Question: Non-Dimensionalisation of PDEs

Hi, please can someone help on how non-dimensionalize PDEs. 

I have tried the following, but is not working:

restart:
eqn := (diff(theta(x, z, t), x))^2*(K[1]-K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))+(diff(theta(x, z, t), x))*((diff(theta(x, z, t), z))*(-K[1]*cos(2*theta(x, z, t))+K[3]*cos(2*theta(x, z, t)))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*u(x, z, t)+2*u(x, z, t)*cos(2*theta(x, z, t))))+(diff(theta(x, z, t), z))^2*(K[3]-K[1])*cos(theta(x, z, t))*sin(theta(x, z, t))-(1/2)*gamma[1]*(diff(theta(x, z, t), z))*(4*sin(theta(x, z, t))^2*v(x, z, t)+2*v(x, z, t)*cos(2*theta(x, z, t)))+(diff(theta(x, z, t), z, x))*(-2*K[1]+2*K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))-(diff(u(x, z, t), z))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(2*sin(theta(x, z, t))^2+cos(2*theta(x, z, t))))-(diff(v(x, z, t), x))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(-2*sin(theta(x, z, t))^2-cos(2*theta(x, z, t))))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*(diff(theta(x, z, t), t))+2*(diff(theta(x, z, t), t))*cos(2*theta(x, z, t)))+((diff(u(x, z, t), x))*gamma[2]-(diff(v(x, z, t), z))*gamma[2])*cos(theta(x, z, t))*sin(theta(x, z, t))+f[2](theta(x, z, t))*(diff(theta(x, z, t), x, x))+f[1](theta(x, z, t))*(diff(theta(x, z, t), z, z));

varchange := {t = T*tau, u = xi*h^2*U/alpha[4], v = xi*h^2*V/alpha[4], x = X*h, z = Z*h, K[3] = K[1]*k[3], f[1] = K[1]*F[1], f[2] = K[1]*F[2], gamma[1] = mu*Gamma[1], gamma[2] = mu*Gamma[2]};

PDEtools:-dchange(varchange, eqn, [tau, U, V, X, Z, k[3], F[1], F[2], GAMMA[1], GAMMA[2]]);