Two important characteristics of geochemical data complicating their analysis are its compositional nature and the presence of values that laboratories have not been able to measure because of concentrations below the detection limit of the instruments. Logratio transformations are used to convert any compositional data in the simplex to samples in real space, thus allowing the practitioner to apply classical statistical techniques valid in real space. Nondetects can be regarded as a special case of missing values with a lower and upper bound. Recent works have proposed dealing with compositional values below detection limit using a multiplicative replacement, a modified expectation maximization (EM) algorithm, or a univariate bootstrap approach. In this work we revise in detail these techniques and propose a multivariate approach based on a novel algorithm that combines bootstrap simulation and the EM modified algorithm by adapting the procedure for those compositional data sets without closure.