Hi, Would you mind explaining a bit more on the difference between the wave speed (x/t) and the injection rate (q_t) ? It seems like they are proportionate with a factor v_D (which is usually > 1 at saturation front). Using the construction you have in the video, this means that the actual injected water will arrive at the producer in less time if I use the speedwave t1 = L/v = L/(x/t) than if I do some simple t2 = L/q_t. In essence I don't get why the wave speed is faster than the actual injected speed, what's driving it? Thanks in advance :)
qt is the Darcy flux, not a speed: it is the volume of water injected per unit area per unit time. In single-phase flow the actual speed of the injected water would be qt/phi, where phi is the porosity - think about this carefully - the injected water can only occupy the pore space. The vD we calculate is the speed that a water saturation value moves at. The shock can indeed travel faster than qt/phi (which corresponds to vD = 1) - this is the wave of water moving in response to the injection.
@@BoffyBlunt Thanks for the swift answer! :) I was surprised that the shock wave can be faster than qt/phi (been spending all day thinking about it), but after your comment and putting some thoughts into it, this happens also because this is a multi-phase flow. We have two phase in the pore space competing for the total velocity and relative permeability curves are the ones driving the velocity proportion wrt saturation. This would also mean that in one-phase flow, qt/phi = x/t. Please correct me if I am wrong! *In my initial comment, I was referring to q_t in 1-D sense, I guess I was a bit unclear. I hope I am using better notation in this comment.
@@iffanhannanu332 Yes, you are correct for single-phase flow. If you define qt as volume flowing per unit area per unit time, you do not need the A term (as in my video). The wave speed can be larger because we have multiphase flow and water does not occupy all the pore space.
Yes, you can find the pressure profile analytically from the fact that the total velocity is constant. We assume that the fluid properties are not functions of pressure and that the temperature is constant.
@@haithmsalahhagar5350 You can calculate pressure gradient, but to find an absolute value of pressure you do need to specify pressure - normally at the inlet (injection well) or outlet (production well).
Hi,
Would you mind explaining a bit more on the difference between the wave speed (x/t) and the injection rate (q_t) ? It seems like they are proportionate with a factor v_D (which is usually > 1 at saturation front). Using the construction you have in the video, this means that the actual injected water will arrive at the producer in less time if I use the speedwave t1 = L/v = L/(x/t) than if I do some simple t2 = L/q_t. In essence I don't get why the wave speed is faster than the actual injected speed, what's driving it? Thanks in advance :)
qt is the Darcy flux, not a speed: it is the volume of water injected per unit area per unit time. In single-phase flow the actual speed of the injected water would be qt/phi, where phi is the porosity - think about this carefully - the injected water can only occupy the pore space. The vD we calculate is the speed that a water saturation value moves at. The shock can indeed travel faster than qt/phi (which corresponds to vD = 1) - this is the wave of water moving in response to the injection.
@@BoffyBlunt Thanks for the swift answer! :) I was surprised that the shock wave can be faster than qt/phi (been spending all day thinking about it), but after your comment and putting some thoughts into it, this happens also because this is a multi-phase flow. We have two phase in the pore space competing for the total velocity and relative permeability curves are the ones driving the velocity proportion wrt saturation. This would also mean that in one-phase flow, qt/phi = x/t. Please correct me if I am wrong!
*In my initial comment, I was referring to q_t in 1-D sense, I guess I was a bit unclear. I hope I am using better notation in this comment.
@@iffanhannanu332 Yes, you are correct for single-phase flow. If you define qt as volume flowing per unit area per unit time, you do not need the A term (as in my video). The wave speed can be larger because we have multiphase flow and water does not occupy all the pore space.
@@BoffyBlunt Thanks for the reply! I like your videos, please keep uploading them! :)
Hello dr, Do the BL considers pressure? also does viscosity depend on Pressure and temperature? thanks
Yes, you can find the pressure profile analytically from the fact that the total velocity is constant. We assume that the fluid properties are not functions of pressure and that the temperature is constant.
@@BoffyBlunt so i shouldn’t have pressure in the input data, I can calculate it from the velocity.
@@haithmsalahhagar5350 You can calculate pressure gradient, but to find an absolute value of pressure you do need to specify pressure - normally at the inlet (injection well) or outlet (production well).
in the Fw formula where is the qt from the previous lesson. Why you omitted it in the gravity term?
Yes you are correct - I made a mistake and the gravity term should be divided by qt. Thanks for spotting this.
@@BoffyBlunt Thank you for your reply.