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balance. 2 remain static for 10 minutes, the maximum dial deflection is reported as the 10-min gel. These as well as other non-Newtonian parameters are discussed in detail in Chapter 4. However, it is sufficient that the beginning student view these parameters as diagnostic indicators that must be kept within certain ranges. Example 2.1. A mud sample in a rotational viscometer equipped with a standard torsion spring gives a dial reading of 46 when operated at 600 rpm and a dial reading of 28 when operated at 300 rpm. Compute the apparent viscosity of the mud at each rotor speed. Also compute the plastic viscosity and yield point. Solution. Use of Eq. 2.1 for the 300-rpm dial reading gives Fig. 2.6-Marsh funnel. 11-a = 300 () N N APPLIED DRILLING ENGINEERING 300 (28) 300 = 28 cp . Similarly, use of Eq. 2.1 for the 600-rpm dial reading gives 11-a = 300 (46) = 23 cp. 600 Note that the apparent viscosity does not remain constant but decreases as the rotor speed is increased. This type of non-Newtonian behavior is shown by essentially all drilling muds. The plastic viscosity of the mud can be computed using Eq. 2.2: 11-p = 8600-()300 = 46-28 = 18cp. The yield point can be computed using Eq. 2.3: Ty = 8300 - 11-p = 28-18 = 10 lbf/100 sq ft . 2.1.4 pH Determination. The term pH is used to express the concentration of hydrogen ions in an aqueous solution. pH is defined by pH = log[H + ] , ..................... (2.4) where [ H + ] is the hydrogen ion concentration in moles per liter. At room temperature, the ion product constant of water, K w, has a value of 1.0 x 10- 14 mol/L. Thus, for water Fig. 2.7-Rotational viscometer. I DRILLING FLUIDS TABLE 2.1-RELATIONS BETWEEN pH, (H+] AND [OH-] IN WATER SOLUTIONS [H +I pH [OH] pOH Reaction 1.0x 10° 0.00 1.0x10- 14 14.00 .. 1.0x1o- 1 1.00 1.0x1o- 13 13.00 1.0x 10- 2 2.00 1.0 X 10- 12 12.00 1.0x1o- 3 3.00 1.0x 10- 11 11.00 Acidic 1.0 X 10- 4 4.00 1.0 X 10- 10 10.00 1.0x1o-s 5.00 1.0x 10- 9 9.00 1.0x 10- 6 6.00 1.0x1o- 8 8.00 1.0x1o- 7 7.00 1.0 X 10- 7 7.00 Neutral 1.0x1o- 8 8.00 1.0x 10- 6 6.00 1.0x 10- 9 9.00 1.0x1o-s 5.00 1.0x10- 10 10.00 1.0x1o- 4 4.00 1.0x10- 11 11.00 1.0x 10- 3 3.00 Alkaline 1.0x 10- 12 12.00 1.0 X 10- 2 2.00 1.0x1o- 13 13.00 1.0x1o- 1 1.00 1.0x1o- 14 14.00 1.0x10° 0.00 HzO""H+ +OH- Kw= [H+] [OH-] =LOx w- 14 . For pure water, [H+] = [OH-] = 1.0 x w- 7 , and the pH is equal to 7. Since in any aqueous solution the product [H + ] [OH- ] must r~main constant, an increase in [ H + ] requires a corresponding decrease in [OH- ]. A solution in which [H + ] > [OH- ] is said to be acidic, and a solution in which [ OH - ] > [ H + ] is said to be alkaline. The relation between pH, [H + ], and [OH- ] is summarized in Table 2.1. The pH of a fluid can be determined using either a special pH paper or a pH meter (Fig. 2.8). The pH paper is impregnated with dyes that exhibit different colors when exposed to solutions of varying pH. The pH is determined by placing a short strip of the paper on the surface of the sample. After the color of the test paper stabilizes, the color of the upper side of the paper, which has not contacted the mud, is compared with a standard color chart provided with the test paper. When saltwater muds are used, caution should be exercised when using pH paper. The solutions present may cause the paper to produce erroneous values. The pH meter is an instrument that determines the pH of an aqueous solution by measuring the elec- tropotential generated between a special glass electrode and a reference electrode. The elec- tromotive force (EMF) generated across the specially formulated glass membrane has been found em- pirically to be almost linear with the pH of the solution. The pH meter must be calibrated using buffered solutions of known pH. Example 2.2. Compute the amount of caustic required to raise the pH of water from 7 to 10.5. The molecular weight of caustic is 40. 45 c#~'f' •• -~ ...... ~·. ·' :aw Fig. 2.8-Two methods for measuring pH: pH paper (left) and pH meter (right). Solution. The concentration of OH- in solution at a given pH is given by = lO(pH- 14). The change in OH- concentration required to increase the pH from 7 to 10.5 is given by: .l[OH- ]=[OH -h -[oH-11- .:l [OH- ] = 10(10.5- 14) _ 10o -14) = 3.161 X 10- 4 mol/L. Since caustic has a molecular weight of 40, the weight of caustic required per liter of solution is given by 40(3.161 X 10- 4 ) = 0.0126 g/L. 2.1.5 The API Filter Press - Static Filtration. The filter press (Fig. 2.9) is used to determine (1) the filtration rate through a standard filter paper and (2) the rate at which the mudcake thickness increases on the standard filter paper under standard test con- ditions. This test is indicative of the rate at which permeable formations are sealed by the deposition of a mudcake after being penetrated by the bit. The flow of mud filtrate through a mudcake is described by Darcy's law. Thus, the rate of filtration is given by r!!J. = k A t:..p -- , .................... (2.5) dt 11- hmc where • 46 MUD SAMPLE Fig. 2.9-Schematic of API filter press. dVJ!dt = the filtration rate, cm 3 Is, k = the permeability of the mudcake, darcies, A = the area of the filter paper, cm2 , Ap = the pressure drop across the mudcake, atm, 1-' = the viscosity of the mud filtrate, cp, and h me = the thickness of the filter (mud) cake, em. At any time, t, during the filtration process, the volume of solids in the mud that has been filtered is equal to the volume of solids deposited in the filter cake: fsm V m = fsehmeA • where fsm is the volume fraction of solids in the mud andfse is the volume fraction of solids in the cake, or fsm (hmeA + Vf) = fsehmeA · Therefore, h = fsm Vr me A (fse - fsm ) .... (2.6) Inserting this expression for hme into Eq. 2.5 and integrating, v2 k J :J_ = - A 2 ( ~ - I) t:.p t , 2 1-' fsm or Yt A Y,J. . . ..... (2. 7) APPLIED DRILLING ENGINEERING SPURT LOSS v Fig. 2.1 0-Example filter press data. The standard API filter press has an area of 45 cm2 and is operated at a pressure of 6.8 atm (100 psig). The filtrate volume collected in a 30-min time period is reported as the standard water loss. Note that Eq. 2. 7 indicates that the filtrate volume is proportional to the square root of the time period used. Thus, the filtrate collected after 7.5 min should be about half the filtrate collected after 30 min. It is common practice to report twice the 7 .5-min filtrate volume as the API water loss when the 30-min filtrate volume exceeds the capacity of the filtrate receiver. However, as shown in Fig. 2.10, a spurt loss volume of filtrate, vsp, often is observed before the porosity and permeability of the filter cake stabilizes and Eq. 2.7 becomes applicable. If a significant spurt loss is observed, the following equation should be used to extrapolate the 7 .5-min water loss to the standard API water loss. V3o =2(V7_5 - ~p) + Vsp· .............. (2.8) The best method for determining spurt loss is to plot Vvs. Yt and extrapolate to zero time as shown in Fig. 2.10. In addition to the standard API filter press, a smaller filter press capable of operating at elevated temperature and pressure also is commonly used. The filtration rate increases with temperature because the viscosity of the filtrate is reduced. Pressure usually has little effect on filtration rate because the permeability of the mudcake tends to decrease with pressure and the term .J kt:.p in Eq. 2. 7 remains essentially constant. However, an elevated pressure is required to prevent