Emenike Iheanyi

Data Analysis with SPSS Client name: Godwin Field: Engineering Aim and Objective This project aims at studying the effect of locally processed micronized starch on the various rheological properties (such as apparent viscosity, yield point, gel strength etc) of the drilling mud. The study also seeks to study the effect of particle size reduction. SECTION 1: T-TEST TO CHECK FOR THE EFFECT OF REDUCTION OF STARCH PARTICLE SIZE Effect of particle size reduction In this section we study the effect of particle size reduction on the rheological properties of drilling mud. The following hypothesis will be tested for the effect of particle size reduction on the 3 rheological properties of drilling mud considered. The general hypothesis will be of the form shown below: H0: There is no significant difference in the rheological properties of drilling mud when the particle size is reduced H1: There is a significant difference in the rheological properties of drilling mud when the particle size is reduced Decision Rule: If p-value is less than 0.05 (level of significance), reject H0, otherwise accept. Group Statistics Particle Size N Mean Std. Deviation Std. Error Mean Plastic Viscosity 63 micron- .20020 75 micron- .20134 Apparent Viscosity 63 micron- .55049 75 micron- .46053 Yield Point 63 micron- .74854 75 micron- .65857 Independent Samples Test t-test for Equality of Means t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Plastic Viscosity 4.451 70 - .28393 - Apparent Viscosity 3.512 70 - - Yield Point 2.535 70 - .99701 - Plastic Viscosity The null and alternative hypotheses are postulated thus: H0: There is no significant difference in the plastic viscosity of drilling mud when the particle size is reduced H1: There is a significant difference in the plastic viscosity of drilling mud when the particle size is reduced With a p-value less than 0.05 we reject H0 and conclude that the plastic viscosity of drilling mud is affected by the particle size, with the smaller particle size (63 micron) giving a higher Plastic viscosity than the particle size of 75 micron. The average difference in plastic viscosity between both particle sizes is 1.26 centipoise. Apparent Viscosity The null and alternative hypotheses are postulated thus: H0: There is no significant difference in the apparent viscosity of drilling mud when the particle size is reduced H1: There is a significant difference in the apparent viscosity of drilling mud when the particle size is reduced The p-value for Apparent viscosity is 0.001(<0.05), hence we reject H0 and conclude that Apparent viscosity of drilling mud is affected by particle size reduction. The result shows that the smaller particle size gives a higher apparent viscosity than the large one with a mean difference of 2.52 centipoise. In other words, the reduced particle size led to increased apparent viscosity Yield Point The null and alternative hypotheses are postulated thus: H0: There is no significant difference in the yield point of drilling mud when the particle size is reduced H1: There is a significant difference in the yield point of drilling mud when the particle size is reduced With a p-value less than 0.05 we reject H0 and conclude that the yield point of drilling mud is affected by the particle size, with the smaller particle size (63 micron) giving a higher yield point than the particle size 75 micron. The average difference in yield point of both particle sizes is 2.53 lb./100ft2. With the above results we can infer that the smaller particle size enhances the rheological properties of drilling mud. SECTION 2: ANALYSIS OF VARIANCE (ANOVA) In this section we study the effect of locally processed micronized starch, temperature and concentration on the rheological properties of drilling mud. The Subject summary table below applies to all the rheological properties that follows: Subjects Summary Value Label N Concentration 1.00 0.5 gm 28 2.00 1.0 gm 28 3.00 1.5 gm 28 Starch Sample 1.00 Yam 24 2.00 Potato 24 3.00 Rice 24 4.00 CMC 12 Temperature 1.00 30 deg. 21 2.00 50 deg. 21 3.00 70 deg. 21 4.00 80 deg. 21 Plastic Viscosity The effect of concentration, temperature and locally processed micronized starch on the plastic viscosity of drilling mud is tested using the table below; The decision rule described above still applies. Tests of Between-Subjects Effects Dependent Variable: Plastic Viscosity Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 502.696a- .000 Intercept- .000 CONC- .000 STARCH- .000 TEMPT- .000 CONC * STARCH- .851 .540 CONC * TEMPT 4.738 6 .790 .671 .674 STARCH * TEMPT 1.683 9 .187 .159 .997 CONC * STARCH * TEMPT 6.884 18 .382 .325 .993 Error- Total- Corrected Total- a. R Squared = .922 (Adjusted R Squared = .821) The following hypotheses are tested TEST FOR SIGNIFICANCE OF CONCENTRATION LEVELS H0: there is no significant difference in the plastic viscosity of drilling mud at the different concentration levels H1: there is a significant difference in the plastic viscosity of drilling mud at the different levels of concentration DECISION: since the p-value < 0.05 we reject H0 and conclude that the plastic viscosity of drilling mud indeed differ at different levels of concentration. In other words, when the concentration level is varied, it leads to significant changes in mud plastic viscosity. TEST FOR SIGNIFICANCE OF STARCH USED H0: the starch sample used does not significantly affect the plastic viscosity of drilling mud H1: the starch sample used significantly affects the plastic viscosity of drilling mud DECISION: since the p-value < 0.05 we reject H0 and conclude that the plastic viscosity of drilling mud is affected by the starch sample used. TEST FOR SIGNIFICANCE OF TEMPERATURE LEVELS H0: there is no significant difference in the plastic viscosity of drilling mud at the different temperatures. H1: there is a significant difference in the plastic viscosity of drilling mud at the different temperatures DECISION: since the p-value < 0.05 we reject H0 and conclude that the plastic viscosity of drilling mud indeed differ at different temperatures. Post Hoc Tests Here we probe into the variability between subjects that affected mud plastic viscosity, which in this case are all of them. Concentration Multiple Comparisons Dependent Variable: Plastic Viscosity LSD (I) Concentration (J) Concentration Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound 0.5 gm 1.0 gm -1.1250* .28996 .000 -1.7131 -.5369 1.5 gm -1.9286* .28996 .000 -2.5166 - gm 0.5 gm 1.1250* .28996 .000 - 1.5 gm -.8036* .28996 .009 -1.3916 -.2155 1.5 gm 0.5 gm 1.9286* .28996 - 1.0 gm .8036* .28996 .009 - Based on observed means. The error term is Mean Square(Error) = 1.177. *. The mean difference is significant at the 0.05 level. The column for p-value are all found to be less than 0.05, which implies that there is a significant difference in the plastic viscosity of drilling mud at all the concentration levels. This means that the plastic viscosity from 0.05-gram concentration differ from those of 1.0 and 1.5 grams, and that of 1.0 gram also differ from that of 1.5. The details of the mean difference in plastic viscosity is shown on the column for mean difference in the above table. Starch Sample Multiple Comparisons Dependent Variable: Plastic Viscosity LSD (I) Starch Sample (J) Starch Sample Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Yam Potato -.2292 .31319 .469 -.8644 .4060 Rice .5625 .31319 .081 -- CMC -5.9792* .38358 .000 -6.7571 -5.2012 Potato Yam .2292 .31319 .469 -.4060 .8644 Rice .7917* .31319 .016 - CMC -5.7500* .38358 .000 -6.5279 -4.9721 Rice Yam -.5625 .31319 .081 -1.1977 .0727 Potato -.7917* .31319 .016 -1.4269 -.1565 CMC -6.5417* .38358 .000 -7.3196 -5.7637 CMC Yam 5.9792* .38358 - Potato 5.7500* .38358 - Rice 6.5417* .38358 - Based on observed means. The error term is Mean Square(Error) = 1.177. *. The mean difference is significant at the 0.05 level. The row for CMC with p-values all less than 0.05 shows that the plastic viscosity of drilling mud when CMC is used differed significantly when the other starch samples were used. The other starch samples did not show significant difference in plastic viscosity, except for potato and rice with a p-value of 0.016, with potato giving a higher plastic viscosity by an average of 0.79 centipoise. Temperature Multiple Comparisons Dependent Variable: Plastic Viscosity LSD (I) Temperature (J) Temperature Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound 30 deg. 50 deg. -.6905* .33482 .046 -1.3695 -.0114 70 deg. -1.2619* .33482 .001 -1.9409 -.5829 80 deg. -1.9524* .33482 .000 -2.6314 - deg. 30 deg. .6905* .33482 .046 - 70 deg. -.5714 .33482 .096 -1.2505 .1076 80 deg. -1.2619* .33482 .001 -1.9409 -.5829 70 deg. 30 deg. 1.2619* .33482 .001 - 50 deg. .5714 .33482 .096 -- 80 deg. -.6905* .33482 .046 -1.3695 -.0114 80 deg. 30 deg. 1.9524* .33482 - 50 deg. 1.2619* .33482 .001 - 70 deg. .6905* .33482 .046 - Based on observed means. The error term is Mean Square(Error) = 1.177. *. The mean difference is significant at the 0.05 level. The result from the above shows that, there is no significant difference in the plastic viscosity of drilling mud at 500C and 700C with a p-value of 0.096 > 0.05. However, all other temperature levels differed significantly in plastic viscosity of drilling mud as they had p-values < 0.05. FOR ILLUSTRATION PURPOSES, OTHER VARIABLES ARE TRUNCATED HERE A sample Function written in R (for an iterative task) Client name: Peter Field: Mathematics function(u.old,x.old,lambda.old,h,itra){ #h is d step size #u.old is d initial guess #x.old is d initial guess #lambda.old is d initial guess x.new