I'm working currently on an analytical model for of a pressure transient well-test (build-up). Using formula from Lake's Petroleum Engineering Handbook Vol. 1, which describes pressure change in Laplace domain, i then use mpmath.invertlaplace() function with Stehfest algorithm to inverse it and get the results in time that i need. import numpy as np import matplotlib.pyplot as plt from mpmath import * q=46 #m3/day rw=1.08 #m h=8.61 #m fi=0.164 Ct=1.67E-04 #1/(kgs/cm2) mu=3.90 Bo=1.12 #m3/m3 Cs=0.15 k=0.199 Sm=-2 nu = k / (fi * mu * Ct) def run_invertlaplace(tt, fp): y = [] for i in np.arange(0, len(tt)): y.append(invertlaplace(fp, tt, method='stehfest')) print(i,y) return y deltaTT=np.linspace(0.001,76,100) fp = lambda s: q*Bo*mu/(2*np.pi*k*h*s)*((besselk(0,np.sqrt(s/nu)*(rw+0.001))+Sm*np.sqrt(s/nu)*rw*besselk(1,np.sqrt(s/nu)*rw))/(np.sqrt(s/nu)*rw*besselk(1,np.sqrt(s/nu)*rw)+24*Cs*mu/(2*np.pi*k*h)*s*(besselk(0,np.sqrt(s/nu)*(rw+0.001))+Sm*np.sqrt(s/nu)*rw*besselk(1,np.sqrt(s/nu)*rw)))) y=run_invertlaplace(deltaTT,fp) print(y) plt.plot(deltaTT,y,color="black") plt.xscale('log') plt.yscale('log') plt.grid() plt.show() The problem occurs, when the Sm (skin-factor) value is negative. As you can see, black line contains some abnormal values that experimental data isn't. Is it the problem with modified bessel functions? What can i do to solve the problem? P.S I deeply apologise for my bad English. Continue reading...
