**5. Case study demonstration: model selection**

#### **5.1 Case study I**

An additive has been verified as a viscosifier in water-based muds and used to prepare a mud formulation for use in a sandstone reservoir. Given in **Table 3** are Fann viscometer readings (measured) from the mud sample determined by the use of the American Petroleum Institute (API) standard test procedures [50] taken at ambient temperature. The rheological parameters for Power Law (PL) and Herschel-Bulkley (HB) models are provided in **Table 4**. Propose a model suitable for hydraulic calculations for the mud? Provide the reason for the choice of model.


**Table 3.**

*Viscometer dial readings.*


#### **Table 4.**

*Rheological parameters.*


**Table 5.** *Computation steps.*

The results are summarized in **Table 5** and plotted in **Figure 4**. Herschel-Bulkley model was selected because it has a lower absolute average error value.

Note: For the sample question, the rheological parameters have been provided. Times always occur when an engineer is expected to determine the rheological parameters using all the six data points.

#### **5.2 Case study II**

The dial readings from a six-speed viscometer taken at ambient temperature have been provided in **Table 6**. Analyze the data and propose rheological parameters that represent the flow behavior and attempt to find a suitable model for the prediction of the characteristics of the fluid formulation.

*Perspective Chapter: Rheological Considerations for Drilling and Enhanced Oil Recovery… DOI: http://dx.doi.org/10.5772/intechopen.106897*

#### **Figure 4.**

*Rheograms for three models combined.*


#### **Table 6.**

*Viscometer dial readings.*

**Figure 5** is rheograms of viscometric readings while **Figure 6** is the log-log graph. The equation shown as insert (**Figure 6**) is non-linear. From **Figure 6**, it could be observed that n = 0.4885 and k = 2.6487 lb.Sec<sup>n</sup> /100 ft2 .

To get the yield stress, if the fluid is a Herschel-Bulkley fluid, Versan and Tolga's [51] approach could be applied. Alternatively, the 3 rpm reading could be used as the yield stress. If it is a Bingham Plastic fluid, a formula could be used or intersect the graph. Both yield different results as shown in **Table 7**. **Figures 7**–**9** show the plots for comparison.

**Figure 5.** *Rheogram of viscometric readings.*

#### **Figure 6.**

*Log-Log graph with power equation showing k and n.*


**Table 7.** *Summary of results.*

**Figure 7.** *Rheogram of viscometric and HB model from SOLVER®.*

*Perspective Chapter: Rheological Considerations for Drilling and Enhanced Oil Recovery… DOI: http://dx.doi.org/10.5772/intechopen.106897*

**Figure 8.** *Bingham-Plastic plot with parameters from equations.*

**Figure 9.**

*Rheogram of viscometric and Bingham-Plastic from SOLVER.*

#### **5.3 Yield stress determination**

The SOLVER® regression algorithm for the determination of the yield stress yields consistent results [47]. Eqs. (18)–(20) are applicable for yield point stress determination.

$$\tau = \frac{\tau^{\*2} - \tau\_{\text{min}} \* \tau\_{\text{max}}}{2 \* \tau^{\*} - \tau\_{\text{min}} - \tau\_{\text{max}}} \tag{18}$$

$$
\gamma^\* = \sqrt{\gamma\_{\text{min}} \gamma\_{\text{max}}} \tag{19}
$$

Therefore,

$$
\gamma^\* = \sqrt{\gamma\_{\text{min}} \gamma\_{\text{max}}} = 72.25 \,\text{sec}^{-1} \tag{20}
$$

The corresponding value of shear stress *τ* <sup>∗</sup> is determined by interpolation. The value is 17.30 lb/100 ft<sup>2</sup> . Therefore,

$$\tau = \frac{\tau^{\*2} - \tau\_{\text{min}} \* \tau\_{\text{max}}}{2 \* \tau^{\*} - \tau\_{\text{min}} - \tau\_{\text{max}}} = 3.25 \,\text{lb}/100 \text{ft}^2$$

(ii) A suitable model for the mud is chosen after the values of absolute average error between measured and model data have been determined. The EAA for Herschel-Bulkley and Bingham Plastic models are 0.12974 and 0.19551 respectively. Hence, the HB model could be said to be a suitable model since it has a lower value for the EAA. All hole cleaning and hydraulics calculations should be based on the associated HB model parameters and correlations.

#### **6. Summary**

Drilling and enhanced oil recovery fluids designs are tailored to optimize rheological properties and parameters that include viscosity, gel strength, yield point, flow behavior index, and consistency factor. Rheology of drilling fluid formulations for oil and gas well drilling operations is considered for effective hole cleaning and adequate cuttings suspension when drilling (pump) is interrupted. Others include averting barite sag and prevention of excessive pipe surge and swab pressures. Similarly, the rheological characteristics of enhanced oil recovery fluids are monitored to retard pore blocking and prevent polymer loss during the fluid injection process. A low shear rate viscosity value is important in both drilling and EOR fluids. During drilling activity, it is the laminar flow regime that dominates flow in the wellbore-pipe annulus. The flow condition is desirable because a turbulent flow regime is considered to encourage borehole wall erosion and it places an upper limit on allowable flow conditions. Also, turbulent flow causes excessive pressure loss. With drilling fluids, the viscosity at low shear rates encountered in the annulus in the laminar flow regime has to be sufficient to suspend cuttings and enhance hole cleaning. Moreso, in enhanced oil recovery during fluid injection, the flow out of the wellbore into the reservoir is rather slow. The desire would be to make the displacing fluid possess viscosity to make the viscosity ratio, M ≤ 1. It has to have the capacity to behave viscoelastic.

Considering these conditions, analysis of the rheological behavior of the fluids at low shear rate conditions is important in rheological considerations.

#### **7. Conclusions**

To properly evaluate the rheological behavior of drilling fluid, all the readings taken from the viscometer at low and high shear rates should be analyzed together. That would give a proper representation of fluid behavior. The rheological parameters determined would represent both flow behavior in the pipe and annulus. The ability of the fluid to perform the functions should be checked with the results. The parameters would be used to select the suitable rheological model and applied in the equations during hydraulics analysis.

#### *Perspective Chapter: Rheological Considerations for Drilling and Enhanced Oil Recovery… DOI: http://dx.doi.org/10.5772/intechopen.106897*

To prevent pore blockage by the use of an EOR fluid, it is desirable to have a viscoelastic and shear thinning fluid. These fluids must have the ability to accelerate and decelerate when passing through narrow pore channels to maintain a constant volumetric flow rate. Stretching and extensional forces are generated along the flow axes. Also, contact of fluids with pore walls generates shear forces. For cost efficiency, the prevention of polymer loss is desirable by the creation of a stable fluid front. This is achieved by a mobility ratio less than one that would prevent viscous fingering. Rheology test results from viscometer readings taken at low shear rates might be preferable for tests on EOR fluids. Type 1 viscometers might be considered most relevant for the purpose. In other words, low shear rate viscosity should be monitored. This is because too high viscosity at low shear rates for injection into the reservoir away from the wellbore might cause an undesirable pump pressure increase. Also, since the desire is to maintain a stable fluid front as well as excellent flow behavior, the application of fluids that exhibit shear thinning and shear thickening behavior is preferable. Synthetic polymers tend to exhibit such qualities and might be preferable to biopolymers that are merely shear thinning.

### **Nomenclature/abbreviation**

