[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Speaker: Nay wells are affected by a well\Nskin, a low permeability layer that
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,surrounds the well and causes the drawdown\Nin the skin to be less than- er to be
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,greater than the drawdown that\Nwould be expected otherwise.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, we can see this in the, in the sketch.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This line here is the expected drawdown\Nusing, uh, the Jacob analysis, or
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,perhaps some other analysis, but as we\Nget right in the vicinity of the well, we
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,see that there's a low permeability zone\Nhere, and the head goes like so, follows
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,this dashed line.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And as a result, this is the expected\Ndrawdown based on our theoretical analysis.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It is using the properties of the aquifer,\Nuh, out here away from the well
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,[stammering] in this region, but in fact\Nwe observe that the drawdown at the well
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is here, so the drawdown is greater, um,\Nand that results from the extra headloss
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,due to the well skin.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we want to characterize this, and one\Nway to characterize it is to use the well
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,efficiency, which is the ratio of the\Nexpected drawdown from our theoretical
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,analysis to the observed drawdown,\Nwhat actually occurs in the field.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we need a way to calculate what the\Nexpected drawdown is, and we can do
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,this with the Jacob analysis.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,What I'm showing here is a version of the\NJacob analysis that's set up to calculate
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the head- er I guess this is the drawdown\Nhere, um, as a- at a particular time.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, the important thing to recognize is\Nright here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The radial distance that we're using here\Nis the radius of the well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,What we used in the previous analysis\Nwas the radial distance of the monitering
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,well, where our data were made.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,In this case, we need to use the radial-\Nthe radius of the well itself.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This time here, that's the time, the\Nelapsed time, for a data point that we're
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,gonna use to determine the observed\Ndrawdown.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The calculation goes like so: we put in\Nthe observed time and the radius
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,of the well, and everything else is pretty\Nmuch the same, the s and the t we've
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,calculated using a monitoring well out\Nhere in the formation.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The performance here of the monitoring\Nwell, the head in the monitoring well, is
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,not effected by the skin, so when we\Ncalculate TNS from the monitoring well
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,data, we're getting something that's\Nreally just affected by the, um,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,formation properties.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And there is the same T and this is \NQ, which we already know, so we can
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,go and calculate what this is, this gives\Nus an expected drawdown, which we then
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,take the ratio of, that calculated value\Nto the reserve drawdown at that time.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That gives us the well efficiency.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Note also that it's possible, under some\Ncircumstances, for the well efficiency
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,to be greater than one.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,In many cases, and in the one that I'm\Nshowing here, there's a low
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,permeability region around the well, and\Nthat often occurs as a result of drilling
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,or perhaps bacterial fouling, uh, during\Noperation of the well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But if possible that the well has a, uh,\Nhigher permeability region around
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,it, um, for example, here's our screen, \Nand if it, if the well has been
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,hydraulically fractured, for example, or\Nif the well intersects a region at its
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,higher permeability than the formation,\Nthen, uh, the drawdown that's expected
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,might be greater than the observed \Ndrawdown.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, if this is a more permeable region, \Nthen we might have something that
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,looks like this, then goes like that.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so the gradient here is less than\Nwhat's expected.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The specific capacity of a well is the\Npumping rate, Q, divided by
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the drawdown.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So during a transient test, this is going\Nto be constantly changing.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If we hold the pumping rate constant, the\Ndrawdown will be increasing, and so this
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,will be decreasing.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This ratio.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But, if we have a shallow well, and we \Npump it for a while, then the drawdown
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,tends to stabilize, and the well goes to\Nsteady state, in which case, the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,specific capacity reaches a constant \Nvalue.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And this is a very important value to \Nknow because for a reasonable
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,range of drawdowns, in many cases, \Nthis constant, or this, this uh, specific
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,capacity is constant.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So if we know what it is, then we can\Ntell what the drawdown will be for
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,a specific pumping rate.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And this is really, probably the best way\Nto characterize the performance of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,a well, at least if you're interested in\Nhow much rate you could get, how much
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,water you could get to come out of\Nthis well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,For a specific, if you know the specific\Ncapacity, then you can tell what the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,drawdown will be if you pump it at \Na certain rate.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So for example, if there is a certain \Namount of drawdown that you can't
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,exceed, that'll be the maximum drawdown\Nthat you could tolerate, then you can
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,determine what the pumping rate would\Nbe when you reach that, if you were to
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,hold that, um, that drawdown to be \Nconstant.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, so, for shallow wells, the way that \Nthey go to steady state is by interacting
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,with the stream.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And the way that you analyze this is to\Ntake a well over here, let me back up a
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,second, so this is what we're thinking is\Ngoing on, here's the well, over here this
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,red circle, and we're pumping out, and \Nthere's a stream over here, shown by
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,this blue band.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And when a well goes to steady state, it's\Ninteracting with that stream, and that
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,interaction is what allows it to go to \Nsteady state.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So to analyze this situation, the way that\Nyou do it is to use what's called an
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,image well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, if we have a well here, and if we use\Njust the Jacob Analysis, and we're
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,pumping out of this well, and we assume\Nin the Jacob Analysis that the aquifer
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is infinite, so it's an infinite lateral \Nextent, and there is no boundary.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,But what we do then is we say, well\NI'm gonna put in another well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is just an artificial well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It doesn't really exist, but I'm gonna\Nput it in there because if I, if I take
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that well and then I inject into it, and\Nif I inject into it at a rate that's
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,equal to the pumping rate that I'm \Ndoing over here, then this injection
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,offsets the pumping over on the \Nleft side, and as a result, the zone,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the line that's halfway between these\Ntwo has no drawdown.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so it's, it's the head along that\Nline is maintained at constant value.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Alright, and as a result, this, uh,\Nanalysis, it's only valid for this
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,region over here, it's not really valid\Nover here because this pumping
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,well doesn't really exist.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So it's a way of taking a, a simple\Nanalysis for an infinite la-aquifer, and
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,turning it into an analysis that will \Nallow us to evaluate the effects of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,a constant head boundary that represents\Na string.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So that's what I'm showing here, that the,\Nthe drawdown will equal the actual
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,drawdown from the pumping well, plus\Nthe drawdown from this image well
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that's over here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Here's how you do it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is the Jacob Analysis that we've\Nseen before.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,What we're gonna need to do is to \Nwrite this now, in terms of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,X and Y coordinates.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So there's X, and there's Y, and the\Norigin of coordinates is at the, uh,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,pumping well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, in order to do that, to make the\Nswitch, what we have to do is go in
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,here, and recognize that when we \Nfirst did Jacob, we wrote it in terms of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,radial distance away from the pumping\Nwell, that's because it was exactly
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,symmetric, and what we can do then is\Nrecognize that R squared is equal to
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,X squared plus Y squared.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That's the Pythagorean theorem.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we just do that substitution, and we \Nget this version of the equation, so
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that's Jacob Analysis right there, we see\Nthis guy here, that's the, that's the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,substitution that we've done.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So this is just the pumping well, and we\Ncan repeat this for the image well, and
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,here's what it looks like.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is the image well, and we're gonna be\Ninjecting instead of pumping out, so the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,sign changes right there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And the image well is, is here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's at X equals 2L.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So L is the distance the distance to\Nthe stream, and this distance here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is 2L.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So the way that we write this image well\Nis to replace X here with X minus 2L.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That's right there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That kind of slides this image well over\Nhere to the origin of coordinates.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Otherwise, this is just the same as the\Npumping well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So the image well, with just two small\Nchanges, we can, we can determine what
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the drawdown is over here at the\Nimage well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And now what we do is add them together,\Nso this is another superposition problem,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we saw earlier that we did the analysis or\Nrecovery by superimposing two
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,solutions from different times, here we're\Nsuperimposing two solutions from
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,different locations.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is the pumping well, and this is the \Nimage well that we just drew out here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And what we see is that this term here can\Nbe factored out, and then we have log,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,log of this stuff here, minus the log of\Nthis stuff there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so we can combine those logs using\Nthe rule of logs when we have log of A
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,minus log of B, that equals the log of\NA divided by B.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we do that, we combine them and \Nwe get this.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Um, these terms, this stuff here, it's \Njust gonna cancel, when we do this
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,division and we end up with the stuff\Nthat I'm showing here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, so that's the total drawdown, this\Nwould give us the drawdown throughout
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,this region here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Alright, so let's go to the next page, and\Nhere's the thing that we just developed.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, what we do is say, well, we're really\Njust interested in, for this specific
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,capacity calculation, and what the \Ndrawdown is at the well.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,What we have here is X and Y, so, the \Nsolution that we have here is really
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,valid over the whole aquifer, but if we \Njust say that the particular point we're
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,interested in, we say that Y is equal to\Nzero, so that would be right here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well, it'd be right here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And X equals RW, so that's gonna be\Nright at that point there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Um, and if we also assume that two\Ntimes L is much, much greater than
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,RW, so that's, I think makes sense, so\N2L is, um,