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What Is Radius Of Investigation?
Radius of investigation is a term often used in well testing, referring to how far into the reservoir a pressure transient has traveled. Pressure transients are created by a disturbance in the reservoir, typically caused by a change in the flowrate of a well. These pressure transients travel through the reservoir in concentric circles from the well, similar to how ripples travel through water after a pebble is thrown into a pond.
Pressure transients moving away from the well in concentric circles
The speed at which the pressure transients move through the reservoir is dependent upon the rock and fluid properties. Specifically, the velocity of the pressure transient is a function of the hydraulic diffusivity, η, where:
It should be noted that the image above, showing the pressure transients moving in perfect concentric circles, that a perfectly homogeneous and isotropic reservoir is assumed. As the reservoir parameters change across a section of rock, the pressure transients will travel faster or slower depending on the change. In this scenario, the concentric circles will skew into something less circular.
Pressure transients move slower across lower perm section of the reservoir
While it is unlikely that the pressure transients travel in perfectly concentric circles, we typically assume a mostly homogeneous reservoir for the purpose of a well test. To do otherwise would simply be too time-consuming and costly for the small improvement in accuracy that this would provide. Generally speaking, with a well test we are focusing on the area around a particular well, not the entire field, and therefore it is fairly safe to assume a homogeneous reservoir.
With that in mind, the radius of investigation can be calculated using the following equation:
An interesting observation is that the above equation does not include flow rate. This means that the flow rate does not impact the speed at which the transients travel through the reservoir. You will also see that as the permeability increases, so does the hydraulic diffusivity and thus, pressure transients travel faster in high-permeability reservoirs.
You will also notice that the time is an important factor in radius of investigation. This makes sense as the longer you wait, the further the pressure transient travels. This is important to note because it means that longer well tests give a greater radius of investigation, and thus we get a deeper look into the reservoir and a more accurate test analysis.
Why Is This Important?
The purpose of well testing is to get a look at the reservoir and help us more accurately determine critical reservoir parameters, particularly permeability. When we calculate permeability from a well test, we are calculating the average permeability across the area of the reservoir that we tested. This is different from the permeability we get from core samples, which only looks at a single point in the reservoir and could be higher or lower than the average permeability surrounding the well. The average permeability obtained in a well test is a much more meaningful number when it comes to predicting well performance.
By understanding our radius of investigation, we can determine the geometric area that we are testing. For instance, if we determine that our radius of investigation is 1,000 ft, then we can estimate that we have tested an area of 3,141,593 square feet or 72.1 acres. Therefore, we are calculating an average permeability across all 72 acres, which is going to be much more representative of the reservoir than a core sample that is just 4 inches in diameter.
Additionally, if a boundary is observed during a pressure transient test, then we can determine the distance to the boundary based on the elapsed time at which the boundary was observed. For example, if there is a fault acting as a boundary, then we can see the effects of that boundary on the well test data, and we can use the radius of investigation to determine how far away that fault is.
Radius of investigation can be a very useful tool in well test analysis. By understanding how quickly our pressure transients are moving, we can gain even more insight into our reservoir. Your well has many secrets to tell, and radius of investigation is a key tool in unlocking some of these mysteries.
Your well has a story to tell. Are you listening?
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