In this presentation, we are going to discuss some aspects related to Design of Cathodic Protection Systems. Now, the design of a cathodic protection system is a complex task which may involve several iteration. However, on a fundamental level, the key question that we need to address are; one, how many anode we need to deliver the protection current, two, how much material we need for a sacrificial system such that we can deliver enough current for enough time, and three, where should we place the anode such that the current is delivered adequately to the structure. Now, in order to approach the problem of determining the number of anodes and their shape, it is useful to consider the electrical equivalent circuit of a cathodic protection system. In this slide, we can see such an equivalent circuit for unimpressed current system. In particular, we can see that the equivalent circuit contains three resistances and one power supply. The three resistances represent the resistance of the anode to ground, the resistance of the structure to ground, and the resistance associated to the flow of current in the metallic conductors, which is associated to the resistance of the cable connecting the anode the structure and the electrical resistance of the structure itself. It is immediately evident from this schematics that the three resistances are in series. Therefore, the total resistance that is seen by the power supply is the sum of the three, which in the equation in this slide, equals to the term RT. Recalling Ohm's law, the current flowing in the circuit is given by the delta V, which is the voltage provided by the power supply, divided by the total resistance. We need to keep in mind that for later on. Now, let's consider a IC PC system from this perspective and see which value of resistances would be ideal. Let's start from the structure. You want the resistance of the structure to be as high as possible. This is because what you want to obtain is a larger shifting potential of the structure's surface. Even if that's not strictly correct, you could think of the polarization of the structure as the potential drop across RS. It is immediately evident that if RS is high, then a very small current will induce a large polarization, which is good, because it means that your structure is protected using a little current. For example, if you apply an organic coating to the structure, you will increase its resistance to ground, and therefore you reduce the overall current demand. On the other end, you want your anode resistance to be low since the if it is low, you will be able to deliver the required current without having to apply a large potential to overcome the anode resistance. If you deliver the same current at a lower potential, the overall energy consumption of the power supply is less since the power is given by the product of current by voltage. Exactly for the same reason, you want the resistance of the cable and generally of the metallic path to be as low as possible. So the overall problem boils down to this. The structure resistance, that means the current demand. The remaining part of the circuit needs to be adjusted such that the required current can be provided. Overall, the most critical value to be able to determine is the resistance of each anode to the ground, because if we know that, we can then establish how many anodes are needed. The resistance of the anode depends mainly on its shape, on its dimensions, and on the resistivity of the soil surrounding the anode. In this slide, I have reported some equations that can be used for different anodes' shapes taken from the DMV standard for cathodic protection design. As you can see, the resistance of each type of anode can be readily calculated depending on shape, size, and soil resistivity, the thing in this slide is represented by the Greek letter on. Take care that different standards may use different units. So it's important that you convert appropriately if and when needed. So once you know the anode resistance from the equation below you, can then calculate the current output for each individual anode by dividing the total voltage available by the resistance of the anode. The total voltage available will be for impress the current, the voltage that is provided by the power supply, and for sacrificial system, the difference between the operating potential of the anode and the protection potential of the structure. The total number of anodes that you need is obtained by dividing the total protection current needed by the current that is delivered by each individual anode. Obviously, you will have to round up the number to the nearest larger integer. Now, at this point, it is important to stress the effect of the resistivity of the soil nearby the anode. If the resistivity is high, then the resistance increase and therefore you will need more anodes. As a consequence, it is important to control the resistivity nearby the anode such that it is as low as possible. This is normally accomplished by not placing the anode directly in the soil, but by preparing groundbeds that contain specific backfill material, that reduce the resistivity, in close proximity of the anodes. For sacrificial anodes, the purpose of the backfill material is to provide an environmental which has a good content of ions that reduce the resistivity and that can retain water. This is generally accomplished by using calcium and sodium sulfate as a source of ions, and by using bentonite as a material that has the capability of retaining water. Remember that the resistivity of the soil will increase if there is a shortage of ion or if the soil becomes excessively dry and there is a shortage of water. The situation for impressed current anodes is slightly different. In this case, the permanent anode is made of a relatively inert material such titanium with specific surface treatment, and this type of anodes are generally placed in a groundbed that is filled with carbon coke, which is a very cheap but still electrically conductive material. Carbon coke can conduct electricity and can support well the anodic reaction. As a result, the effective area on which the anodic reaction can take place becomes very large with a consequent decrease in resistance and increase in the life of the impressed current anode. Here, is important to stress that placing the sacrificial anode in a groundbed of carbon coke designed for the impress the current system, is a detrimental effect, because the carbon will behave cathodically with respect to the sacrificial anode. As a result, the sacrificial anode will be consumed very rapidly with only a very small amount of usable current being produced. Now for sacrificial anode, so once we know how many anodes we need to place in order to deliver the required protection current, we also need to calculate the total amount of anode material that we will need to deliver a current for the entire lifetime of the structure. This aspect is directly related to the mass and not to the number of the anode neither. From first principle, this is a problem that can be approached by Faraday's law, and in particular, using Faraday's constant. As explained in this slide, the Faraday's constant is the charge that is contained in one mol of electrons and it equals 96,485 coulombs per mol. So if you want for example to calculate what is the capacity of one kilogram of Zinc, you need to first obtain the number of mols that are contained in the in one kilogram of Zinc. To do so, you will have to divide a 1000 grams of Zinc by the molecular weight of Zinc which is 65 gram per mol and this will give you the number of mols in a kilogram. Then if you want to calculate the charge associated to the 100 gram of Zinc, you need to multiply this number by two because each atom of Zinc releases two electrons when it oxidizes and then we need to multiply the result by the Faraday's constant. Once you have obtained the total charge in coulombs which is ampere per second, you can then compare the debt charge in ampere per hour or ampere per year. So by doing this calculation you will be able to find out theoretically how many ampere hour or ampere years that can be delivered by one kilogram of Zinc anode. Now for example, say that you need to calculate how much anode material you need for a structure that requires one ampere for 20 years. In this case therefore the total charge needed is 20 ampere years. Now you can't use straight away the theoretical value that we had discussed before because there are another two numbers that are quite important in the calculation and those two numbers are the anode efficiency and the utilization factor. The anode efficiency is less than one, and it is less than one because not all the electrons that are released by the oxidation of zinc are actually entering the cable and they can be used for the cathodic protection system, but some of them will be consumed directly on the anode by a local cathodic reaction. So as a result, the current that is usable to the cathodic protection system is less than the theoretical current that is produced by the oxidation of a certain mass of anode material. The utilization factor is related to a more practical consideration and in particular to the kind of end of life stages of cathodic protection system because as the anode consumes, it might have been that some parts of the anode are disconnected simply because the corrosion is not homogeneous. So as a result, those disconnected parts cannot contribute in terms of current to the protection of the structure. So these element needs to be accounted for. So based on what we have learned in our lecture so far, we can review a basic workflow process for the design of a sacrificial anode system. Our starting point is a particular structure environment combination. The first step would be to define protection criteria that will ensure that the acceptable corrosion rate are attained in those particular condition. Once we have established the protection criterion, we need to either estimate empirically or calculate how much current we need to attain that criterion. In one of the next lecture, we'll discuss how the current can be empirically determined. Regardless, the protection current is needed as our key design information. Once we have the protection current, we then need to select an appropriate anode material for the operating environment, and in some cases, we might have more than one option. Then calculate the delta V available to drive the cathodic protection system. This delta V will be the difference between the protection potential of the structure set at the beginning of the process and the operating potential of the anode that is generally available in the data sheet provided by their anode supplier. We then need to pick an anode side and shape based on what is available and economical on the market and calculate the anode resistance based on the information on soil resistivity and or ground bed properties. Then we need to calculate the current output of the anode or the anodes, and verify that this is equal or slightly larger than our current requirement. If it is not, we can increase the number of funnels or change their shape such as we meet the current requirement. If it becomes evident that too many anodes are needed, we may also consider using an impressed current system. However, assuming that a reasonable number of anodes will deliver the current required, we need them to check if the total amount of anode material is sufficient for the lifetime of the structure and modify our calculation accordingly. The process can be iterated several time until we have found an optimum or and optimize the combination of anode size, shape, weight, and cost. It is also relevant to stress that in case we are designing a new structure, if the cathodic protection requirement appears to be too high, rather than adding a lot of anodes or anode material, it may be more economical or practical to improve the coating on the structure such as the current demand is reduced. The workflow for an impressed current system is very similar with the difference that we have an option of increasing arbitrarily the voltage delivered by the power supply such as the current requirement is met. However, in this case we need to be careful, especially on large structure, not to induce over protection in those regions nearby the connection point of the anodes because over protection can have detrimental effects both on the coating and on the structural integrity of some structure. As a result, in the case of impress the current system and specifically impressed current system on long structures such as pipeline, it becomes particularly important to also be able to calculate in detail the spacing between anodes such as the distribution of current through the structure is optimized. We'll see this particular aspect in one of the following lectures. So in summary, today's lecture has focused on some aspects related to the design of cathodic protection system. In particular, we have learned that when designing a cathodic protection system, the number of anodes needs to be calculated. The number of anodes depends on the protection of current on the delta V available and on the individual anodes resistance. The anodes resistance depends on the anode size and shape and on the resistivity of the soil that is in the close proximity of the anode. Such resistivity can be minimized by placing the anode in an adequately designed ground bed. For sacrificial anode system, not only the number of anode is important but to also the total amount of anode material that needs to be provided because the total amount of final material directly related to the lifetime of the cathodic protection system. This process is essentially iterative in nature because we need to meet multiple conditions at the same time, and we also try to maintain the costs to a minimum.