For fully brine saturated porous media, three different mechanisms contribute to the relaxation: bulk fluid relaxation, surface relaxation, and relaxation due to gradients in the magnetic field. In the absence of magnetic field gradients, the equations describing the relaxation are:
:  on S
with the initial condition
: and 
where  is the self-diffusion coefficient. The governing diffusion equation can be solved by a 3D random walk algorithm. Initially, the walkers are launched at random positions in the pore space. At each time step, , they advance from their current position, , to a new position, , by taking steps of fixed length  in a randomly chosen direction. The time step is given by:
The new position is given by
The angles   and  represent the randomly selected direction for each random walker in spherical coordinates. It can be noted that  must be distributed uniformly in the range (0,). If a walker encounters a pore-solid interface, it is killed with a finite probability . The killing probability  is related to the surface relaxation strength by:
If the walker survives, it simply bounces off the interface and its position does not change. At each time step, the fraction  of the initial walkers that are still alive is recorded. Since the walkers move with equal probability in all directions, the above algorithm is valid as long as there is no magnetic gradient in the system.
When protons are diffusing, the sequence of spin echo amplitudes is affected by inhomogeneities in the permanent magnetic field. This results in an additional decay of the spin echo amplitudes that depends on the echo spacing . In the simple case of a uniform spatial gradient , the additional decay can be expressed as a multiplicative factor:
where  is the ratio of the Larmor frequency to the magnetic field intensity. The total magnetization amplitude as a function of time is then given as: