1 minus beta into V 0 plus plus plus plus plus plus plus plus plus plus plus plus alpha into V into small k by the way why alpha is there because I am multiplying it by capital V which is a total volume because from outside I am just going to look at a total volume I do not know how much is the active volume. So, total volume into alpha total volume into alpha. So, V S for V S I have substituted and got alpha into V. So, this expression you can derive it from this I get this is very simple because you know the expression for V S. V S is 1 minus beta into V 0 1 minus beta into V 0 1 minus beta into V 0. So, this V S is going to come out as 1 minus beta into V 0. So, you can derive it on your. So, this is the expression that I have got for C A S and that is what I want in this equation. So, substituting for C A S here from here from here I substitute for C A S here what is this? This is out late concentration overall out late concentration overall concentration that I get it out late as a net effect of these two strings bypass and this. So, I have incorporated bypass I have incorporated bypass I have incorporated dead volume as well through alpha. Fine, now I get the expression by substituting for C A S if I do that then C A by C A 0 is equal to 1 minus x you know that no C A by C A 0. See, I had expression for C A I am just dividing by C A 0 that is nothing but 1 minus x I want conversion ultimately. And if I substitute for C A S I will get the expression you can derive it on your own see what is more important is a methodology and not a final expression that you get of course you need to get a right expression, but then methodology is important more important rather. What do I see on the right hand side? Beta and alpha these are the two parameters these are the two parameters this takes care of the dead volume this takes care of bypass case rate constant first order reaction I have considered here and tau is a residence type there is no total volume do not forget that nothing to do with V S total volume that I I know of in the sense I just go into measurement in the in the actual reactor I measure the diameter I measure the length and from that I calculate a volume blindly I do not see what is the active volume I just see why this is a liquid level height and this is a diameter pi d square by 4 into L. So, this is what I am going to calculate so that is so tau will be based on that volume volume divided by volumetric flow rate. So, this is the expression for conversion is a two parameter model now the question is how do I get this these two that is the only question once I know how to get these values I have a two parameter model for a CSTR not CSTR what is third tank which is behaving in a non ideal way with bypass and dead volume I can predict the conversion for the given volume given flow rate. So, the next question is how to get alpha and beta of course I am of course the answer is tracer experiments E curve or C by C T C T versus time curve. So, for the same system can I write unsteady state balance look at this this particular reactor system I will say network can I write unsteady state balance for this that is simple because this is there is no hold of here there is no hold of here. So, I can write this and there is no interaction with this part of the reactor. So, I have to write a unsteady state balance for this part only right. So, what is that unsteady state balance let us write that unsteady state balance for the CSTR for the CSTR for the CSTR it is V s C T 0 now this tracer experiment C T 0 minus V s C T s coming out of CSTR is equal to can I write reaction though I am calling this CSTR is no reaction this third tank tracer experiment. So, D N T s divided by D T D by D T of N T s accumulation term which is nothing, but V s into D C T s by D T unsteady state balance for tracer no reaction no reaction. And what are the conditions for the positive step input at time less than 0 C T is equal to 0 and I have to write C T is equal to at time greater than 0 or equal to 0 C T is equal to C T 0 C T is equal to C T 0. Tracer equation I know the conditions for the positive step inputs are this now what I need to do because see again what I am going to see at exit H sorry at exit concentration is this. So, I need to combine these two now these and this. So, I need to take balance at this particular point now what is that balance we already seen that. So, balance at this point for the tracer is C T is equal to V B into C T 0 plus C T s into V s divided by V 0 sorry at this point I hope it is clear I am just writing balance for the C T coming out here C T is here and it is a combination of these two. So, they have two terms here and we know V s is equal to alpha into V V B is equal to beta into V 0 plus C T and tau is equal to total volume divided by V 0. Now, just a matter of integrating this equation integrating this equation and substituting for substituting for V B and V s. So, what we get is the final expression in terms of alpha beta and tau that is rest of the incidence time. So, the final expression after doing all this is C T s divided by C T 0 is equal to 1 minus exponential minus 1 minus beta alpha T by tau. So, this is the expression for the tracer experiment or tracer concentration at exit C T s. Oh sorry not at exit sorry sorry this is this is at at the outlet of C S T R at the outlet of C S T R here sorry here because I have the equation for C T s the unsteady state balance has been written for C T s. So, if I solve this I get expression for C T s, but that is not enough because what I am going to see through my tracer experiment is the concentration see sorry here this is my C T I am going to see this concentration. So, this is no mean I am not going to measure this I am going to measure this right and for that I have the expression I have the expression for C T what is that expression we already seen this C T right this expression. So, now I know the relationship between C T s and C T I have already determined C T s this. So, I need to just get C T. So, just substitute this here and get C T that is it. So, if I do that I get an expression for C T which is nothing but C T divided by C T 0 is equal to 1 minus 1 minus beta exponential minus 1 beta divided by alpha T by tau s. So, this is the outlet concentration this is the inlet concentration for the tracer beta alpha and tau with respect to time. So, I have got a relationship out C T changes with respect to time if I have these parameters out of which tau is known because total volume and volumetric flow rate are known to me all right. So, in this expression if I know beta and alpha I get C T or the other way round if I know C T as function of time I get a values of beta and alpha I get a values of beta and alpha. So, I can probably for calculation purpose I need to I will just rearrange this equation and I will put it in this particular form C T 0 C T 0 minus C T is equal to l n 1 by 1 minus beta plus 1 minus beta divided by alpha into T by tau the same as this you can you can spend some time doing this. But why I have done this because now I have a linear plot of what time versus C T 0 divided by C T 0 minus C T. So, of course, if I if I do log log. So, if I if I plot l n C T 0 minus sorry C T 0 divided by C T 0 minus C T 0 divided by C T 0 minus C T l n versus time what I am going to see is a straight line you see is a is a time y is equal to m x plus c y is equal to this m x plus c right. So, I am going to see a straight line for which the slope is what is the slope slope is 1 minus beta divided by alpha into tau and you know the intercept it is l n 1 minus beta right. So, if I do experiments in the laboratory and plot this versus this I get a straight line the slope gives me this and the intercept gives me this. So, with these two expression I can determine beta and alpha right. So, if I determine beta and alpha at my job is over because I know the conversion in terms of beta and alpha and tau because I already derived an equation for the conversion before what is that equation this is the equation right beta alpha and tau k of course is to be known and now I have told you the procedure to get alpha and beta right through experiments through tracer experiments. So, once I know the values of alpha and beta I can get a value of conversion two parameter model stirred tank with bypass and pockets I have incorporated both these effects through two different parameters called alpha and beta is one example you may come across some other non ideal reactor or a real reactor where something else is happening right. So, what is that? So, let us consider another example just to appreciate that it is not that difficult to consider the effect of flow patterns or non-ideality what is more important what is different here we have used the same reaction engineering principles that we have learned earlier. Only difference is the tracer experiment is able to give me the idea about a flow pattern so that I can formulate a reactor model non ideal reactor model with different parameters in it right and this model is able to give me the right conversion fine. Now, this is another example where you are talking about a reactor a reactor where you have a nozzle and there is a stirrer it is a long reactor relatively long reactor and is a pipe that is coming in sorry that is for the field. See what happens now kind of flow pattern I do not know like it all depends on kind of impeller that I am using so it is quite possible that you have in the upper part you have some circulation happening the lower part also you have some circulation happening sorry. Now, what is the difference in this reactor and normal reactor difference is that you can see that is no flow path or rather there are very few flow paths which are taking streams from here to here there is always some exchange between these two, but you can see that there are distinct zones formed there is like upper part where there is a mixing happening lower part also there is some mixing happening there will be some exchange there will be some exchange this is not stagnant there will be some exchange, but then this concentration may not be same as this concentration because of the extent of mixing that is happening and the exchange that is happening between these two. The exchange is such that the concentration is not same the concentration is not same in these two regions. So, can we treat this as a normal CSTR or ideal CSTR we cannot because ideal CSTR means that the concentration is uniform everywhere constant everywhere right. So, how can I formulate a model for this particular reactor now first of all whether this happens or not who will tell me again a tracer experiment. So, sometimes the tracer experiments tell you about a flow patterns. So, the see now if you are exporting this field then the moment you see the tracer experiment results C T versus T or E T curve you know what what is happening inside a reactor. So, it is like doctor examining a patient based on a symptoms he would know what exactly is happening similarly based on this tracer experiment you know what is happening inside. So, try to understand importance of tracer experiments E curve right fine. So, this can be looked upon as two CSTRs exchanging matter and a feed is going to this CSTR and the product is coming out from here as simple as that you see there is a CSTR here feed is going in product coming out and this is exchanging mass with the upper CSTR. If this nozzle was here I would have put a outlet here as simple as that this is this is a network now this is the network.  So, whatever going in would come out whatever going in would come out and of course, this has to be v 0 this would be C A 1 and this would be C A 2 they cannot be same if they are same then they know point in making two different zones why they are two different zones because the concentrations are different right. So, this is my network model now you can identify the parameters what are the parameters first parameter will be v 1 divided by v 0 this is one ratio and the other parameter would be the volume of one of this CSTRs divided by the total volume. So, v 1 divided by capital v this is another parameter. So, this can be beta this can be alpha the meaning of alpha and beta are different here and they are not same as what we either it was that there it was bypass ratio, but in order. So, I can use some other symbol is not an issue but then it is very clear like say v 1 by v 0 this flow rate is one parameter and this is another parameter what am I going to do now I am going to write equation for both of them right both this CSTR combine them solve them together now it is it is like exchange. So, I have to solve this equation simultaneously see I have to solve this equation simultaneously. So, mathematical exercise will become slightly difficult because your model is a relatively complex model, but not nothing to worry much about it. So, solving the model system what you see is like see v 1 is equal to beta into v 0 capital v 1 is alpha into v capital which means v 2 is equal to capital v 2 is equal to 1 minus alpha into v tau is equal to v by small v 0 this is capital v this is total volume total volume. So, if you can derive equation write the equations of both the CSTR solve them together what I would get is C A 1 is equal to what is C A 1 look at this C A 1 and that is what I want that is coming out here it will have impact of what is happening here as well for this reactor see is going in and coming out going in and coming out from this reactor. So, this is in what is coming out from this reactor is inlet for this. So, this has two inlets here. So, this will be determined not only by this, but by this as well fine. So, C A 1 is equal to C A 0 divided by 1 plus beta plus alpha tau k first order reaction beta square divided by beta plus 1 minus alpha tau k this is what it is I not writing equation solving them in front of you, but then you can very well appreciate I just write those equations for both CSTRs and then solve them simultaneously I get this expression and this is nothing, but of course this is nothing, but C A 0 into 1 minus x sorry 1 minus x is conversion. So, see the similarity between this problem and earlier problem though geometry was different methodology is quite similar I am just formulating a model coming up with parameters getting an expression for the exit concentration which is related to conversion and. So, I am I know conversion how it depends on the parameters alpha beta right tau of course it has to depend on tau residence time and the rate constant and inlet concentration of course this will get cancelled C A 0 C A 0 for the first order reaction alright. Now, again the same procedure how to get alpha and beta how to get alpha and beta same question and same answer pressure experiment I have a system where I have a CSTR which is exchanging mass with another CSTR it is not a dead volume do not forget it this exchange happening earlier dead volume there is only one line that I had drawn now there is a arrow which is going here and there is an arrow going here right. If I write unsteady state balance for this non reactive conditions because the tracer that is going in the tracer that is that I am that is going in. So, if I write unsteady state balance for both the reactors and convert it to beta alpha tau and k I get expression like this tau alpha you can derive it on your own right now I am just writing it directly to show you or explain or rather demonstrate how similar the entire exercise is compared to the earlier one. So, this is for this reactor 1 for 2 there will be another equation tau 1 minus alpha look at this 1 minus alpha d C 2 by d t is equal to beta C t 1 minus beta C t 2 every terms tells you something. So, you can imagine very well imagine how this equation is come nothing great about it is coming in going out accumulation similar thing happening here. So, but then now what is happening here is like you have two equations they coupled they coupled because C t 2 is appearing here and C t 1 is appearing here. So, I cannot independently solve them. So, I have to solve them together I have to solve them together this is a set of O d is to be solved together you can use numerical technique or one can do it analytically also right and get a values of alpha and beta. Now, the in I have to solve this earlier case it was quite easy for us to get a value of alpha and beta because it will linear plot we plotted some l n C t 0 divided by C t minus something versus time and then that plot slope and intercept gave us some values of alpha and beta. Here it is going to be a bit difficult because I have O d is I can even get some equation after solving this after solving this I may get some equation and that equation analytical expression for C t 1 because C t 1 is something that is coming out and I need to compare. So, this plot of C t 1 versus time I may see something like this I am just giving you some picture just guess something that C s t r. So, it is going to go like this I will get value at 0 also very close to t is equal to 0 right. So, I am going to get something like this let us assume that now this is by experiment and by solving these equations by solving these equations I will get some behavior. Now, these equations if I want to solve these equations I need to have values of beta and alpha. So, the procedure may be you assume some value of alpha and beta you may get a behavior like this which is much different from this. So, there is some error there is some error right and this error we need to minimize you minimize it in such a way or other assume the values of alpha and beta in such a way that this error is minimized right. I think we have seen this before also you have to have use a least square optimization technique. So, it is a numerical technique it is not so easy to determine the values of alpha and beta in this particular case because I do not get a straight forward linear relationship I cannot rearrange those equations. So, that way this particular problem is slightly complicated compared to the earlier one, but methodology procedure is quite similar. So, go on changing the values of alpha and beta systematically there are techniques available such that this error is minimized or least square error is minimized that means c t 1 predicted minus c t 1 experimental square divided of course, you can normalize it c t 1 experimental square if this this is minimized. So, this is you have to minimize this for the values of alpha and beta. So, this becomes a optimization problem. So, get a values of alpha and beta in such a way that this is minimized this function is minimized and you can do it using software or rather they can be a solver they can be an optimizer a least square method which uses least square method and you know why square and why it is called a least square method and all that square is because like I do not want to consider the sign of the error. Otherwise two errors may compensate each other and they may give you the function to be they may say that function is 0, but that may not be a situation you are much away from the actual real values. So, that is why square. So, it make sure that you have a positive values all right determine alpha and beta. So, like this there can be different situations that you may come across a simple scenario. Now, there are many possibilities how do I identify what kind of model I may I should go for from the e curve itself. So, let us let us consider a situation I have a tubular reactor, but not a simple tubular reactor where I just have one inlet there are two inlets at the reaction of A plus B giving C. Now, C sorry B is coming this way as jets all along the periphery. So, I have I am showing two jets, but they can be multiple jets along the circumference and is one reactant coming in this A and all the B is going this way. There is a reason why because I want these these two mix get well mixed here both these reactant as and when they come because if there are some zones where only B remains or only A remains then there is a problem because it may go undergo side reaction. So, in this zone I want them to mix thoroughly and later on I do not have any problem let them go together or in a plug flow manner once they are mixed well. Now, this is one reactor this is one reactor how do I model this reactor it is very simple is not it. If I before that if I just do a tracer experiment on this that means in a non reactive conditions suppose I inject a tracer at the inlet what will I see at the outlet there is a material flowing like this I am just injecting tracer now there is no reaction I am just sending some inert in this flow pattern is similar when the reaction is taking place. What is what what will I see here I have injecting a tracer a pulse what do I see here if it was a simple plug flow tubular reactor I will see a pulse at time tau right, but now because there is some mixing happening I am going to see something different. So, let us assume that this part of the reactor is well mixed.  So, what I am going to see is initially at this point suppose I take measurements I will see a CSTR type behavior right. So, this is a CSTR. So, this is a CSTR this is a CSTR and here it is PFR. So, after this it is going to behave like a PFR. So, this this particular response is going to come out at this point exactly at as after the time interval equivalent to the residence time spent here. So, the behavior is going to be like this. So, if I see an E curve or C curve whatever like this then I may say it is a combination of PFR and CSTR in series of course, you have to remember one thing whether it is first the PFR or CSTR because in both the cases you are going to get a same E curve. Then you will have to think about what is a real situation. Now, I know that I am sending z CSTR. So, definitely first part is CSTR. So, without knowing this just based on this I cannot make a reactor model. There are many possibilities of combination of these reactors that can give rise to same E curve. So, one E curve is likely to give you different reactor models, but knowing more about the real reactor you can shortlist them and come up with the final model. So, for this particular case my network is this a simple network is this a CSTR followed by PFR. Once I know this I can definitely find out the conversion what is the parameter for this model? There is only one parameter here I know the total volume how much of the total volume is covered by or other is taken up by CSTR and how much of it is PFR that is the only parameter now. It is a one parameter model, but if for some reason I see some dead zone here that means area under the curve for E curve is not one. Traces still comes out like it keep coming out long time in area under the curve calculated based on the total volume is not matching one that means there is some dead volume. So, that means there is some dead volume sorry I can say that there is a dead volume here not here sorry this is a real reactor. So, this is a dead volume here that is how I look at it. So, then the dead volume becomes another parameter alpha something that we used before. So, that is why that is how we look at different types of reactors and at the same time from the E curve or C curve I can very well get some idea about what kind of flow patterns you may have inside a reactor otherwise. So, there are many possibilities just one of them you have a tubular reactor and some streams are lagging behind some streams are going ahead from. So, it gets divided for some reasons this is going very fast and this is going slow. What is the model for this? The model is that you have a feed that gets divided into PFRs right is again one parameter model how much goes here how much goes here oh sorry it is a two parameter model how much goes here how much goes here and the volumes of this. So, again is a two parameter model there is a possibility that you have something like this there is a mixing happening here and this is going straight. So, you this is equivalent to sorry this is equivalent to PFR and CSTR in parallel right again two parameters how much goes here and what is the ratio here the volumes right. So, many such scenarios you can have even more complicated that you may have some 3 4 CSTRs in series then there is one parallel PFR. So, many things happening depending on what kind of situation you are in normally for a chemical plant our reactors are well shaped reactors, but if you are talking about some natural reactors reaction taking place in space or reaction taking place underground in that case geometry is not in your hand then that case will have to make assumptions or it can be a more complicated or a complex network of different ideal reactors and bypass dead volume and so on. What is the key is a tracer experiment the E curve the C curve tracer experiment you should learn to read the tracer experiment results properly if that happens then your job is easy of course mathematical treatment is something that you can definitely do, but then solving the equations numerically and all you may need to take help of software and all, but a method law is very clear. So, it is a tracer experiment that gives you an idea about a reactor behavior as far as the flow patterns is concerned. So, this is all about how we use multi parameter models for real reactors I have shown you two parameter model here, but you can very well imagine scenarios where you can have now the same case here like for example, in this case like you have two streams giving, but you may have another rather some part of the reactor where you will have an intermediate velocity. So, you will have third PFR in series. So, and then the parameters would increase as simple as that how number of parameters will grow that will depend on the complexity. So, first thing is you need to come up with the proper reactor or multi zonal model or network. How do you do that? The two things that are required for this first is your E curve tracer experiment and the knowledge of the system as I said only E curve can give rise to multiple networks giving the same E curve. Out of those multiple networks whether it is first CSTR and then PFR or first PFR or then CSTR that I would know based on some knowledge of the system of the reactor that I am going to use. These two will tell me or these two will help me formulate a network. Once you have a network write down balance equations get the expression for the conversion and from in that expression you will have the parameters for the network those parameters are to be determined through tracer experiments. So, I will just write down quickly what it is formulate a model formulate a model this is going typically going to be a network which will have CSTR, PFR, bypass, dead volume. We have not seen many other cases a recycle exchange many features possible. Who will this is based on what? This is based on based on E curve or tracer experiment and knowledge of the reactor system. Why do I say system? Because not just reactor geometry, but where is the inlet nozzle, where is the outlet nozzle all these things will matter. Once you have once you formulate a model network write balance equation and get x conversion. You may get expression for this or you have to solve these equations numerically. In terms of model parameters for example, alpha, beta and so on. Now, third step would be get parameters from the tracer experiments and then evaluate x. Now, this step may need use of optimization solvers say least square or whatever. So, this is overall procedure. I hope this is clear like how to incorporate or how to consider non-ideality in real reactors and predict the right conversion with the help of E curves. Thank you very much.