[Music] you can now mute yourself and also share the screen now your audio is not clear i am saying that you can share your screen and also you can try to share your screen now yeah yeah okay okay ah you you please give me permission to record for me okay so try now yeah i mean i would like to record records okay okay yeah unless you give me permission you know i will not be able to record it okay so you can record now yeah you have to give me permission yes i gave you the permission so my audio and video both are clear right yes okay uh shall we start mr abdullah uh yes professor i will do in its presentation okay and then you can start can you proceed okay uh so welcome everybody to our webinar so far modeling fundamentals just i will do a presentation about reservoir solutions so far solutions is a company that specializes in providing technical studies and courses for oil and gas companies and also professionals the company incorporates many professionals with diverse technical 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through fractured reservoirs from indian institute of science dr surish has many publications actually for books and 131 articles also he participated in five practical approaches for our webinar rules you can ask your question into the zoom chat and i will collect all the questions to ask the instructor also mute your microphone and camera fill in in case that you wanted to get a certificate for this webinar you should fill into the form that will be sent into the zoom check join our telegram channel for upcoming webinars and courses and you can contact us through the email and also the whatsapp just one minute for our newest course the pvt and the equation of speed modeling using pvt software the topics that will be discussed into this course resourceful fluid properties pvt experience and sampling for reservoir fluid data qc adjusting the pvt qc with contaminated symbols reservoir fluid characterization through assurance studies and eor pvd exhibit the benefits that you will have from joining this course that you will have the recorded videos the study materials the actual datasets will be delivered the excel application sheets also will be sent to the participants at the end of the course you will have two days of project and after the course you will have complete mentorship by the instructor on the course whatsapp the course fees is only first for 40 usd for the working professional and for the students you can enroll for only 225 usd to enroll into this course i will send the i will send the registration link into the zoom chat thank you all and uh doctor sirish you can start professor you can start now yeah yeah thank you abdullah so the outset i would like to welcome you all and uh i would like to thank visualize solutions for providing me this opportunity to share my thoughts on reservoir modeling am i audible clearly am i audible yes yes yeah thanks well uh i'd like to thank you all for joining with us despite your business schedule and i hope uh you will enjoy this lecture well uh before i proceed further i would like to caution you that this is not a conventional presentation with a case study and field waiter or numerical results rather this lecture will focus on very very fundamental concepts of reservoir modeling associated with the hydrocarbon reservoir as you all know reservoir simulation in the oil industry has become the standard for solving reservoir engineering problems simulators for various recovery process have been developed and you know what they are being developed for various new oil so recovery processes our prime concern we got to develop and use simulators that describe the reservoir performance under various operating conditions see there are several types of reservoir simulators based on you know dimensions such as one dimensional simulator two-dimensional simulator three-dimensional simulator and then based on coordinate system writing on radial coordinates cartesian coordinates then you know based on the types of reservoir fluids such as renewable gases oil oil reservoir black oils oil gas condensate reservoir and so on choice of the proper simulator to represent a particular reservoir requires an understanding of the result the careful examination of the data available a reservoir model or a simulator is useful only when it fits the field case however it remains very challenging see when a reservoir simulator is implied to assist in planning the development of a virtue required then obviously the reservoir description is typically limited consequently only a minimal degree of optimization would remain possible however some useful insights can still be obtained with the aid of a simulator that can minimize the number of decisions one must make in planning the field development simulation studies at the development stage because of the uncertainties involved or regarded as preliminary typically they are periodically updated as more information becomes available this means that early development plans arising from the first simulation studies should be sufficiently flexible in order to accommodate future contingencies as one learns more about the result this presents a severe challenge where the reservoir in question is highly complex large in extent or in an unfriendly environment all of which may require large investments to put it on production in a broader sense reservoir simulation has been practiced since the beginning of petroleum engineering in the 1930s see the very purpose of reservoir simulation is to estimate the field performance under variety of producing schemes now let's try to have a look at the difference between a real field scenario and that with using reservoir model so see we will be able to use it excuse me professor uh just the screen is not sure sorry i'm not kidding screen is not sure please no i i i'm not sharing anything okay okay okay thank you yeah so you know now let's try to have a look at the difference between what happens in a real phase scenario and that when we use reservoir modeling see we'll be able to produce only once in a real fee scenario and that too at the expense of considerable cost right however in reservoir simulation a model can be produced or run many times at low expense or a very short period of time observation of model performance under different producing conditions aids in selecting an optimum set of producing conditions for the result well you know before 1960 the calculations performed to predict reservoir performance consisted largely of analytical methods zero dimensional material balance and then one dimensional buccal liberate calculations see the term simulation became common in the early 1960s as predictive methods evolved into relatively sophisticated computer programs and during 1960s reservoir simulation efforts were devoted largely to two-phase gas water and three-phase black coil reservoir problems so if we look at carefully until 1960s they were essentially aiming in developing a single simulation model which is capable of addressing maximum encountered reservoir problems in fact such a general model has attracted to operating companies because it's significantly reduces the cost of training and usage and potentially the cost of model development and maintenance however the picture changed market during 1970s the scenario was completely different we had a short rise in oil prices and it was all the way for eur projects due to the curtis funding from the government sector towards field projects so a big change was happening during 1970s what was that there was a significant departure from this single model concept because individual models were developed to represent various newly developed eor process like miscible flooding chemical flooding co2 injection steam flooding hot water injection in such a combustion extract however during 1970s late 1970s and early 1980s the concept of reservoir simulation was looking like a kind of magic because it was the newest reservoir tool at that point of time see you feed something in the name of input and you get back something else in the name of output without having any knowledge on conceptual modeling or mathematical model or numerical modeling what you are doing with package you just feed some input data you have no clue about what is happening in between if it's a kind of black box for us and you get some output and you are happy with it right so you know we have no clue about what exactly causes the oil recovery now you have to conceptualize here was it due to fluid expansion with pressure depletion or was it due to the displacement of oil by gas or by injected water or by encroached water was it due to gravity drainage resulting from density differences leading to bottom motor drive or was it due to capillary and vibration associated with the lateral water floods in heterogeneous reservoirs with large vertical variation of permeability what exactly cost we absolutely have no idea and this is where we got to carefully handle the already available existing petroleum software packages because these packages can become a dangerous tool for us if we start using it without understanding the fundamentals and in turn the real power of reservoir simulation will be misunderstood because you know some of the numerical solution techniques you know whichever use it can calculate meaningless results with incredible precision and this is where reservoir engineering community will easily lose hope on reservoir simulators and they do not believe us so easily not only individual reservoir simulators many oil companies have been burned due to the in inappropriate use of these reservoir simulators see in the absence of sound knowledge on geology reservoir engineering principles mathematics and coding skills and since we directly started using software packages some reservoir managers became disappointed with the concept of reservoir simulation and in fact there were they were no longer interested in being fooled by this technique see the mistake is on our path we have not approached learning the concept of reservoir simulation proper the fact is that there are several critical steps to be understood before we can think about using this artifact you know then slowly people started realizing the importance of this tool with significant improvements in reservoir simulation techniques in reality simulated results always do not succeed because the people applying this technology either did not understand the required concepts of geology reservoir engineering principles mathematics and coding skills are they did not properly communicate their assumptions and corresponding limitations of the simulated results so we need to clearly understand that reservoir modeling has both strengths as well as weaknesses and it is only one of the many tools available see with experience it becomes painfully obvious that many reservoir engineering estimates reservoir engineering plants reservoir engineering scheme have fundamental flaws identifying the central cause of the problem remains very very challenging unless you have sound knowledge almost on all allied related disciplines and not only in reservoir so now we have a kind of very much attached to the reservoir simulated whether we like it or not for example the concept of pressure transient analysis pta using hardwood plots were carried out by engineers you know by hand long back and while doing so the type curves did not reveal much information however nowadays no one does pta manually it's all done with simulation using a derivative analysis so now we cannot detect reservoir simulation from the community of reservoir engineers in a sense it is no more an option let me put this in this way a reservoir simulator does the job of understanding and assimilating what cannot be seen or what cannot be touched it essentially allows us to test quantitatively how different processes affect production results now i mean it also allows us to evaluate the complex geometries that cannot be solved easily by analytical methods the bottom line is that although reservoir simulation allows us to evaluate complex problems it is still a passive tool only why is it so because it can only evaluate for the fed input while it is not capable of determining the input itself that should have been entered we understand whatever input we fed for that it simulates so we are not determining the input the quality of input is a very big question one so we keep collecting data from you know different scales from we keep collecting data you know from nano scale sub microscopic scale microscopic scale poor scale core scale laboratory scale not this macroscopic scale and some from larger fields you see so many data from different scales now what you do without even normalizing all this data on a common platform you just bring in everything and then you feed it as input data to the package what will happen god only knows so we have you know many different skills with this we got to be very careful we treat all the data on a common platform without normalizing it we got normalized please remember non-diamond sterilization is different normalization of scales is different don't get confused between these two things see the this is a basic reason why we are not able to upscale our results from the laboratory scale to a larger field scale problem well this is a different research topic all together let's not get into that right now in fact you know carlson she has beautifully pointed out that the art of reservoir engineering involves patent recognition it's like an art is no more like a science the model results from many different techniques that they must be integrated to develop a correct interpretation of reservoir behavior since we deal with different types of data the input screening is required frequently not all of the data desired or required is available right in this case what will happen properties will have to be evaluated estimated from other resources all of this must be very mental and the best estimate has to be made by yourself to make matters worse many of the sophisticated techniques used by reservoir engineers provide interpretations that are not unique multiple solutions often exist for example for for a given reservoir problem a geologist will suggest something a geophysicist will suggest something reservoir engineer will suggest something a production engineer will suggest something so what happens as a consequence here the science gets a little fuzzy and eventually the science becomes an art experience comes heavily reserved this leaves the new reservoir engineer in a catch 22 position one needs experience to do the job and one can't get it without the experience of having done it so back to simulation what exactly we mean by simulation or modeling but it's a wise simulation we are supposed to infer the behavior of a real reservoir from the performance of our developed model so the basic question is how exactly are we going to develop our model where are we going to start our modeling process this is the very basic question that i will be addressing in this lecture today where to start how to stop the time is anything this is what i'm going to discuss today right well simulation or modeling you know is not about using the existing software packages as such these packages are meant for industrial experts and strictly speaking not for academicians academicians got to learn the basics the fundamentals in an academic environment during their graduation so that they can and precisely forecast model results deduced from the software packages during their field application associated with their industry life so as a student you are expected to learn the fundamentals of modeling aspects so that you can make use of the software packages to be used later in the industry efficiently now what exactly we mean by fundamentals of model what is what is the fundamental is all about well modeling is not about directly venturing into either analytical modeling or numerical modeling reservoir modeling has three fundamental components they are we got to develop conceptual model first and then mathematical model and then numerical model followed by verification validation aspects and finally you know forecasting the reservoir performance using our numerical results now you see most of us we have never bothered about the concept of conceptual model at all we have not been tuned to get into mathematical model at all some fraction they directly get to the numerical modeling and then you know they are focusing more on the improved numerical solution so what is missing we are not you know tuned to get into the concept of conceptual model and mathematical modeling at all what what we are doing generally we directly take the equation from some textbook or from some references that is most dangerous so now today we are going to understand the importance of conceptual model and mathematical model before we can move on to numerical model but what we generally do is that we never bother about the first two modeling steps right above conceptual modeling and mathematical model and we mostly attack the numerical modeling component directly that is the last step the last component of the modeling process directly so first try to understand very clearly in reservoir modeling most of us do not touch part one part two step one and step two directly we get into step three what is step one developing conceptual model what is step two developing mathematical model we miss both these steps i will discuss why we are missing why we are not interested in this why we directly get into numerical solution now so what remains missing is that we have no clue about conceptual and mathematical model why is it so because if you want to start from the first step that is if you want to start from conceptual modeling you then got to break your boundaries you cannot climb yourself to be a reservoir engineer you cannot climb to be yourself you know to be a geologist it is beyond boundaries for example if you want to characterize a petrol in this wire we then got to understand the fundamental principles of reservoir engineering we got to have a sound the knowledge on solid mechanics we got to have a sound knowledge on fluid mechanics we got to have a sound knowledge on thermodynamics along with the sound background on mathematics as well as geology now you see if we want to do something with reference to reservoir modeling you should know geology reservoir engineering principles fluid dynamics solid dynamics thermodynamics geology math coding skills right this is where we have problem see we actually have no boundaries associated with this for example all these boundaries you know in geology geophysics is reservoir we have created on our own i will tell you you know the reality see you know i mean what i try to convey there is actually no boundary associated with it for example you are thinking darcy's law it is is something you know attached with petroleum engineering right no darcy's law based on which is based on hydraulic gradient has nothing to do with petroleum engineering that gentleman henry darcy he figured out this law he is a civil engineer he figured out this law in 1856 and it has nothing to do with petrol engineering in fact darcy has never used the term pressure or pressure yet like what we use in petroleum engineering what he has used was hydraulic head right so uh strictly speaking you know uh petroleum engineers borrowed this concept from them civilians from civilization now how about darcy did he develop the law on his own no henry darcy he deduced this concept from fix law in 1855 fixed law based on concentration gradient which is attached with chemical engineering chemistry you see darcy borrowed the concept from fixed law in 1855. now go back to fix the other fix he originally developed allah no fix he borrowed the concept from ohm's law electrical engineering in 1827. do you understand the cycle now worms if you go to ohms developer home salon ohms borrowed this concept from four years law of heat conduction mechanical engineering he reduces law in 1822 see and it keeps going you see mechanical engineering electrical engineering chemical engineering petroleum engineering civil engineering where did we have the boundary then why are you unnecessarily climbing petroleum engineering you know reservoir production engineer you know geologists geophysicists had darcy won to fix our fourier thought like that i'm a mechanical engineer i'm a civil engineer i am a nova uh chemical engineer you know they don't have deduce these loans so we should try to look at the problem holistically and you know we should we should not get confined in a small volume uh so so the point is what we need to understand is that we should not try to get into a small boundary and keep climbing that i am a geologist or engineer we actually require the philosophy to be understood not only the respective engineering concepts and that's why you know they confer as doctor of philosophy not the doctor of reservoir engineering so all these linear homogeneous laws are essentially energy dissipation equations relating driving forces to their conjugated fluxes now back to conceptual modeling see you are supposed to bring in what exactly we mean by conceptual modeling step one you are supposed to bring in a three-dimensional picture of the reservoir in front of your eyes close your eyes try to bring in three-dimensional reservoir in front of your eyes virtually now you try to see what is that you find within the box within the reservoir to start with are you visualizing are you conceptualizing the two fundamental entities what is that solid grinds and pore spaces are visualizing that are you conceptualizing that to start with we have two fundamental entities solid groins and pore spaces then you try to see how exactly your pores you know are getting distributed that is whether you have you know all the ports are hydraulically connected from one end to another end or wherever you have dead ends isolated ports and what exactly you know what i mean slowly try to focus on the complex zigzag fluid flow pathways within the reservoir you have to focus because this is not like flow through pipes your our stream lines will not be horizontal as we expect it is a porous medium our poor path is is not going to be horizontal or straight it's going to be highly tortuous it's going to be highly complex now try to bring in can conceptualize so look out for dead end force or isolated force and you've got the why why why do you need to conceptualize the dead encores or isolated force you you need to get it off those pores what is required we require only those pathways which are hydraulically connected between far away from well to the production level we don't want any other ports right so total porosity will not be of interest to us we will be interested only in effective porosity right so you should start conceptualizing uh the pores which are hydraulically connected so uh where exactly you have the hydraulic connectivity between various pores and check whether there exists a continuous fluid flow from far away uh from the well towards the production valve now you see now next you think conceptualize now you you ha you were able to conceptualize there is some continuity of fluid flow because if i do not have continuous fluid flow i will not be able to make use of equations i need to have continuous fluid flow which is very very essential because in petroleum reservoirs when you talk about snap-off mechanism the fluid continuity will remain missing please understand whenever fluid continuity gets missed we will not be able to apply any equation we will not be able to apply any mathematical model so the base fundamental thing is we must ensure that there is continuous fluid flow that is very very important now having conceptualized that there is a continuous fluid flow through the complicated torches both paths for the next step next thing what exactly drives the fluid flow something drives a flow from far away from the well towards the production well right what exactly drives a fluid flow now conceptualize whatever i mean sources you have you have it may be due to pressure gradient you have gravity forces you have capillary forces and then you try to try to conceptualize what are all the different you know uh sources which drive the fluid flow then you think whether all these three forces pressure gradient gravity and capillary now what you've got to think better when oil is being driven far away from the well towards the production well what you need to ask whether all these three forces remain dominant throughout the reservoir first question is whether all the three forces remain dominant r is the only two forces or is it only one force are coupled that is combination of two forces remain dominant these are all the things you've got to think we want to conceptualize next out of these forces reservoirs you know so lengthy whether all these forces remain dominant throughout the length of the reservoir we don't know this is where you know you got to conceptualize thing pressure gradient gravity capillarity drives a fluid flow now you have location spatial location whether it is x-axis or radial coordination cartesian guarding the variable coordinates from the drainage boundary up to the production well what is happening what exactly drives the fluid flow if you want to get the answer for this thing then you have to have an understanding about pore size distribution then only we will be able to get answer for this unfortunately you see what we require is poor size distribution means what we require the data on average forces have you ever got have you ever gotten the data on poor size average both sides please think in reservoir in petroleum engineering have you ever got this data no nowhere then what is the data i mean you are getting the data which you are getting is grind size what we require is the size of the poor but what we use is grandsons mean grandsons what we have because it is not practically possible for us to deduce mean pore size that's the reason why we we assume that the size of the pore is you know approximately equal to the size of the solid grain and then we try to deduce the average value of the solid grain maybe daytime d20 or you know d50 in general d mean right you know so you have to have some knowledge on poor size distribution for you to decide which of these forces to remain dominant then so we have completed the forces then start conceptualizing we are still in step one conceptual modeling then think what is that then regarding miscibility you have multiphase so oil water gas all those things so the concept of miscibility becomes important so regarding miscibility it is nearly impossible to encounter scenario such as you know fully visible fluid flow in an oil reservoir right and if it is not possible do we have a reservoir replicating the partially miscible flow models partially miserable actually you know in reality it will be partially visible but you know we do not follow it because the equation will become very complex so you conceptualize what exactly you are doing are you handling completely fully miscible fluid flow are partially miscible fluid flow and then you check what kind of equations you use i don't want to you know uh explain further at this point of time i will explain later then conceptualize regarding the flow direction see it is very difficult to find a reservoir either with perfectly horizontal flow or you know with perfectly vertical flow mostly it is going to be an inclined fluid flow because we predominantly have anti-climate reservoirs right if that is the case whether the fluid flow reminds always towards gravity or whether the fluid flow reminds i mean does it flow against the gravity these are all the things you know you've got to check then we also have to have a look at conceptualize what happens at the fluid fluid interface such as you know oil water contact does it remain horizontal no mostly it will not be if it is inclined we need to look at the cause of the inclination what caused this inclination why it is not horizontal and you know what we should immediately bring in the concept of hydrodynamic trapping now you see you are bringing other concepts then regarding fundamental reservoir properties regarding porosity and permeability we need to have some idea about the distribution in the real field scenario we got to conceptualize whether the porosity is normally distributed or not you've got to conceptualize then permeability whether permeability is log normally distributed or not see in in general we expect porosity to get distributed normally and permeability to get distributed log normally whether we find the same thing in the respective reservoir or is there something else conceptualized see in conceptual modeling you don't have pen paper anything you don't have any data you don't have paper you don't have pen with you only your thoughts conceptualization visualization you are trying to bring in the three-dimensional picture in front of your eyes so no data no experiment no field you are conceptualizing if not you know so we we have to think what kind of porosity and permeability distribution do we have then think conceptualize to what extent we have the degree of standard deviation or variance with reference to the mean value of porosity and permeability you got to answer so that you know we can conceptualize you see you first you have to have some idea about how exactly the porosity has gotten distributed in a reservoir is it normally distributed right how about permeability how is it how it has got distributed is it log normally distributed you see now think whatever data you have you know you have some mean value and you also have some variance of standard deviation now you try to look at the value of variance or standard deviation now you see just from the mathematical number for example see if you have 10 data sets of porosity value or 10 data sets of permeability values assume that you are you have given me only 10 data sets of permeability value nothing else from this 10 data i will be able to roughly figure out whether the reservoir is nearly homogeneous or moderately heterogeneous are completely heterogeneous in the absence of any other data how is it possible simple how you have 10 data with you try to take the mean value you have some average value you also take the standard deviation or variance you compute the standard deviation or variance now if the value of the standard deviation or variance is closer to zero having much lesser value it indicates that your reservoir is more or less homogeneous on the other hand if the value no is significant when the variance is significant when the standard deviation is significant it clearly indicates that the reservoir of interest is highly heterogeneous now you see you have not gone gone to the field you are you are not done any other experiment you don't have much data with you with simple 10 data you can roughly estimate you can talk tell about the reservoir resolving just with mathematics now in so as i told if we have a significant deviation standard deviation uh of from the mean value then we cannot simplify the permeability distribution see what we generally do in reservoir simulation whatever may be the nature of reservoir whether it is you know merely homogeneous or moderately heterogeneous or completely heterogeneous whatever may be the case i will have only one average permeability value that's all now you see when your variance or standard deviation remains significant then it literally indicates that the reservoir of interest you know is no more homogeneous it's you know kind of significantly highly heterogeneous if the reservoir is significantly or highly heterogeneous then please understand we can no more use simple permeability value on average value for the entire reservoir we got to use permeability tensor right mathematically i mean you are telling you go we have to use permutation but how about the data where will i go and get the data but because we have to have a value of permeability in nine different directions absolutely not possible so please here what i'm trying to convey i'm not i'm not telling you that you have to get the data you know in all nine different directions no what you need to understand when the when the data about when we bother about permeability data we are not even concerned about its precision while for some other data maybe you know your pvt data or you know other fluid properties you are giving so much importance what i am trying to convey you are feeding input to the package to the simulator you have a bunch of data with you you are supposed to feed right for some data you are so much bothered about precision of data for some other data you are not even bothered about its distribution this is where the problem comes see irrespective of whatever may be your mathematical model numerical model if you we do not justify our input data then it becomes very very difficult for us now you know uh as i told when the permeability i mean when the reservoir is a kind of highly heterogeneous what will happen the permeable reservoir permeability may not be proportional to the square of the pore size generally what we do permeability is proportional to the square of the disquiet square of the port size it will not be the more and more heterogeneity is added into the reservoir you know the relation will slowly get filled up it will vanish we got to come up with new relation so uh we have to have a special relation to currently porosity and permeability in such a heterogeneous voice then regarding relative permeability see the notion of relative permeability depending only on saturation levels essentially results from experiments and as such it is only an approximation to reality for example in a two phase fluid flow system like an oil water system the experiment will heal different relative permeability curves according to whether the saturation of the waiting fluid increases or decreases that is whether the saturation of the wetting fluid is getting imbibed or i mean is it getting drained out so in such cases the concept of hysteresis hysteresis also should be brought in during our conceptualization see the point is we always ignore the hysteresis of relative permeability because we already have a set of equations that reminds very very difficult for us to solve even in the absence of including relative permeability hysteresis so avoiding or ignoring this hysteresis effect is not a big deal but during our conceptualization we should clearly highlight that we have this important assumption with us during our conceptualization itself why is it important because when we try to interpret or forecast the results of relative permeability versus water saturation recollecting this assumption will really help us to forecast the concepts such as reversal of better ability with caution so as a model what is expected from conceptual modeling that we got to conceptualize that is we got to figure out we got to details the list of various physical process one by one various chemical process one by one and various biological processes one by one to start with unless we have strong knowledge on physics chemistry and biology we will not be able to do justice at the very first step itself you may ask me why all of a sudden without any relevance biology comes into picture in reservoir model well it is those indigenous microbes which will essentially clog the pores and in turn will reduce the reservoir permeability as observed in a typical microbial you are we got to understand the metabolism of thermophilic bacteria in order for us to understand the growth rate and decay rates of indigenous microbes associated with the petroleum result these microbes essentially release environmental friendly natural surfactants through its egg treatment as against the relatives costlier chemical surfactants and you know these surfactants you know tend to reduce the interfacial tension between oil and water and subsequently they enhance the oil production and you know you very well know about the role of chemistry as to inject your chemicals like you know alkaline surfactant polymers associated with a chemical you are you got to understand how exactly these chemicals are getting transported and during its transportation how exactly they get diffused how exactly they you know they get dispersed along with their advective motion we got to understand we got to conceptualize the presence of chemical reactions such as precipitation dissolution ionic chain you know and so many other chemical reactions during their mobility towards the sweeping volume so many chemical reactions are associated with the petroleum result particularly during the implementation of chemical you are so now you know we were talking about biology we were talking about chemistry now we are going to talk about the role of physics regarding the physics of the problem we got to understand the displacement of oil by water we got to understand the concept of differential attraction resulting from two different geological units with extremely varying porosity and permeability that will cause differential advection then we got to understand the concept of channeling we got to understand the concept of viscous fingering discussing we got to conceptualize whether the displacing fluid has a tendency to move faster than than the displaced or not we got to conceptualize it then we got to observe whether the fluid fluid interference remains stable or does it remain unstable we go to concentrate we got to observe whether the tons of displacing fluid starts propagating at the interface we then got to understand the relative mobility of the fluid in the horizontal direction with reference to the vertical direction and so on so you see so many conceptualization it's not an easy easy thing not an easy process because again i'm telling you you don't have paper you don't have pen you don't have any data you are not going to laboratory you are not going to feel you are just sitting in a room you are close to your eyes and you are trying to bring in the free diamond reservoir you are in step one conceptual model so think now think about the pressure how many turns we have with reference pressure we call it reservoir pressure average reservoir pressure then pressure in the oil oil pressure water pressure gas pressure capillary pressure and so on are we really going to use all these pressures in the real field scenario absolutely no then then what exactly we require to start with we require only the average reservoir right only one data if it is so then why do we need to solve water pressure oil pressure and gas pressure have you ever think about it and it's in a related capillary equation because no what you need is average porosity average permeability average pressure right that's what you need then unnecessarily why are you wasting your time in finding your pressure in oil pressuring water pressure and gas conceptualizing so where exactly you are using these values what you need is average zero expression but you are solving a separate equation for po i i phase pressure then pw what is pressure and pg gas expression think how you are going to correlate how you are going to translate these phase pressures into average reservoir pressure please also understand these phase pressures are attached with the poor skin microscopic scale and what you project in the name of average result pressure is not at the fourth scale at the macroscopic scale there are the different scale so we got to be very careful in using these pressures you know different kinds of pressures but see in the context of capillary pressure since we have in over two different pressures one for the oil and the other for water we actually need an additional relation what for in order for us to to get a close system of equations and this additional relationship is referred to as the capillary pressure law which essentially results from the curvature of the contact surface between the two fluids so strictly speaking they admit that the curvature depends only on the saturation level of the two fluids which is a kind of huge approximation and this is where we got to be very very careful during our conceptualization i mean will it be feasible for us conceptually to delineate any other dominant parameter that will dictate the fate of capillary pressure apart from water saturation because we got seriously think unless you seriously conceptualize this you will take it for granted that you know it's capillary pressure is a function of only various acids yes approximation is fine but your your all the reservoirs are not always homogeneous we have plenty of heterogeneous so the next question is how exactly to translate phase pressures into average reservoir pressure even before calculating average reservoir pressure how should we go about calculating average water pressure in an oil reservoir say as a function of pressure gradient while doing so did i conceptualize and finalize my reference data like c surface it's not that simply you know you have pressure gradient and you have depth multiplied with it no you must have a reference datum that is very very important for that you know if you can understand the integration principle from reference to you know up to the desired pressure you have to integrate the pressure and then you will get the averages or pressure then if we have the reference of 100 watt saturation then how exactly should we distinguish between oil water contact and free water what exactly decides the vertical thickness between oil water contact and free water can be conceptualized the displacement pressure or the entry pressure as a function of the vertical thickness oil water contact and free water you've got to conceptualize then how am i going to conceptualize the transition zone see if you look at a typical capillary pressure versus water saturation curve the capillary pressure increases up to the entry pressure at 100 water saturation and then capillary pressure further increases with the decreasing water saturation until the capillary pressure becomes infinite at irreducible saturation right now from this virtual plot will it be feasible for us to delineate the zones of oil-free water and then zone where we have more oil with less water and then the zone with less oil with more water and then the fourth zone you know the zone of you know water free oil conceptually you have to have you know conceptualize you have capillary pressure which is water saturation curve and then you can bring in the relative permeability conceptually you have only two plots with you with these two plots in the absence of any other data you should be able to figure out all these four zones conceptually no other data is required why this is important unless we are clear about these four zones then we are not sure about where exactly we should proceed into perforations perforation is well you know i'm at the bottom of the which where exactly we should have preferences and then you know uh we should have some idea about what's going on all these problems will pop up then by default you know we take it for granted that our reservoir is either strongly water wet or strongly avoid always whenever we do reservoir simulation we have only two options no other option because you know it's complex we don't want to unnecessarily get into trouble we want to make our life very simple but unfortunately what we have in reality is neither strongly watered nor strongly oil with what we have is either fractional weight or intermediate with see the point is although you simplify your reservoir model to be either strongly oiled or strongly oiled i mean during your conceptualization if you highlight this very clearly during your conceptualization this particular reservoir you know is more towards fractional vector or this reservoir is more towards intermediate path then it will help us to better conclude our forecast on reversal of vectability in your reward projects you are asked to figure out whether you know by injecting chemicals have you encountered vector builder reversal right so when you when you are concluding better reversal this thing will help you because in reality we do not have strongly water wet nor strongly oil what we have is fractional wet or intermediate then we got to conceptualize the locations of various wets placed within the reservoir and where exactly these valves have the perforations with reference to their oil water contact gas oil contact or free water you know and in the process of conceptualization ensure that you have equally made a balance between fluid flow considering the reservoir pressure and saturation then the mass transfer involved the transport of injected solutes the role of geomechanics considering poor elasticity and finally bringing energy equation representing the reservoir to the end of non-isothermal conditions so uh you know what similarly you know what uh regarding the phase equilibrium i am not a completed step one next thermodynamics part phase equilibrium regarding physically below thermodynamics see when we are interested in deducing the phase diagram for a multi-component natural gas mixture then we got to clearly conceptualize two important phenomena name first one isothermal retrograde condensation where liquid condenses when pressure decreases and isoboric retrograde vaporization where liquid vaporizes as the temperature decreases these two are important phenomena you've got to conceptualize then in facilities operations the understanding of where the process is on a phase diagram it will help help the engineers and operators to avoid extremely embarrassing design and operating mistakes so try to bring in these phase diagrams also during your conceptualization so at the end of conceptual modeling we will have a lengthy list of various physical process various chemical processes and various biological processes now having listed out the individual process again you you get into your three-dimensional conceptualized result you now try to look into those physical chemical and biological process which remind very sensitive or which remind very dominant what for then only we will be able to get rid of all the unnecessary and unwanted physical chemical and biological process please understand nobody else will help you you got to decide and that too you don't have pen or paper with you everything you are doing here in your with your mind mind game because you are still in conceptual mode so you have listed out the various physical process chemical process and biological process one by one now you are cross checking process in physical process number one is it dominant or sensitive yes or no second process is it sensitive or dominant yes or no tick tick tick or no no no no one by one so you are delineating you are getting rid of all the process that remind lesser sensitive or insignificant so what we have now is that a separate list of sensitive or dominant physical chemical and biological process we then have to look at the means by which how exactly a physical process gets correlated with the chemical process how exactly a physical process gets correlated with the biological process and how exactly a chemical process gets correlated with the biological process mind game didn't have to see how are they correlated are they correlated linearly or non-linear then you see the intensity of coupling between physical chemical chemical biology and biology and physical have i mean have they been coupled by what means is it weakly coupled or strongly so finally we have to deduce the intensity of couplings or correlation between various physical chemical and biological processes this is virtually the end of conception one so at the end of conceptual modeling we will have complete list of dominant linearly or non-linearly coupled either weakly coupled or strongly coupled physical chemical and biological process of interest associated with the petroleum reservoir now you see this is this is how you should get into conceptual modeling so we we are really missing this very first step because you know we are not tuned to think in the absence of pen and paper we always want something with this you know some gadget whether it is you know a laptop desktop you know some gadget you have otherwise you know you will not be able to work this is how we have been tuned no conceptual modeling is all about you know bringing your three diamonds from this wire in front of your eyes precisely and that's where you know what uh you will excel in your resource model but also remember that successful reservoir simulation requires detailed knowledge of geological models as well this will immediately put many of us you know into you know out of our comfort zone we will immediately point out that we are not challenges in fact it is necessary to carry out the i mean of course it is not necessary you know to carry out the job of geological model i mean which is supposed to be carried out by geologists but it is the reservoir engineers you know responsibility to understand demand we have to understand the model geology the greater or lesser extent affects all the critical elements of reservoir description like you know size and shape of the reservoir well locations nature of the reservoir fluids fluid flow properties and then driving mechanism and the nature of flow patterns all these things so reservoirs have many features that can be categorized into a number of geological models an understanding of geological principle is very very essential to a reservoir simulation engineer however we got to note that model changes with the time it's not a constant stuff conceptual water will keep on changing as you know when a reservoir matures and when more and more wells are drilled more and more pieces of puzzle are obtainable of course the conceptual model of the reservoir we keep on changing with time in fact in most cases the model needs to be refined continuously well in some instances you know conventional and accepted ideas will have to be discarded and all together you know and a newer model requires to be developed these are all the things i mean uh you will face in reality not like you know conceptual model means once you have decided something it will not get carried out you know throughout your reservoir cycle no it will keep on changing if it keeps on changing then if your conceptual model changes the mathematical model will change if your mathematical model changes your numerical model will change if your numerical model changes then you will have problem in your history matching if the chain continues so that's the reason why we are scared to get into this concept of conceptual modeling at all so the point is we should be flexible enough to accommodate the latest latest developments associated with this wire during the conceptualization process so that our conceptual model also gets updated and improved simultaneously along with the reservoir life cycle so with this you know conceptual modeling part one comes to an end we next we move on to step two mathematical modeling now you can take your pen and paper so far it was all about mind so if you if we have very good knowledge on reservoir engineering principles geology solid dynamics fluid dynamics thermodynamics mathematics you will be able to better conceptualize and if you have any boundaries in between it's up to you well we move on to step to mathematical modeling now as the name itself indicates we require a very strong background on mathematics whatever in order for us to get into the mathematical model see what are we supposed to do in mathematical modeling see from the previous step you have conceptualized the intensity of coupling or correlation between various physical chemical and biological process right now with our mathematical background we should be able to translate the various physical chemical and biological processes into an equivalent mathematics who who will do we will run away right immediately already we are not interested in visual assimilation and if you ask me to translate whatever you have conceptualized whatever you have visualized into equal and mathematics once for all you will run away from resource english because this is a relatively tough job mathematical modeling see in general yeah you know we don't want any mathematics with us we don't want any differential equations to be honest you know we are not even in the position to understand the physical significance of a given mathematical model most of us will not be able to understand the nature and the physical significance of a given partial differential equation we simply borrow from somewhere else and then you know we keep on applying for example if we are dealing with an elliptic pathway differential equation see let us try to understand the physical significance because we keep on playing with equations without understanding the basics there are three different kinds the elliptic pattern from the equation parabolic partial differential equation and in a hyperbolic percentage equation if we are dealing with an elliptic partial differential equation where we do not even have any derivative with reference to time the kind of equation essentially indicates us that the physical system of interest has already reached the steady state condition and in turn we are just trying to estimate the value of the dependent variables within the physical domain given its values along the boundary there is no time associated with this elliptical boundary an elliptical pd which means what in petroleum reservoir we are concerned with production time we got the forecast what will be your production at the end of five days ten days one year two year three years which means so you can easily rule out that you will not be dealing with elliptic pde so easy because it doesn't have any time component then what are the other two options either you've got to deal with parabolic pde or you've got to deal with hyperbolic pd right now see when we deal with parabolic or hyperbolic pde it essentially indicates us that we are concerned with the initial boundary value problem here we do have the partial derivatives with reference to time and hence such partial differential equations are addressed as time margin problems now how exactly to differentiate the hyperbolic pd from parabolic pd see when we try to solve a transient parabolic partial differential equation we will always end up with relatively good numerical solution at relatively larger time moments how is it possible this is because a parabolic partition equation will have fluctuations it will have perturbations it will have noises to start with that is during the initial time periods it will have fluctuation it will have noises however with larger time levels all the introduced numerical errors will get suppressed with the time and it will have a closer match with the exact solution so if you are dealing with the simple parabolic partial differential equation and if you want to show the verification plot of your numerical results with the existing analytical solution all you got to do is run your simulation for a relatively larger time level and project your verification part in other words all the noises are associated only during early timelines this is because mathematically if you look at if parabolic pde implies that i mean every parabolic reading it will try to reach a steady state condition with larger time levels mathematically this is what its nature for example in a petroleum reservoir the pressure pumps will get diffused completely when it reaches a steady state condition so it is not a great deal just to solve a simple transient parabolic partial differential equation numerical even if we commit mistakes that is even if errors are introduced due to the selection of the discretization methods or so the parabolic nature of partial differential equation will try to eliminate all the errors with the time this is the beauty of a transient parabolic particle differential equation that's the reason why you always have diffusivity equation in the absence of hyperbolic term are you getting now if you have parabolic equation mathematically it will always try to reach steady state condition whether you like it or not that is its nature mathematical mathematical nature unless you understand mathematics you will not get it but the moment you bring in hyperbolic term it will be different now let's try to understand what exactly will happen with the hyperbolic pd like what we have in buccal liberating which in bachelor level at every equation what we have is a hyperbolic partial differential equation so if we have a hyperbolic partial differential equation what will happen hey when you when we try to solve a hyperbolic partial differential equation this is where we have the real challenge why is it so because mathematically a hyperbolic pde is conservative by nature in other words it will try to conserve the system properties unlike the kind of you know diffusion uh as observed in parabolic particle equation in other words you know what any error introduced when solving a hyperbolic partial differential equation it will get accumulated with the time and finally it will lead to convergence and stability issues so a hyperbolic pde is similar to the lifestyle of a rigid person in the absence of any flexibility while a parabolic pde is like the lifespan of a common man where as a kid he will be hyperactive and then when you get into your adolescence you acquire some knowledge and wisdom and as a result you become more mature and silent the oscillations become suppressed and at a later stage we become immobile and philosophically trapped which is as good as you know reaching a steady state condition initially you have oscillations then oscillation gets suppressed and finally you have steady state constricts this is the nature of parabolic pde but hyperbolic pd is rigid very rigid straight line it will conserve its properties so you you should try to understand the mathematical nature of these partial differential equations before you get into reservoir simulation then it will really help you how in your simulation process now in mathematical modeling we got to convert that is we got to translate our conceptualization that is our conceived figure should be into equal mathematics right that's what i was talking about so each and every process listed at the end of conceptual model requires a translation that is virtual observation needs to be converted into equal mathematics you see you see here virtual observations actually you have seen right your reservoir whatever you have seen virtually now you got to convert into equivalent mathematics this is what mathematical modeling is all about have you really done this now you see though you are a reservoir engineer in case if you do not have a sound mathematical background you will not be able to get into mathematical component mathematical modeling component at all that is the very reason why most of the reservoir engines have no clue about deducing your mathematical model so what is expected from a mathematical model whatever you virtually have seen in your three dimensional reservoir you got to translate your visuals that is the nature of the fluid flow into an equivalent mathematics equivalent mathematics this is where i mean it will differ it will differ from person to person you may have sound mathematics knowledge i may not be having sound mathematics so whatever mathematics knowledge i have accordingly i will convert but you may convert into in better equation so even mathematical knowledge it will differ from person to person you have to be careful so you may think about innova generally what we think had the equations which we are dealing with had these equations been a simple algebraic equation without a partial differential equation our life would have been very simple right then why do we require a differential equation why are they making our life so complex why do we need partial differential equation see i keep visualizing fluid flow through complex pores associated with the petroleum reservoir it is not a single phase fluid flow it is a multi-phase fluid flow having formation water oil and gas it's not a one-dimensional wire where we have a single line in the absence of any thickness what we have is a real three-dimensional reservoir we are not dealing with an incompressible fluid in a petroleum reservoir what we have is either slightly compressible or fully compressible and we are not dealing with flow through pipes since we are dealing with flow through porous medium i need to locate the presence of weak or strong inertial forces if you have inertial forces for some or other reason then my fundamental assumption will be at a what is the fundamental assumption flow through a porous medium will have significant friction and in turn the kinetic head associated with the knowledge equation can be gotten rid of so what we have is the hydraulic head resulting from the summation of datum head and pressure head in the absence of kinetic head based on that we have reduced darcy's law now we have no rights to bring bring in any inertial forces in the picture now i need to ensure that there are no hypermilitizones or fractures or any other heterogeneity within the reservoir which may contribute initial forces because if there are inertial forces then i will be violating darcy's law so now when i try to look at the flow of fluid through pores associated with the result what i essentially require is that i need a mathematical equation in order to translate the physical process on the mobility of oil and gas through this complex continuous core system so now if i am mathematically not sound then maybe i will only be able to translate the physics on the mobility of oil and gas by a much simpler algebraic equation an altitude equation can talk about what's the problem with algebraic equation an algebraic equation it can it can tell us about whether it will increase or decrease of a particular parameter or at the maximum it can tell us that a particular parameter will vary radically or cubically or in general you know non-linearly now what an algebraic equation cannot tell us this is very very important because now we are in mathematical modeling step algebraic equation cannot tell us how a particular parameter varies in response to the variation of so many other parameters and this is where we got to introduce partial differential equation which essentially imposes relations between the various partial derivatives of a multivariable function while order differential equations form a subclass of partial differential equations corresponding to functions of a single variable once we decide we would prefer partial differential equations instead of a relatively simple algebraic equations then we really got to think about well positiveness where we should have an unique and consistent solution for the continuously varying dependent variable in the name of you know mathematical modeling we cannot have some equations where we will end up with multiple solutions we should have only one solution and that too that solution should be consistent you see how careful we should be in mathematical modeling when you try to translate your visuals into mathematics you should come up with some equation which should in this case partial differential equations which should have unique solution which should be consistent but please note that even well post problems can be ill condition where small changes in data lead to large errors in the solution in general a well-conditioned problem will have a low condition number which essentially depends on the maximal and minimal eigenvalues of the given matrix so in mathematical modeling particularly when we try to characterize fluid flow through a petroleum pressure we will end up with a partial differential equation now it's our duty to provide the required number of initial and boundary conditions for a given partial differential equation so how exactly to figure out the required number of initial boundary conditions just look at the spatial derivative in your partial differential equation then look at the highest order of the spatial derivative present this highest order will provide you the required number of boundary conditions similarly you try to look at the temporal derivative in your partial differential equation then you look at the highest order of the temporal derivative that is present in your equation this highest order will provide you the required number of initial conditions for example the first order wave equation will have one initial condition and one boundary condition so at the end of mathematical modeling we will have a set of partial differential equations along with their initial and boundary conditions so we are supposed to have a mass conservation equation and a momentum conservation equation when you actually want to deduce a momentum conservation equation you should really think about why can't we apply already existing naver strokes equation because you are a mathematical modeling step you just like that you know okay somebody has given you some some text or some paper and you can't cut and paste here you should think why can't we apply why i can't make use of already existing momentum conservation equation that is navier stokes equation what is the problem with the navy state equation why can't we apply neighbors equation for in a porous medium where exactly is the problem now you know why did darcy you know why why did we require darth vader uh to come up with a separate momentum conservation equation now let us try to understand what exactly neither stokes equation physically tell us see that a fluid parcel fluid partial acted upon by forces what are the forces surface forces and body forces you have two different forces when the fluid parcel moves from one point to another point how exactly the fluid parcel gets accelerated what does it never stokes you can talk about how exactly a fluid parcel gets accelerated when it gets transported from point one to point two that's all now in this equation in porous medium we will not be having kinetic head inertial forces in black so let us ignore let us remove local acceleration kinetic acceleration we still have only surface forces and body forces right now what is the problem why can't we apply navy strokes equation in a porous medium we generally so so the question is even after getting rid of inertial forces local and convective acceleration why can't we apply neither stokes equation a force medium see the if you look at navy stokes equation let's go through pipes the problem is we have a well-defined boundary on the microscopic scale or at the poor scale when you talk about flow through pipes now the question is can you deduce is it possible for you to come up with the well-defined boundary can you come up with a well-defined boundary at the microscopic scale when when you are trying to characterize flow through forex medium this is a simple question if we have an answer for that there in the matter what what was the question do you have a well-defined boundary at the post or at the microscopic scale where in flow through porous medium we don't have that's a problem at the port scale or at the microscopic scale it is not possible for us to deduce a well-defined boundary and this is the very reason why we will not be able to make use of no naver stokes equation and dorsi all the way reduce this equation but please understand that you know this is where you know we introduce the concept of representative elementary volume or even representative elementary volume it is the smallest volume over which a measurement can be made that will ail the value representative of the whole please understand for volumes smaller than representative elementary volume a representative property cannot be defined i don't know how many of you are following this because those who are doing particularly experiments core flooding please get this concept very clearly i am again repeating when you deal with a volume that is smaller than representative elementary volume for those things a representative property cannot be defined and the continuum description of the material for those cases involves statistical volume element or stochastic volume and random fields do you understand what exactly i try to convey if you are dealing with the parameter at a scale that is lesser than representative elementary volume that is lesser than darcy scale then you can no more use continuum concept you can no more make use of differential calculus you can never make use of our different liquid i mean whatever fluid flow equation you have diffusive equation cannot make you soft you have to think about stochastic volume element or random fields so particularly you know in lab setup if if you are deducing data on interfacial tension or contact angles which have been measured through a smaller volume than the representative elementary volume a representative property cannot be defined and the continuum description of material involves stochastic or statistical volume elements and random phase above all at the poor scale we have different varieties of complex boundary conditions in the form of various sizes of solid grains surrounded by mobile flowing hence it is nearly impossible to deduce a constant well-defined boundary at the fourth scale that will describe fluid flow of the forest medium so what so i cannot apply already existing navigators equation and that's the reason why henry darcy all the way deduced his darcy's law by doing a series of experiments despite he being very very serious and bedridden in the hospital so we now have a momentum conservation equation in the form of that islam by substituting this law in the main conservation equation we'll nail the fluid flow equation right what is the time now how long i have taken i'm not sure now i'd like to add you know a few more points if you are uh i don't know how many of you interested here uh can i continue or would like to wind up the next five ten minutes you can continue yeah you can't continue see i would like to add the danger associated with this mathematical application see the consistent use of mental image that is your conceptualization what happens a reservoir model has you know serious danger see the problem is for you when you are in conceptualization you have to be very careful those who are in step one that is in conceptual model for those guys the model itself can become reality to the reservoir engines sophisticated reservoir calculations particularly mathematical models have [Music] almost they have an hypnotic quality higher end max and higher in the programming codes etc but still it is absolutely necessary for us to ask whether the answers from the model results are really relevant while developing the cash flow for a producing company so at the end of mathematical modeling we will have a weekly or strongly coupled non-linear a set of you know non-linear set of partial differential equations with required number of initial conditions and boundary conditions this is this is where when we will we will complete our mathematical morning step two is over so what is so we have now a set of non-linear algebraic partial differential equations with respective initial conditions and boundary conditions now we are getting into step three numerical modeling see finding numerical solution to the deduced mathematical model here we need to think about accommodating a real field reservoir within a two-dimensional box or three-dimensional box what we have to do is that we got to subdivide the numerical solution domain into a network of grid blocks either in two dimension or three dimension right in one dimension it may look as simple as the oil volume entering a grid cell during a time increment the you know delty minus the oil volume leaving that cell during the same time increments equals the change in oil volume in the given grid block and the size of a grid block is generally selected based on you have to select the size of the grid block how do you select the size of the grid bar you need to select the grid size based on reservoir geology and size of the reservoir then based on the data available for israel description then based on the type of the fluid displacement or depletion process to be modeled then based on the numerical accuracy desired then based on the past and anticipated field development then based on the available software options then based on the objectives of the simulation study then based on the competence of the simulation engineer and then based on the available computer resources time constraints and project budget you see you've got to deduce the size of the grid block based on so many things but in reality what we do directly we take some some value 10 centimeters 50 centimeters 1 meter 5 meters 10 meters without getting into know without answering for these questions so you have to be careful just like that you know we should not select the width of the cell nowadays you know they have varieties of grids that offer local grid refinement like hybrid grading uh stream tube grid uh waterline grid dynamic grid etc in fact you know local grill say local grid refinement will definitely improve parameters like water oil ratio and gas oil ratio predictions when sharp saturation gradients exist near wells as encountered in coding problems no we have to really we have to be you know very smart in selecting our grids now back to the basic grid block see the volumetric material balance equation needs to be written for each fluid phase and for each grid block thus for each grid block we have the values of pressure then we have oil water and gas saturation values then its associated time level see if there are m grid blocks we will then have m equations for each phase suppose if you have three phases oil water and gas then you need to multiply by 3 that is we will have a total of 3m equations now the solution of these equations is the major core of reservoir simulation please remember that the phase flow rates between each grid block and this adjacent block need to be represented by darcy's law which is again to be modified in order for us to accommodate the relative permeability concept further all the reservoir properties such as porosity and permeability and all the fluid properties such as pressure saturation temperature and fluid composition are generally assumed to be uniform throughout a grid block based on the representative elementary volume otherwise we can also vary these rock and fluid properties from one grid block to the another in fact they can also vary the fluid properties for each grid block varying as a function of time during the simulation period it all depends on your comfort zone but please remember they are not entitled to vary any rock or fluid property below this representative elementary volume very very important if you have really understood the meaning of this particular statement then you will really think about coupling the values of interfacial tension that sigma and then contact angles you know whichever you you got it from your lab directly with darcy's law you have to be careful well back to numerical models that we are in third step now here i will confine myself to numerical simulation and i will just let you know the fundamental differences between finite difference finite element and final volume so if you consider finite difference technique see any derivative of a function f x will remind valid only in the limit del x tends to zero but we want this del x to remind finite not ten to zero it should remain finite for this purpose we introduce an equivalent approximation of the derivative and as a result of which we get forward backward and general differences but how good are these approximations and this is where tyler series comes into picture which are essentially expansions of a function f of x for some finite distance del x to f of x plus del x so toilet series essentially provide us the information on what is the approximate value of a given function or its derivative at the desired location and how can we calculate the weights for the neighboring points this is what tyler series talks about now the catches in the finite difference technique we do not have any control over the value of the dependent variable what's our dependent variable may be pressure or saturation pressure and saturation we do not have control over the value of these dependent variables pressure and saturation where between any two successive nodes between any two adjacent nodes in a fine in finite difference technique this is a big big problem big limitation so when using software packages what you do you simply take your salvage to be one meter five meters ten meter that is del x you take five meters ten meters just like that now you see what is the big problem in finite difference in finite difference you have discretized your solution domain into number of nodes so many nodes are there what is the problem with finite difference it is not possible for me to find the value of the dependent variable that is it is not possible for me to find the value of pressure or saturation where between any two adjacent no it's not possible now you see what the theory says this cell wave should be tending to zero then only finite difference will try to match exact solution but what we do in reality we take our del x to be meters 1 meter 5 meters 10 meters 20 meters then how will your results you know will replicate reality see this is a problem finite difference you got to understand the limitation of finite difference so you know we have no control over the value of pressure or saturation between any two nodes so this is the limitation now now what should we do next then came the concept of finite element method in finite difference over now we move on to finite element what did they do in finite element in finite element they call it element what is the element now you see between any two adjacent node or consecutive nodes they introduce an element one line that that they call elements what for they have introduced they have introduced this line this element in order for us to have control over what control of dependent variable that is how exactly my pressure is getting distributed how exactly my saturation is getting transported from one node to another node through this element this is the funda finally finally how do we how do we control we have introduced a guess function through this element what for to have a control control of pressure or saturation between these two nodes through this element this is the fund of finite element technique so definitely finite element technique is better than finite difference but now i have a question for you in finite element technique you have so many triangles right now try to focus try to look at a triangle which is having the least possible area smallest area you have a triangular mesh so many triangles are there right what is that i'm asking try to find try to focus yourself to this smallest possible triangle now my question is what happens to a pressure what happens to a saturation within that triangle do you have answer for it if you have fracture if you have any heterogeneity how will you capture we have no clue nobody has no idea so this is the drawback with finite element so in finite element what is happening within the triangle within the smallest possible within within the triangular zone i do not have any control over my pressure or saturation this is a problem with finite element technique then later we went we moved on to finite volume technique and improved technique you know in finite wall what is the fundamental finite volume technique here we do not miss any spatial region within the reservoir domain we have not missed we will not be missing any any any a special special regime here the physical domain of interest is subdivided into n in a n number of smaller volume sets we then integrate the value of the dependent variable over each sub cell and then get an average value since this finite volume method is based on conservation principle this method reminds more reliable to solve fluid flow problems like flow through petroleum is y now whether it is finite difference or finite element or finite volume in all these techniques we essentially convert complex partial differential equations into a set of linear or non-linear algebraic equations where we are translating we are converting differentially partial differential equations which are complex into relatively simpler algebraic equation this is what this finite difference finite element or finite volume has done now what we finally get after getting you know set of algebraic equations what we finally have is a x equals b form what is the a x equals b a is your coefficient matrix x is your unknown column vector and b is your known column vector on your right side now if it is if your coefficient matrix is small when when will it be small if your reservoir is say one centimeter if your resolve length of the reservoir is one centimeter width of the reservoir is a point one one like you know one centimeter rod and thick xyz all are you know one centimeter one thing that one centimeter then your coefficient matrix will be very small number of nodes will be very small but in reality the length of the reservoir runs over several hundreds of meters runs over several tens of meters thickness several tenths of meters so what is happening you have numerous nodes plenty of nodes millions of nodes billions of nodes your coefficient matrix is so large so huge now so it is not possible for you to simply go ahead with matrix inversion you can't do that um x equals a inverse b you can you can't do that this is where you you you got to solve this unknown column vector either by direct methods or iterative methods now you may be wondering to know just by looking at the nature of the coefficient matrix you will be able to understand how exactly your reservoir is there in the field scenario you understand are you getting what i'm trying to convey without you getting into field you can comment just by looking at the nature of the coefficient matrix whether your field is more or less homogeneous or moderately heterogeneous or completely heterogeneous how look at your coefficient matrix if your coefficient matrix is a regular abandoned matrix then you are dealing with the system which is nearly homogeneous on the other hand if you if your coefficient matrix is a sparse matrix what do you mean by sparse matrix you will not be having elements in in a banded way you will have elements here and there randomly in the coefficient matrix so if you look at your coefficient matrix you will be able to comment about the nature of the reservoir without getting into the field you see the strength of mathematical numerical modeling just by looking at how exactly you have ended up with your uh coefficient matrix you will be able to comment the nature of resurrection so there are you know so many things now you know finally you have to verify our numerical results with the existing analytical solution and also validate with experimental data you know uh or you know field data please remember mere verification under validation of your numerical results does not ensure that you are on the right track because a profile from a numerical solution can still match either with experimental data or field data despite being undergone altogether different physics it it could have undergone different chemistry it would have undergone different biology this is a next higher level of doing surgery at the deduced numerical results we should also keep in mind that we have fed data from very different scales as i told you know about nanopore core we have very different skills here we should be very careful while dealing with the coefficients are constants associated with the given mathematical model because i may trade some coefficients to be a function of only independent variable while you may treat the coefficient associated with the equation to be a function of dependent variable now you see we have same equation but now i am talking about the coefficients attaching the equation same equation same problem but the way i handle the coefficients may be completely different from the way you handle the coefficients how can it be different i may handle the coefficient to be a function of only independent variable simple on the other hand you may handle the coefficient to be a function of dependent variable what is the difference the moment you make the coefficient to be a function of dependent variable then the equation will become non-linear it is difficult to solve that's the reason why generally you know people try to avoid that depend you know they don't want coefficients to be a function of dependent variable by default they will treat it as a constant they want to make their life simple they don't want to you know make complexities see it is not that voluntarily deliberately we are introducing complexities most of the fluid properties if you look at they are dependent on pressure but still you know we try to treat you know as a constant see in in the context of numerical modeling the concept of numerical dispersion reminds very very sensitive it essentially refers to the spatial truncation error in infinite different simulator results in physical terms error generally appears as falsely smeared spatial gradients of water saturation in water flooding temperature in steam flooding solvent and miserable flooding and chemical agent in chemical flooding this excessive smearing occurs primarily in the aerial direction that is x y and if it is not controlled properly we then have model results in two early calculated breakthrough times of water at production levels this numerical dispersion generally increases with increasing aerial grid block sizes also numerical dispersion is an inherent property of reservoir simulation this numerical dispersion is due to the representation of the reservoir by cells or grid blocks in which the properties are averaged when a saturation front enters a grid block essentially it is spread out over the grid block in order to arrive at average saturation values however numerical dispersion can be minimized by decreasing the salvage at the expense of increased cpu time see apart from numerical dispersion we also got to understand the concept of instability numerical techniques do not yield exact solutions the reason error associated with these numerical solutions this error sometimes grows very rapidly causing the numerical solution to blow up in other words the numerical solutions become physically unrealistic the most common cause of this instability is excessively large changes in pressures excessively large changes in saturations during the given time step usually this condition may be improved by reducing the size of the time step similarly you know see when we have the same set of equations same initial condition same boundary condition and the same numerical method as i told we have to be careful when we handle the coefficients we now we never know the importance of developing a conceptual model and a mathematical model before venturing into numerical model now having developed a good numerical model we got to get into history match the very first step in history matching is to calculate the reservoir performance using the best data available the model results are then compared with the field record histories of the webs if the agreement is not satisfactory you know what then the data such as porosity permeability saturation relative permeability etc they need to be varied from one computer run to another until a match is achieved the simulator is then used to predict the performance for alternative plans of operating there is a wire see the behavior of the reservoir is influenced by many factors porosity permeability thickness saturation distribution relative permeability you know all so many parameters that are never known precisely all over the reservoir all these data porosity permeability thickness saturation relative removability all these data are never known precisely all over the reservoir so what the engineer arrives at is only a combination of these variables which results in a match this combination is not unique so it may not represent precisely the condition the actual condition of the result when the simulator after a match is used to predict it is not sometime that the physical picture of the reservoir described in the simulator will give predictions sufficiently close to the actual reservoir performance but in general the longer the matched history period the more reliable the predicted performance will be further in reality for a given reservoir problem you know everyone will have our own idea geologists geophysics reservoir engineer and so on so what we require is a one-man army as a reservoir engineer you got to know the reservoir characterization from geological perspective from geophysical perspective from a production perspective from a drilling perspective from a mathematician perspective and so on then only we will be able to forecast or interpret the reservoir characteristic reasonably to some extent because characterizing a reservoir means you are not supposed to have any boundaries between different allied disciplines and if you try to look at the problem of interest holistically in order for you to succeed in a real case scenario now you know i think we have taken a couple of hours i would like to stop here if you have any questions you can proceed okay thank you so we can now start questions okay so if anyone has any question you can you can unmute yourself and ask your questions yeah one of the questions uh um [Music] how about using machine learning and not ai techniques according to you which technique is best for resource simulation well you know i will leave it uh listening to industrial experts see in machine learning or artificial intelligence you are essentially dealing with a lot of data right without for example if you are a fresher and without having enough experience or background if you directly venture into dealing with the data i don't think you know uh it may not help you yes the point is you should try to understand the physics the chemistry the biology of the reservoir before you can deal with the data definitely i mean you can deal with data but my point is having understood the physics of the problem having understood the characteristic characterization you know by all means completely then you can handle you can think about a i or ml i personally won't suggest you know a undergraduate or graduate student directly to get into a i remember because what happens yes when you deal with different kinds of algorithms it will be very very you know attractive but without understanding the physics of the problem only dealing with the data i don't know to what extent you know it will help the student so industrial experts those who have worked for 10 years 15 years 20 years those who have fairly good idea about reservoir characterization they will definitely can use a i or m1 having enough background having enough knowledge on reservoir characterization they can really wonders using a ai ml but not the beginners wow during one dimension simulation while formulating mathematical models of pde how to decide which type of boundary condition the inlet and outlet well as i told you know when you see one of you have asked about one dimensional problem the one dimensional problem means what what we have is only one line without any thickness that is whatever one dimension right if you don't have thickness and if you have one line how can you how do you think you will be able to justify characterizing miserably but what does it physically mean your rock properties and fluid properties vary only along one direction while in other two directions all the properties remain uniform do you think all your rock properties fluid properties and rock fluid properties will remain uniform in other two directions will it vary only in one direction you know one dimensional problem it's it's really i mean helpful uh as stage one that is you cannot directly learn 2d problem or 3d problem first you have to learn one dimensional problem then you got to move into step two two dimensional problem then you can learn three dimensional problems during your learning curve you may have one day two day and three days but for your entire work deducing conclusions based on one dimension only will be too simplified for example if your reservoir is highly homogeneous are nearly homogeneous and isotropic one dimensional problem is fine but in reality we do not have nearly homogeneous isotropic reservoir what we have is kind of heterogeneous reservoirs the moment we have heterogeneous and if you are still dealing with one dimensional problem you know our forecast may not be justified so you've got to be careful so if you think your reservoir is you know completely homogeneous isotropic you can very well go ahead with one dimensional problem on the other hand if you think your reservoir is significantly heterogeneous then better to avoid one dimension and try to come to the 2d problem at least so that your forecast will be more reliable will be more reasonable uh i want that i i don't understand one of you my mother time my mother time now um i know you know english and tamil but i don't know about a motivational for the students well uh uh what's that um garbage in garbage this is a milestone of professional software driven yeah most of you know have raised questions about using software please understand i am not talking about you know using only numerical model as a student when when you are in academics try to learn this modeling technique so that you will be able to understand the fundamentals you will be able to understand the basics of conceptual modeling mathematical modeling you will have some idea about differential equations you will have some idea about initial condition boundary condition nature of apache differential equation see all these things you are trying to understand during work when you are attached to the academies once you are complete i mean after completing your academy once you get into industry definitely you will be using software packages but when you use software packages these basic learnings in your academy during your undergraduate graduation will help you to better predict your package results please understand you have package and you are going to forecast you are going to take a decision based on the package results interpretation is going to play a very crucial role so if you have a very strong basic understanding of conceptual and mathematical numerical modeling it will help you when you use your package results in your industry later in the life so part during the early stage try to learn you know mathematical conceptual model mathematical model and numerical model then later in life you make use of all these software packages so that you can confidently forecast confidently predict the reservoir performance because from software package if you generate results if you ask a fresher his perception will be different if you ask an experienced industrial expert his response will be different same result the way you interpret the way you forecast is going to be different so my suggestion is as an academician if you can spend more time on learning the basics like conceptual mathematical numerical modeling it will really really help you when you get into industry and where we mean when you start using packages so your interpretation and and forecasting will be much much better later in your life uh then you know uh one of the best i have listened okay when you experience a numerical dispersion at a given time step reducing the good size and time the only solution to resolve the issue can you accept a simulation result with only one numerical dispersion at a given time step well see uh numerical dispersion one of you have raised the question on numerical discussion as i was telling previously suppose you have a plot you have a curve from the package you have a package that relates you've seen whatever you have some package with you and you have fed some input and you have got some output and you have some you now you have a profile some profile some curvilinear profile and you got to understand what exactly the profile conveys now you see when you use package and you have gotten the profile now i am not sure i do not know whether the profile is correct or not now the source of error can be associated either with the kind of numerical solution technique that has been used in the package are the the source of error can be the kind of mathematical equation used with the package are the source of error can be due to the lack of data improper data are the source of error could be the insufficient physics attached with the mathematical model now you see the source of error in a given profile can be from very different scenarios how will you find where is the source from whether you have done i mean the error has resulted from your selection of numerical solution technique or the selection of equation or you have missed some physical process or is it because you have missed some chemical process or is it because your data whatever you are fed is not you know appropriate or is not correct how will you know what is the source of error so unless you are very strong on input data unless you you are using very strong no very good numerical solution technique it is very very difficult to find out the source of error you know from your packages it's very difficult that that is where you know i told you got to spend some time on mathematical modeling you got to spend some time on numerical modeling so that you will have some idea about possibly this could be the source of error because you are solving a huge two-dimensional or three-dimensional result it's very difficult very very difficult to point out the source of error and you know particularly with one data permeability data mostly because that one data you know [Music] we we use a distribution and what kind of distribution you use for permeability is a very big question you may use some distribution i may use some distribution some other distribution you know not only you know rock properties all the properties so we have problem while feeding the data we have problem whether all the physics and chemistry and biology whether all these processes have been converted into equal mathematics we are not sure and then even if we have a very good mathematical model do we have proper numerical model we do not know because we are just feeding some input and we have some output so how do you figure out numerical dispersion without understanding what kind of equations have been used what kind of boundary conditions have been used what kind of discretization techniques have been used in the package directly i mean we cannot comment on numerical dispersion so this is where you know i would suggest you should have some knowledge on conceptual as well as mathematical modeling i mean also numerical modeling before you start analyzing before you start interpreting results from the package uh your suggestion on doing research on petroleum i i have i do not know about uh i mean i don't have an answer for this question but what i personally know is oil and gas will be there for at least for next 40 50 years without any second thought uh we cannot divide off you know we cannot get rid of oil and gas from our lifestyle for next few decades so no question of you know replacing oil and gas by it's not replacement maybe you know the percentage of other sources may increase in the near future but we have to deal with oil and gas but about petroleum research i have only i mean one one answer from my perspective you see in all other disciplines mechanical engineering civil engineering chemical take all other disciplines there are plenty of people who pursue phd in turn there is a plenty of r d associated with other disciplines whereas in petroleum engineering the percentage of r d is very very less why is it so because the moment you complete your beta you are getting placed with very high salary right so why do you want to pursue higher studies this is this is the reason for last 30-40 years you get placed as soon as you complete your undergraduation so what is happening in petroleum engineering we have relatively lesser people getting into higher studies in turn we have lesser people for r d so research you know the kind of i don't know about north america but in indian context kind of difficult you know unless you focus on the basics and fundamentals you can't keep on you know uh running your show [Music] with applications alone you got to give some importance to the basic research also so i personally feel we are not giving enough importance to basic or fundamental research in petroleum engineering we are all the way concerned about only applied research so how long r d will sustain in petroleum engineering i don't [Music] know well one of you have asked how to visualize conceptual mode how to visualize it's like meditation you've got to meditate you've got to bring in your three-dimensional reservoir in front of your eyes it's not a joke see for that that's well i mean you have to have backgrounds on reservoir engineering principles geology principle geophysics principle geo-mechanics principle mathematics principle you have to have enough backup in order for you to bring in the actual uh three-dimensional reservoir in front of your eyes you need so much background so getting uh three diameter reservoir is not easy so my suggestion for you is try to break your boundary and try to learn reservoir characterization from geological perspective geophysical perspective from chemical engineering perspective from mechanical engineering perspective from drilling perspective whatever we don't have any boundary with this when you break the boundary then you will try to slowly get into real conceptualization until you are stuck with a particular discipline like i am a geologist i am a geophysicist i am a reservoir engineer it's very very difficult to conceptualize you've got to break your boundary and come out well i would like to stop here uh so uh i i i mean i would like to really thank all the guys who are sitting here patiently for almost uh i think it is nearly uh two and a half hours i think uh so today i have tested your patience i think um thanks again now i would like to hand over this section to uh mr abdullah so ah abdullah i mean you can take over thank you professor and thank you for your efforts and time and this very very interesting session that was admired by all the attendants thank you again and thank you to all the attendants and please remember to fill into the certification form that was sent into the zoom chat also if you are interested into our link is to course or pvt uh and the equation of estate modeling you can you can fit into the registration form that also will be sent now to the zoom chat thank you again and uh remember that on the youtube channel of reservoir solutions we will upload this session also thank you again yeah thank you all you