Hydrogeology 101: Cooper-Jacob

This video is about the Cooper-Jacob (1946) straight-line method of non-steady-state pumping test analysis in confined aquifers. We will look at both the time-drawdown and distance-drawdown methods using the Oude Korendijk data from Kruseman & de Ridder (2000), and how the Transmissivity and Storativity can be calculated manually using formulas, as well as automatically in the Cooper-Jacob XL tool in Excel.
I developed the first version of Cooper-Jacob XL in Ghana back in 2002/2003 with the help of Edwin Dodoo. When Excel removed the feature to move data points in charts, I added the data sliders. The video shows you how to use them to adjust the best fit line to the data.
This is an educational video & part of the Hydrogeology 101 course.
Link to the Cooper-Jacob (1946) paper: www.nrc.gov/do...
Link to the Cooper-Jakob V2 Excel tool: bit.ly/2TrucWM

[@jamiewold231]

Andreas de Jong thank you, thank you and thank you again! For the first time EVER, I actually understand the pumping test and the relationship between the equations and the charts. I may pass my professional geology test because of these videos. Please continue to make videos, they are the best I've found, even compared to my professors.

[@GeosearchInternational]

Hi Jamie, thank you so much for your kind words. I'm sure that you will pass your exam & I wish you all the best for the future! Andreas

[@riceboi89]

I love this hydrogeo 101 series you are doing. I watched the storativity video for a refresher, then proceeded to watch all of videos you made. Amazing presentation and your explanations are so concise. When you started talking about effective stress and strain hardening of clay in the storativity video, I knew I had to watch all of the videos. I really hope you take this video series progressively into more advanced hydrogeo topics, I'm super excited to see where you decide to go. Cant't wait to see the Neumann solution and the Papadupolous solution next!

[@GeosearchInternational]

Thanks for your support! I really appreciate it! Yes, I will try to make some more hydrogeology videos over the summer, but the priority is controlled by my ongoing support to capacity building of my Afghan colleagues and their main focus at the moment is building new dams. That is why I'm doing a series on catchment delineation in QGIS, which will lead to basin water balances using remote sensing data. Interesting also for hydrogeologists as abstracting groundwater needs to be balanced by recharge. All the best, Andreas

[@abhishek_raj]

Exactly what I was searching for ! You are a lifesaver, thanks !!

[@GeosearchInternational]

Glad I could help! All the best, Andreas

[@miriamrioss]

Thanks for posting these videos. You are really good at explaining the concepts.

[@GeosearchInternational]

You're welcome! All the best, Andreas

[@evanssalah5743]

Great video. Very educative. I can't wait for your video on determination of safe yield of a borehole

[@GeosearchInternational]

Thanks Evans! All the best, Andreas

[@chukwudumoduah7565]

Thank you so much Andreas ! The presentations and exercises were on point !

[@GeosearchInternational]

Glad you like them Chukwudum! All the best, Andreas

[@andresjanz]

Something otherwise complex, made quite simple to understand and use, well done !

[@GeosearchInternational]

Thanks for your kind words Andres! Life is simple, but some people like to make it complicated. All the best, Andreas

[@andresjanz]

@@GeosearchInternational I'd say that most people who dare to talk about GW have the tendency to complicate things, when I fist studied it at uni, it was based on partial differential equations !!!

[@GeosearchInternational]

Hi Andres, the equations are important but they are the details which you can dig into once you understand the big picture. Hydrogeology is such a massive subject, and it is surprising how much can be achieved with just the simple tools. All the best, Andreas

[@abhishekchoudary1341]

thank you keep posting more .. love from india

[@GeosearchInternational]

You are welcome Abhishek! All the best, Andreas

[@travelwonder]

Very good work. Thanks a lot for your efforts

[@GeosearchInternational]

It's my pleasure! All the best, Andreas

[@ziyuelin]

Really really clear!!!! Thank you!!!

[@GeosearchInternational]

You are welcome Ziyue Lin! all the best, Andreas

[@roxxroxxman]

Hello, are we still able to use this solution if the aquifer system in consideration consists of two confined aquifers separated by an aquitard and the well used for the pumping test fully penetrates both aquifers? If not, how could I estimate the hydraulic properties (transmissivity and storativity) of these two aquifers if I have the drawdown data from an observation well? Any insight is greatly appreciated.

[@GeosearchInternational]

Hi Brandon, If your pumping well filly penetrates both aquifers then the drawdown in the pumping well will be a combination of the hydraulic properties of both aquifers. i.e., you should think of them as a single unit, and I suppose you could calculate kind of a combined transmissivity for both aquifers from the pumping test data in the pumping well. You will need at least one observation well in each aquifer to differentiate between their properties. You will also need to estimate how much of the pump discharge comes from each aquifer. For that I guess you would need to carry out flow logging in the well during pumping. Another complication is the properties of the aquitard. Is it releasing water from storage, and how permeable is it? I think you can get some overall ideas from the Cooper-Jacob straight line method - see if you have any leakage, boundaries etc, but for this kind of multi-layered situation you will need more complex software. Have a look at MLU - mlu.app All the best, Andreas

[@roxxroxxman]

@@GeosearchInternational Thank you for your insight, I appreciate you going into such detail. I do plan on using software, I just wanted to manually solve the inverse problem to have something to compare the findings from the software to. Within the system I previously discussed, there is one observation well that penetrates both aquifers, is this a problem? Thank you.

[@GeosearchInternational]

Hi Brandon, If you have a pumping well open to both aquifers and an observation well that also cuts both aquifers, then you will get an average T & S of both of them together. Are there any head differences between the two aquifers - ie is there water flowing up or down the wells? Are there any differences in hydrochemistry between the aquifers? Maybe you could use that to better understand what is going on. All the best, Andreas

[@GeosearchInternational]

I just uploaded a new video on leaky confined aquifer pumping test analysis. Could also be interesting for you. kzbin.info/www/bejne/i3e2emRoopeleK8 All the best, Andreas

[@SANY-ns4ns]

Hello, your all classes are really good. Could you please make videos on pumping test (like your this video ( for Semi confirmed aquifers and for Unconfined aquifers

[@GeosearchInternational]

Thanks for your kind words Sany. If I have time I'm planning to do some more pumping test videos. All the best, Andreas

[@tigistuyisihak1421]

Really thank you!!!! it gives a clue!

[@GeosearchInternational]

You're welcome! All the best, Andreas

[@rantingchinese9958]

Hey, thanks for your Videos. I've got two questions. 1. Can you use the Cooper-Jacob-Method for an unconfined aquifer when you correct the drawdown data with the following formula? s'=s-(s²/2H) 2. Can you use the Cooper-Jacob-Method and calculate T with drawdowns only from the well itself and without an observation well?

[@GeosearchInternational]

1. One of the assumptions for the Theis 1935 solution, of which the Cooper-Jacob method is an approximation, is that the drawdown is small relative to the saturated thickness of aquifer. That can be a problem in unconfined aquifers, which is why we need to apply the Jacob 1944 correction which you mentioned. Note that according to Neuman (1975), Jacob’s correction is strictly applicable only to the late time-drawdown data, which fall on the Theis curve. In practise, it is often difficult to know the exact aquifer thickness so I would always do a quick “non-corrected” analysis first. 2. Yes, you can carry out any pumping test analysis on pumping wells though observation wells are preferred as the data is smoother and we can also get a storativity estimate. If you only have pumping well data you should correct for the well losses which are due to turbulent flows around the well itself. That is why you should always carry out a variable rate (step) pumping test before you do your constant rate pumping test. From the step test you can estimate what % of drawdown is due to aquifer, and what % is due to well losses. Having said that, the best data is usually from the recovery test, so like above I recommend that you always start with a quick “non-corrected” analysis first. Hope that answers your questions. All the best, Andreas

[@rantingchinese9958]

​@@GeosearchInternational Thanks for your quick response, Andreas. So would you say, you can get plausible results when using the Cooper-Jacob-Method on an unconfined aquifer (with or without the correction) or do you have to use a different method to get plausible results for unconfined aquifers?

[@GeosearchInternational]

The Cooper-Jakob method is just a simplified Theis method, which is the basis for all other methods so the results should be in the right ball park. I would always use the Cooper-Jakob straight line method first, as not only is it fast and easy, but you can quickly see if there are any boundaries affected by the pumping test. For unconfined aquifers you should also do a Neuman analysis, which takes a bit longer. Basically you need to look at the results from your step test, constant rate pumping test & recovery test to get a good idea about your well performance and the aquifer parameters. It is also important to be aware of all the assumptions behind the different methods, as they are all just theoretical approximations of reality. All the best, Andreas

[@rantingchinese9958]

@@GeosearchInternational Thank you, Andreas!

[@GeosearchInternational]

Most welcome.... and keep asking yourself these kind of questions! All the best, Andreas

[@samikdas6790]

Sir please elaborate chow's method of aquifer

[@GeosearchInternational]

Sorry I don't have a tool for Chow. I always use Cooper-Jacob. All the best, Andreas

[@abdikadiralibade9074]

Just I need to get how did you get the ro as 450 m? from my side, it seems 500 m?

[@GeosearchInternational]

Hi Abdikadir, it looks like it is closer to 500m but that is the effect of the logarithmic scale. It should be 450m. All the best, Andreas

[@hydrofolks666]

Hi, thanks for the great videos!! Is it possible to change the "u" value in the excel? just curious what will end up if i put "u" value as

[@GeosearchInternational]

Hi Naufal, If you go to the hidden Calcs sheet of Cooper-JacobXL_V2.3.xlsx you can change u from 0.05 to 0.01. It makes the dotted line move from 38 minutes to 192 minutes. However, this would not change the interpretation as all the data points are already on the straight line. All the best, Andreas

[@CivilDisha2024]

Thank you sir.

[@GeosearchInternational]

Most welcome Chandan! All the best, Andreas

[@faisalkhursheed3566]

How do we calculate K after using the variation of this method for an unconfined aquifer?

[@GeosearchInternational]

Hi Faisal, T=Kb so once you have estimated the Transmissivity from the pumping test, just divide it by the saturated thickness (b). All the best, Andreas

[@faisalkhursheed3566]

Hi Andreas, thank you for your reply. What if the saturated thickness is unknown?

[@GeosearchInternational]

Hi @@faisalkhursheed3566 When you drill your well(s) you should get an idea of the saturated thickness, provided that you drill to the base of the aquifer. If you don't have this information then it is better not to guess it. All the best, Andreas

[@faisalkhursheed3566]

@@GeosearchInternational Thank you for your help!

[@GeosearchInternational]

You are welcome Faisal! All the best, Andreas

[@worksupervisiorii3726]

Supervisor how can you get access to spread sheet

[@GeosearchInternational]

The link is In the description: Link to the Cooper-Jakob V2 Excel tool: bit.ly/2TrucWM Just download and open in Excel. All the best, Andreas

[@ahmadsyahmi8278]

for drawdown vs distance, t=140min... where or how you get it?

[@GeosearchInternational]

Hi Ahmad, In the distance-drawdown method we need to measure the drawdowns in the different piezometers at the same time. In the example this time was taken at 140 minutes, which is just a convenient arbitrary time on the late stage of the drawdown plots of all three piezometers. Actually it is still too early, as the furthest piezometer does not plot on the straight line. Have a look at the drawdown plots on p58 of Kruseman & de Ridder: www.hydrology.nl/images/docs/dutch/key/Kruseman_and_De_Ridder_2000.pdf Maybe you can try it with a t=600 minutes - data is on p59. All the best, Andreas

[@worksupervisiorii3726]

i would like to get access to excel sheet

[@GeosearchInternational]

Link to the Cooper-Jakob V2 Excel tool: bit.ly/2TrucWM

[@Ishu1996-v9g]

Very helpfull video sir Thnk u

[@GeosearchInternational]

Most welcome Mohammad! All the best, Andreas

[@collachflames]

Thank you for the video. But how do we get the excel worksheet. Thanks

[@GeosearchInternational]

You are welcome. I have updated the description with a link to the file: bit.ly/2TrucWM Please download it & open in Excel. All the best, Andreas

[@collachflames]

@@GeosearchInternational Thank you

[@DgffyAhdseg]

How can I get your excel file?

[@GeosearchInternational]

The link should be in the description below the video. All the best, Andreas

[@ramonbaccomperi7871]

how do we find the delta s

[@GeosearchInternational]

Delta s is the change in drawdown over 1 log cycle. All the best, Andreas

[@umbertobombace8367]

Just a question about the parameters: what does u represent? Has it got a name? I can't find an explanation for it, neither in the books. Thanks.

[@GeosearchInternational]

Hi Umberto, u = r^2 S/4Tt, where r is the distance to the pumping well, S is storativity, T is transmissivity and t is the time since pumping began. It is just called "u" - I don't think it has another name. In the Theis method we have the Well Function of u, W(u) which is the same u. As I tried to explain in the video, the Cooper-Jacob straight line method is just as simplification of the Theis Method. "u" is important, as it needs to be

[@umbertobombace8367]

@@GeosearchInternational many thanks, sir. How come has the u been elaborated, on the base of what and what is its physical meaning? Is there any article you could advise where it is explained? Cheers

[@GeosearchInternational]

Hi Umberto, If you want to dig into the maths behind it you should read the original paper by CV Theis (1935). You can find it here: water.usgs.gov/ogw/pubs/Theis-1935.pdf All the best, Andreas

[@umbertobombace8367]

@@GeosearchInternational I'll have a look at it. Many thanks.

[@GeosearchInternational]

Welcome! All the best, Andreas

[@mdnaseemahmad1047]

How can we make this excel sheets give tutorial on it

[@GeosearchInternational]

Dear Md Naseem, Sorry, I have no time at the moment. All the best, Andreas

[@sniperM1230]

im confused about the log part for finding delta s how do I work that out in excel do I log my values of t ? then type =slope?

[@GeosearchInternational]

Dear Xlimk, The Cooper-Jacob method is designed so you can easily read off Delta s from a paper plot. It is just the difference in drawdown between two log cycles - e.g. between 10 and 100 minutes or 100 & 1000 minutes. Quite easy to do it manually. In Excel it gets a bit more complicated and I use LINEST (array formula) and LN (not Log) to calculate Delta s, and also t0 which we need to calculate Storativity from observation well data. If you want to see how it works just download the Cooper-Jakob V2 Excel tool: bit.ly/2TrucWM. You can unhide a hidden sheet called "calls", and have a look at how the calculations are made. All the best, Andreas

[@kaleemashraf8324]

Load with all concept... Is it possible to determine T and S value from single pumping well with no observation well.

[@GeosearchInternational]

If you have only a pumping well, you can calculate the Transmissivity. For Storativity, you need observation well data.

[@kaleemashraf8324]

@@GeosearchInternational Thank you..

[@GeosearchInternational]

You are welcome. Andreas

[@nordinator89]

@@GeosearchInternational what if the well has a big diametre like 2m wide can we use r=1m for the observation well?

[@GeosearchInternational]

Hi @Nordinator No, it is not possible. Think of it like this - if we want to measure aquifer storativity we need to stress the aquifer by depressurising it/dewatering it, so that we can see how much water it has in storage. That means that the observation well has to be at some distance away from the pumping well. If you just compare the water levels in the centre of your well with the ones at the side they would be the same. Another, and more important issue is that to apply Theis or Cooper-Jacob methods one of the key assumptions is that the storage in the well is "negligible" i.e., that the well has an incredibly small diameter. This is of course not realistic, so that is why we need to ignore the very early data when we do a pumping test. If you want to analyse a pumping test from a large diameter well, it is better to use a method where well storage is taken into account. For example the Papadopulos and Cooper (1967) method for confined aquifers. Also there are some commercial software which will correct for well storage. All the best, Andreas

[@hamzaameerr1381]

good work

[@GeosearchInternational]

Thanks

[@ketansondarva7509]

very good video

[@GeosearchInternational]

Thanks Ketan! All the best, Andreas

[@Fa-de5vq]

كيف نميز بالسووال اذا كانت منطقة البئر محصوره او غير محصوره اذا لم يذكرها

[@GeosearchInternational]

إذا كانت المنطقة محصورة، فإن مستوى المياه الساكنة في الآبار سيكون أعلى من الجزء العلوي من طبقة المياه الجوفية. ولتأكيد ذلك، ستحتاج إلى سجلات جيولوجية للبئر، أو خرائط كنتورية لمنسوب المياه وأعلى طبقة المياه الجوفية. الطريقة الأخرى لمعرفة ما إذا كان البئر موجودًا في طبقة مياه جوفية محصورة أم غير محصورة هي عن طريق اختبار الضخ، لكنك ستحتاج إلى بيانات مراقبة الآبار. من بيانات بئر المراقبة، يمكنك حساب نسبة التخزين، وسيوضح لك ذلك ما إذا كان البئر موجودًا في طبقة مياه جوفية محصورة أو شبه محصورة أو غير محصورة. If the area is confined, then the static water level in the wells will be above the top of the aquifer. To confirm this, you will need geological records of the well, or contour maps of the water levels and the top of the aquifer. The other way to see if a well is in a confined or unconfined aquifer is by pumping test, but you will need observation well data. From the observation well data you calculate the storativity, and that will show you if the well is in a confined, semi-confined or unconfined aquifer. All the best, Andreas

[@sahebdas4348]

Please upload e video on open well pumping test analysis by Papadopolous-Cooper curve matching method....Thanks

[@GeosearchInternational]

Hi Saheb Das, it is on my list but am busy with other videos at the moment. All the best, Andreas

[@sahebdas4348]

@@GeosearchInternational I will be waiting for that .... no rush

[@GeosearchInternational]

Thanks for your patience! All the best, Andreas

[@amulyar2746]

Thank you sir😊

[@GeosearchInternational]

Most welcome! All the best, Andreas

[@kaleemashraf8324]

Is any equation for leaky aquifer... For steady state condition theim equation ( confine aquifer) and dupit equation ( unconfined) are used. For unsteady condition Theis equation and cooper jacob equation (confined aquifer). are used. Is any other equation available for above work...

[@GeosearchInternational]

I would always start with the Cooper-Jacob straight-line method because it will show you what kind of aquifer you are dealing with, and if there are any boundaries (recharge or barrier). You can use it for all aquifer types - confined, unconfined, leaky etc. After that it may be useful to try other methods - for example Neuman for unconfined, or Walton for leaky confined. Read Kruseman & de Ridder for details. Pumping tests is a massive subject & I remember spending two whole months on it during my hydrogeology MSc, so there is no easy answer. What is important is to understand the theory and the simple methods first, before you start using commercial software.

[@kaleemashraf8324]

@@GeosearchInternational I have no words for thanks. But I want to grab pump test analysis. So I will go through book recommend by you. If you have any info just mention or mail me [e-mail]

[@GeosearchInternational]

I'll make some new videos as soon as I have more time - especially for step test & recovery tests. All the best, Andreas

[@kaleemashraf8324]

@@GeosearchInternational thank you sir

[@kaleemashraf8324]

Hello sir, Is aquifer condition (steady state or unsteady state) determined on the basis of drawadown data??

[@SamielGigarGr]

How to get the spreadshits

[@GeosearchInternational]

Hi Samiel, The links to all files are in the description below the video. Link to the Cooper-Jacob (1946) paper: www.nrc.gov/docs/ML1429/ML14290A600.pdf Link to the Cooper-Jakob V2 Excel tool: bit.ly/2TrucWM All the best, Andreas