Let's say that they just do not want to have sex for some reason after the wedding. Does it mean that their marriage can be annulled by the Catholic Church even if they were married for 10 years?
In the general case marriage requires consummation, but the Catholic Church allows an exception which is called a "Josephite Marriage." This is the kind of marriage that the Catholic Church believes Mary and Joseph entered into: a marriage without sex.
Despite the fact that no consummation took place, a Josephite marriage is not intrinsically invalid. Even so, a marriage that has never been consummated would be more easily exited than a marriage that has been consummated. Indeed the condition of consummation goes hand in hand with indissolubility. If a marriage is consummated, it is indissoluble. If it is not consummated, it is dissoluble. Whether or not it is consummated, the marriage exists.
Dissolution of a marriage is actually different from annulment of a marriage. Annulment says the marriage never existed; dissolution means that a partial marriage is being dissolved. If a marriage is ratified and consummated then there exists the possibility of annulment, but not the possibility of dissolution. If a marriage is ratified but not consummated then both the possibility of annulment and dissolution exist.
Canon 1141 explains the Church's theological understanding of the significance of the consummation of a valid marriage: a marriage which has been ratified and consummated (ratum et consummatum) cannot be dissolved by any number power, or by any cause other than death. If a couple have been validly married, and have consummated their marriage, the Church holds that their marriage is indissoluble. Period.
But if the couple were validly married, yet had never consummated their marriage--a marriage ratum sed non sonsummatum, in other words--the situation is theologically quite different! Such a marriage can be dissolved by the Roman Pontiff for a just reason, at the request of one or both parties to the marriage (canon 1142). A ratum sed non consummatum marriage is not indissoluble, because the indissolubility of a valid marriage comes about through its consummation.
According to Catholicism, what happens when a married couple will never have sex?
As long as they wished to remain married, they shall be be considered as a married couple.
Or for some just reason one or both decide to separate, it is up to the Roman Rota to grant a dispensation from ratified and non-consummated marriage. Since the marriage has not been consummated, an annulment is not necessary. Up to August 30, 2011 only the Holy Father could dissolve a marriage “ratum sed non consummatum”. Pope Benedict XVI had transferred this over to the Roman Rota.
It must first pass through the local ordinary (bishop), who will take the petition to the Vatican. (Source)
Apostolic Letter in the form of a “Motto Prprio”: QUAERIT SEMPER of the Supreme Benedict XVI with which the Apostolic Constitution Pastor Bonus is amended and certain competences transferred from the Congregation for Divine Worship and the Discipline of the Sacraments to the new Office set up at the Tribunal of the Roman Rota for processes of dispensation from ratified and non-consummated marriage and for cases concerning the nullity of sacred ordination.
I have therefore deemed it opportune to transfer to a new Office, set up at the Tribunal of the Roman Rota, the competence for processes of dispensation from ratified and non-consummated marriage and cases concerning the nullity of sacred ordination.
A dissolution of an unconsummated marriage is more in view of a dispensation (dissolution) from marriage vows.
The favor of dispensation from a marriage ratum sed non consumatum is an inherently administrative procedure, while the process for obtaining a Declaration of Nullity (often misleadingly termed "annulment") is an inherently judicial one. In a ratum the valid marriage bond is dispensed from, while in a Declaration of Nullity a marriage is declared to have been null from its beginning. A ratum ends, for a just reason, a marriage that truly is (although never irrevocably and sacramentally "sealed" by consummation) while a Declaration of Nullity juridically declares that a marriage never truly was in the eyes of Catholic theology and matrimonial law. - Dispensation vs. Declaration of Nullity