## PVv v p Vp

For small amplitude motion the effect of convective term of the left hand side of the above equation is negligible, thus we can write:

For a linearly compressible fluid, we define the following:

Derivating of whole equation with respect to time:

The .xx can be written as following:

In which ux is the displacement in the x-direction. Thus we can write:

If we use equation 2.24 to take the divergence of the whole equation we get:

Or we can write the following:

Using equation 2.26 and substitute it in equation 2.27 we get:

We define c = \fK, in which is the velocity of pressure wave in fluid. For

incompressible fluid (K = œ>), therefore, C = œand then we have:

The above equation is the Laplace equation of motion for incompressible fluid.

The equation of motion for reservoir (equation 2.28) obtained based on the following assumption:

b)small amplitude motion, convective terms are neglected c)linear compressible fluid, equation 2.25

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