7. Examples

### 7.1 Field example

[14] presented a field example of a fractured well test. Pressure and pressure derivative data are given in Table 1 and Figure 3. Otherrelevant data are provided below:

$$q = 101 \text{ STB/D} \quad \phi = 0.08 \quad \mu = 0.45 \text{ cp}$$

$$c\_t = 17.7 \times 10^{-6} \text{ psia}^{-1} \quad B = 1.507 \text{ bbl/STB} \quad h = 42 \text{ ft}$$

$$r\_w = 0.28 \text{ ft} \quad t\_p = 2000 \text{ h} \quad P\_i = 2200 \text{ psia}$$

$$\xi = 1$$


Well Test Analysis for Hydraulically-Fractured Wells DOI: http://dx.doi.org/10.5772/intechopen.80996

Table 1.

Pressure data for field example (taken from [14]).

Figure 3. Pressure and pressure derivative against time log–log plot for field example (taken from [14]).

Using a commercial well test software, the following parameters were estimated by nonlinear regression analysis:

$$k = 0.8 \text{ md}$$

$$\text{xf} = \text{82.2 ft}$$

$$k\_f w\_f = \text{300 mol} - \text{cp}$$

The objective is to compute the hydraulic fracture parameters using the TDS technique and compare results obtained from the regression analysis.

7.1.1 Solution

### 7.1.1.1 Step 1: Obtain the characteristic points

Once the pressure and pressure derivative versus time log-log plot is built and reported in Figure 3, the characteristic points are read from such plot as follows:

$$t\_R = 30 \text{ h} \quad \Delta P\_R = 471 \text{ psia} \quad \left(t^\* \Delta P^\circ \right)\_R = 150 \text{ psia}$$

$$\left(t^\* \Delta P^\circ \right)\_{BL1} = 160 \text{ psia} \quad \Delta P\_{BL1} = 40 \text{ psia} \quad \Delta P\_{L1} = 120 \text{ psia}$$

$$t\_{LRi} = 8.2 \text{ h} \quad t\_{BLRi} = 195 \text{ h}$$

### 7.1.1.2 Step 2: Estimate permeability and skin factor

Permeability and skin factor are found in Eqs. (8) and (14) to be 0.76 md and -4.68, respectively.
