Method of avoiding a drill string becoming stuck during drilling

Claim 1

A method of modifying drilling conditions in a well to avoid sticking the drill pipe either mechanically or due to differential pressure while drilling with a water-based drilling fluid, which comprises the steps of: (a) measuring in a multiplicity N of different wells a corresponding multiplicity of related well drilling variables, V, at a given depth in each well bore where a drill string has either (i) become mechanically stuck during drilling or (ii) become stuck by differential pressure between the well bore and a permeable earth formation traversed by said well bore, or (iiii has drilled through depth intervals of wells selected in (i) or (ii) without sticking, (b) forming each of the three group of N wells in step (a) into a matrix in which each of said measured variables V is an element of X ij in a common array (row or column), such matrix including the complementary array (row or column) for each of said N wells selected as a member its respective group, (c) forming a standard mean deviation matrix of each element in each variable array, by first forming a zero-mean deviation matrix whose respective elements are the difference between each measured variable element X ij and said zero mean value X j , and converting each of said deviation matrix elements to its corresponding Standard Mean Deviation S j : wherein said mean variable X j is where j = 1,2, 3,--- V (variables) and i = 1,2,3--- N (wells) and said Standard Mean Deviation S j of each element is (d) from said standard mean deviation coefficient matrix forming the Pearson Product-Moment Correlation Coefficient wherein the value between any two X's, say X ij , j = 1,2 is defined as to express the linear dependence or relationship, of said pair of X's, (say j = 1, k = 2) and so that each of said coefficient R 12 expressed in a square symmetrical matrix to compute the group population R T as where the j's and k's refer to each variable mean for the total population, and each Group correlation is similarily defined so that the i's refer only to the members of that Group and the X's refer to only the mean of that group, (e) then forming said coefficient matrix R in which each element is the sum of the cross-products of one row and one column of said standard mean deviation matrix, said matrix being symetric, square and semi-definite, (f) solving each of said three matrices R T for it size vector coefficients v i in the equation: wherein λ i are the eigenvalues (latent roots) and I is the identity matrix, (g) multiplying each original measured variable element in the original matrix formed in step (b) by its corresponding eigenvector coefficient and scaled by λ i and separately summing the products for each array of variables, (h) plotting the sums of said products with the values of v i and scaled by λ i for each array as a representation of the probability of the well being correctly located in its assigned class, (i) then multiplying and summing the products of v i and λ i for each variable measured in another well whose probability of sticking is to be determined and which is being drilled within said geological province and depth range and (j) visually displaying the plot of said coordinates of said well to indicate its probability of sticking relative to the group mean for each of said three classes of wells.

Claim 2

A method of modifying drilling conditions in a well to avoid sticking the drill pipe either mechanically or due to differential pressure while drilling with a water-based drilling fluid, which comprises the steps of: (a) measuring in a multiplicity N of different wells a corresponding multiplicity of related well drilling variables, V, at a given depth in each well bore where a drill string has either (i) become mechanically stuck during drilling or (ii) become stuck by differential pressure between the well bore and a permeable earth formation traversed by said well bore, or (iiii has drilled through depth intervals of wells selected in (i) or (ii) without sticking, (b) forming each of the three group of N wells in step (a) into a matrix in which each of said measured variables V is an element of X ij in a common array (row or column), such matrix including the complementary array (row or column) for each of said N wells selected as a member its respective group, (c) forming a standard mean deviation matrix of each element in each variable array, by first forming a zero-mean deviation matrix whose respective elements are the difference between each measured variable element X ij and said zero mean value X j , and converting each of said deviation matrix elements to its corresponding Standard Mean Deviation S j : wherein said mean variable X j is where j = 1,2, 3,--- V (variables) and i = 1,2,3--- N (wells) and said Standard Mean Deviation S j of each element is (d) from said standard mean deviation coefficient matrix forming the Pearson Product-Moment Correlation Coefficient wherein the value between any two X's, say X ij , j = 1,2 is defined as to express the linear dependence or relationship, of said pair of X's, (say j = 1, k = 2) and so that each of said coefficient R 12 expressed in a square symmetrical matrix to compute the group population R T as where the j's and k's refer to each variable mean for the total population, and each Group correlation is similarily defined so that the i's refer only to the members of that Group and the X's refer to only the mean of that group, (e) then forming said coefficient matrix R in which each element is the sum of the cross-products of one row and one column of said standard mean deviation matrix, said matrix being symetric, square and semi-definite, (f) solving each of said three matrices R T for it size vector coefficients v i in the equation: wherein λ i are the eigenvalues (latent roots) and I is the identity matrix, (g) multiplying each original measured variable element in the original matrix formed in step (b) by its corresponding eigenvector coefficient and scaled by λ i and separately summing the products for each array of variables, (h) plotting the sums of said products with the values of v i and scaled by λ i for each array as a representation of the probability of the well being correctly located in its assigned class, (i) then multiplying and summing the products of v i and λ i for each variable measured in another well whose probability of sticking is to be determined and which is being drilled within said geological province and depth range and (j) visually displaying the plot of said coordinates of said well to indicate its probability of sticking relative to the group mean for each of said three classes of wells.

Claim 4

A method of predicting the course of a drilling well in accordance with the probability of avoiding sticking the drill string either mechanically or by differential pressure between the well bore and a permeable formation traversed by the well bore,which comprises forming a correlation coefficient matrix for at least two classes of wells in a similar geologic province said two classes including wells selected from the groups consisting of those that stuck the drill pipe (1) mechanically, (2) differentially, and (3) wells that did not stick the drill pipe, said correlation matrix for each class including for each well in its respective class a multiplicity of substantially identical variables variables with respect to a selected depth interval, each class of wells forming a plurality of single valued vectors and each vector representing one well in its respective matrix, determining a first plane separating said at least two groups of vectors and whereby a second plane perpendicular to said first plane defines a two-dimensional mapping surface generally centered about a grand mean for plotting the projection of said'vectors from each of said two classes to a centroid or mean value for each class, said centroids establishing the probability of each well vector being properly classified, then measuring the same variables at a selected depth in a drilling well, generating a single vector representative of the relation of each of said variables to said perpendicular plane and to said centroid projections, said position being determined by the sum of the coefficient values of each measured variable relative to said grand mean on said perpendicular plane, and modifying selected ones of said measured variables in said well to direct said single vector away from the probability centroids of a stuck drill pipe.

Claim 5

A method of predicting the course of a drilling well in accordance with the probability of avoiding sticking the drill string either mechanically or by differential pressure between the well bore and a permeable formation traversed by the well bore,which comprises forming a correlation coefficient matrix for at least two classes of wells in a similar geologic province said two classes including wells selected from the groups consisting of those that stuck the drill pipe (1) mechanically, (2) differentially, and (3) wells that did not stick the drill pipe, said correlation matrix for each class including for each well in its respective class a multiplicity of substantially identical variables variables with respect to a selected depth interval, each class of wells forming a plurality of single valued vectors and each vector representing one well in its respective matrix, determining a first plane separating said at least two groups of vectors and whereby a second plane perpendicular to said first plane defines a two-dimensional mapping surface generally centered about a grand mean for plotting the projection of said'vectors from each of said two classes to a centroid or mean value for each class, said centroids establishing the probability of each well vector being properly classified, then measuring the same variables at a selected depth in a drilling well, generating a single vector representative of the relation of each of said variables to said perpendicular plane and to said centroid projections, said position being determined by the sum of the coefficient values of each measured variable relative to said grand mean on said perpendicular plane, and modifying selected ones of said measured variables in said well to direct said single vector away from the probability centroids of a stuck drill pipe.

Claim 8

A method of determining the probability of sticking a drill pipe in a well bore during drilling thereof, said probability being established by measurement of a multiplicity of measurable variables representing substantially all drilling conditions for said drill pipe in said well bore, including mechanical and drilling fluid quantities related to such drilling, which comprises : establishing a data base for a geological province from a multiplicity of wells drilled therein including at least three classes of wells wherein a drill string has stuck either mechanically or by differential pressure conditions and wells wherein the drill string did not stick, said data base being the well vector solution for each well of the combined matrix of said multiplicity of variables in all such wells measured substantially simultaneously at a given depth in each well, and plotting each well of said vectors as coordinates of a point on a plane surface, each of said vectors being the sum of the relative contribution of each of the multiplicity of variables relative to all other well vectors in said data base.

Claim 9

A method of determining the probability of sticking a drill pipe in a well bore during drilling thereof, said probability being established by measurement of a multiplicity of measurable variables representing substantially all drilling conditions for said drill pipe in said well bore, including mechanical and drilling fluid quantities related to such drilling, which comprises : establishing a data base for a geological province from a multiplicity of wells drilled therein including at least three classes of wells wherein a drill string has stuck either mechanically or by differential pressure conditions and wells wherein the drill string did not stick, said data base being the well vector solution for each well of the combined matrix of said multiplicity of variables in all such wells measured substantially simultaneously at a given depth in each well, and plotting each well of said vectors as coordinates of a point on a plane surface, each of said vectors being the sum of the relative contribution of each of the multiplicity of variables relative to all other well vectors in said data base.

Claim 11

A method of multivariate statistical analysis of a multiplicity of measured well drilling variables to control said variables to decrease the probability of sticking a drill string during the drilling of a well bore, which comprises: recording in matrix form the same multiplicity of measured variables at a given depth in a plurality of wells, including at least two classes of wells selected for the group comprising wells wherein the drill string (1) did not stick, (2) stuck by differential pressure, and (3) stuck mechanically, determining the contribution to the eigenvector value of each of said multiplicity of variables for each well within said matrix, summing the products of said continuation to each eigenvector value, by each of the measured values of said multiplicity of variables in a drilling well to form the coordinates of the current well vector, relative to the mean value of said two classes of wells, and plotting said well vector relative to said mean value of said two classes of wells to indicate the current drilling condition in said well relative to said means of said at least two classes of wells.

Claim 12

A method of multivariate statistical analysis of a multiplicity of measured well drilling variables to control said variables to decrease the probability of sticking a drill string during the drilling of a well bore, which comprises: recording in matrix form the same multiplicity of measured variables at a given depth in a plurality of wells, including at least two classes of wells selected for the group comprising wells wherein the drill string (1) did not stick, (2) stuck by differential pressure, and (3) stuck mechanically, determining the contribution to the eigenvector value of each of said multiplicity of variables for each well within said matrix, summing the products of said continuation to each eigenvector value, by each of the measured values of said multiplicity of variables in a drilling well to form the coordinates of the current well vector, relative to the mean value of said two classes of wells, and plotting said well vector relative to said mean value of said two classes of wells to indicate the current drilling condition in said well relative to said means of said at least two classes of wells.

Claim 14

A method of directing a drilling well in a given geological province to avoid drill string sticking in the well bore,which comprises forming a correlation coefficient matrix for at least two classes of wells in a similar geologic province said two classes including wells selected from the groups consisting of those that stuck the drill pipe (1) mechanically, (2) differentially, and (3) wells that did not stick the drill pipe, said correlation matrix for each class including for each well in its respective class a multiplicity of substantially identical variables variables with respect to a selected depth interval, each class of wells forming a plurality of single valued vectors and each vector representing one well in its respective matrix, determining a first plane separating said at least two groups of vectors and whereby a second plane perpendicular to said first plane defines a two-dimensional mapping surface generally centered about a grand mean for plotting the projection of said vectors from each of said two classes to a centroid or mean value for each class, said centroids establishing the probability of each well vector being properly classified, then measuring the same variables at a selected depth in a drilling well, generating a single vector representative of the relation of each of said variables to said perpendicular plane and to said centroid projections, said position being determined by the sum of the coefficient values of each measured variable relative to said grand mean on said perpendicular plane, and modifying selected ones of said measured variables in said well to direct said single vector away from the probability centroids of a stuck drill pipe.

Claim 15

A method of directing a drilling well in a given geological province to avoid drill string sticking in the well bore,which comprises forming a correlation coefficient matrix for at least two classes of wells in a similar geologic province said two classes including wells selected from the groups consisting of those that stuck the drill pipe (1) mechanically, (2) differentially, and (3) wells that did not stick the drill pipe, said correlation matrix for each class including for each well in its respective class a multiplicity of substantially identical variables variables with respect to a selected depth interval, each class of wells forming a plurality of single valued vectors and each vector representing one well in its respective matrix, determining a first plane separating said at least two groups of vectors and whereby a second plane perpendicular to said first plane defines a two-dimensional mapping surface generally centered about a grand mean for plotting the projection of said vectors from each of said two classes to a centroid or mean value for each class, said centroids establishing the probability of each well vector being properly classified, then measuring the same variables at a selected depth in a drilling well, generating a single vector representative of the relation of each of said variables to said perpendicular plane and to said centroid projections, said position being determined by the sum of the coefficient values of each measured variable relative to said grand mean on said perpendicular plane, and modifying selected ones of said measured variables in said well to direct said single vector away from the probability centroids of a stuck drill pipe.

Claim 16

A method of determining the statistical probability of sticking drill pipe during drilling of a well bore and to modify drilling conditions in accordance with said probabilities to avoid such drill pipe sticking in a wellwhich comprises: in a multiplicity of well bores drilled in a geological province calculating the statistical relationship between a multiplicity of measured mechanical conditions between the drill string, including the drill bit, and the well bore and the measured properties of the drilling fluid used in said well bore, said multiplicity of well bores including a first plurality of wells in which the drill string stuck mechanically, a second plurality of wells in which the drill string stuck by differential drilling fluid pressure in said well bore and an earth formation penetrated thereby and a third plurality of wells in which the drill string did not stick, separately calculating the statistical relationship of the same multiplicity of said measured mechanical conditions and drilling fluid properties in each of said first, second and third plurality of wells, determining by multivariate statistical analysis of substantially all of said measured conditions in all of said wells of each of said three plurality of wells a plotting plane wherein said three pluralities are separated from each other, projecting the well vector for each well in each of said three pluralities onto said plotting plane and then measuring the same variable conditions for a given depth in a well being drilled, and plotting each well in accordance with the sum of the products of the coefficients of each variable for the complete group of wells times the corresponding value of the measured condition to determine the probability that the measured conditions in a drilling well places said well within one of said three pluralities of wells.

Claim 17

A method of determining the statistical probability of sticking drill pipe during drilling of a well bore and to modify drilling conditions in accordance with said probabilities to avoid such drill pipe sticking in a wellwhich comprises: in a multiplicity of well bores drilled in a geological province calculating the statistical relationship between a multiplicity of measured mechanical conditions between the drill string, including the drill bit, and the well bore and the measured properties of the drilling fluid used in said well bore, said multiplicity of well bores including a first plurality of wells in which the drill string stuck mechanically, a second plurality of wells in which the drill string stuck by differential drilling fluid pressure in said well bore and an earth formation penetrated thereby and a third plurality of wells in which the drill string did not stick, separately calculating the statistical relationship of the same multiplicity of said measured mechanical conditions and drilling fluid properties in each of said first, second and third plurality of wells, determining by multivariate statistical analysis of substantially all of said measured conditions in all of said wells of each of said three plurality of wells a plotting plane wherein said three pluralities are separated from each other, projecting the well vector for each well in each of said three pluralities onto said plotting plane and then measuring the same variable conditions for a given depth in a well being drilled, and plotting each well in accordance with the sum of the products of the coefficients of each variable for the complete group of wells times the corresponding value of the measured condition to determine the probability that the measured conditions in a drilling well places said well within one of said three pluralities of wells.